Tantalum pentaoxide is used to make capacitors and glasses with high index of refraction those are used in camera lenses. It is frequently used as a substitute of ...
Hyperfine structure studies of Tantalum and Praseodymium
Dissertation
By ZAHEER UDDIN
under the supervision of Univ. Prof. Dip.-Ing. Dr. tech. Laurentius Windholz Institute of Experimental Physics Technical University Graz September 2006 GRAZ, AUSTRIA
Dedicated To My teachers Prof. Dr. L. Windholz Prof. Dr. G. Guthöhrlein And My mother and my family
Acknowledgement
I would like to pay my heartiest thanks to professor Dr. Laurentius Windholz for his sincere and knowledgeable supervision and guidance which make it possible to perform my studies at the Institute of Experimental Physics, Technical University Graz. During my research I found him very cooperative, very polite, sincere and caring. Besides my research work he guided and helped me in my personal matters too. I am especially thankful to him for his help in getting visa for my family. I am also thankful to him for answering every question related to my research and studies. I am thankful to Professor Dr. G. Guthöhrlein for transferring valuable knowledge via a number of exchanges of emails. I am also thankful for discussions during his short stay here in Graz, which helped me in learning very important techniques related to my research work. I am thankful to Dr. J. C. Pickering and Dr. R. Engleman for Fourier Transform spectra of Tantalum. I am thankful to every one, especially the head of institute, Prof. W. E. Ernst, the secretaries and workshop people, at the Institute of Experimental Physics, Technical University Graz for their support and help. I am also thankful to Higher Education Commission, Pakistan for funding this research program.
Contents 1 Abstract
4
2 Introduction 2.1 Tantalum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 History of spectral and hyperfine investigation of Ta I and Ta II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Praseodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 History of studies of fine and hyperfine structure of Pr I and Pr II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 5
10
3 Atomic Structure 3.1 Element of atomic structure . . . . . . . 3.1.1 Electron-electron interaction . . . 3.1.2 Relativistic term . . . . . . . . . . . 3.1.3 Darwin term . . . . . . . . . . . . . 3.1.4 Spin orbit interaction . . . . . . . . 3.2 Properties of the eigen function of an N 3.3 Coupling of angular momenta . . . . . . 3.4 Central field approximation . . . . . . . . 3.5 Electron configuration . . . . . . . . . . .
12 12 14 15 15 16 18 18 18 19
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . electron system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 8
4 Hyperfine structure 4.1 Magnetic dipole interaction . . . . . . . . . . . . . . . . . 4.2 Electric quadrupole interaction . . . . . . . . . . . . . . 4.3 The tensor operator formalism of hyperfine structure 4.4 Experimental determination of hyperfine constants . .
. . . .
. . . .
20 20 22 24 25
5 Laser Spectroscopy 5.1 Ring dye laser . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Absorption spectroscopy . . . . . . . . . . . . . . . . . . 5.2.1 Two photon spectroscopy . . . . . . . . . . . . . 5.2.2 Spectroscopy with a collimated atomic beam 5.2.3 Saturation spectroscopy . . . . . . . . . . . . . . 5.2.4 Laser induced fluorescence spectroscopy . . . . 5.2.5 Optogalvanic spectroscopy . . . . . . . . . . . . 5.3 Line broadening mechanisms . . . . . . . . . . . . . . . 5.3.1 Natural broadening . . . . . . . . . . . . . . . . . 5.3.2 Doppler broadening . . . . . . . . . . . . . . . . . 5.3.3 Collisional broadening . . . . . . . . . . . . . . . 5.3.4 Stark broadening . . . . . . . . . . . . . . . . . . 5.3.5 Saturation broadening . . . . . . . . . . . . . . . 5.3.6 Combined line profile . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
27 27 29 30 30 32 33 36 38 38 40 41 42 42 42
1
. . . . . . . . . . . . . .
6 Experimental setup 6.1 Hollow cathode lamp . . . . . . . . . . . . . . . 6.2 Measurements . . . . . . . . . . . . . . . . . . . 6.3 Spectrum . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Grating spectra of Ta on photo plates 6.3.2 Fourier transform spectra . . . . . . . .
. . . . . . . . . . . . . . . . . . .
. . . . .
. . . . .
. . . . .
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44 44 46 48 49 49
7 Computer programs 51 7.1 Classification of spectral lines by means of their hyperfine structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 7.1.1 Simulation program . . . . . . . . . . . . . . . . . . . . 53 7.1.2 Finding a new level by combination of the wave numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7.1.3 Determination of a new level by fluorescence lines 55 7.1.4 Determination of a new level by analysis of the hyperfine structure . . . . . . . . . . . . . . . . . . . . 57 7.1.5 Classification of unclassified lines by its hyperfine structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 7.2 Fitter program . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 7.3 Origin Macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 8 Experimental results and discussion 63 8.1 Classification of Ta II lines, determination of hyperfine constants of Tantalum II levels . . . . . . . . . . . . . . . . . 63 8.1.1 Determination of the hyperfine constants of the Ta II level 39758o5 . . . . . . . . . . . . . . . . . . . . . 65 8.1.2 The level 771964 . . . . . . . . . . . . . . . . . . . . . 67 8.1.3 The level 752942 . . . . . . . . . . . . . . . . . . . . . . 69 8.1.4 The level 769233 . . . . . . . . . . . . . . . . . . . . . . 71 8.1.5 The level 777275 . . . . . . . . . . . . . . . . . . . . . . 72 8.1.6 The level 789665 . . . . . . . . . . . . . . . . . . . . . . 74 8.1.7 The level 65329o1 . . . . . . . . . . . . . . . . . . . . . . 75 8.1.8 The new line 2948.679Å . . . . . . . . . . . . . . . . . 77 8.1.9 The new line 3093.006 Å . . . . . . . . . . . . . . . . 77 8.1.10 The classification of the line 2955.608 Å . . . . . . 80 8.2 Classification of Ta I lines, determination of new levels of Tantalum I levels . . . . . . . . . . . . . . . . . . . . . . . . 89 8.2.1 The level 445733/2 . . . . . . . . . . . . . . . . . . . . . 89 8.2.2 The level 50256o11/2 . . . . . . . . . . . . . . . . . . . . 90 8.2.3 The level 514231/2 . . . . . . . . . . . . . . . . . . . . . 92 8.2.4 The level 536413/2 . . . . . . . . . . . . . . . . . . . . . 94 8.2.5 The level 545287/2 . . . . . . . . . . . . . . . . . . . . . 96 8.2.6 The level 54616o7/2 . . . . . . . . . . . . . . . . . . . . . 96 8.2.7 The level 56957o13/2 . . . . . . . . . . . . . . . . . . . . 97 8.2.8 The level 58562o9/2 . . . . . . . . . . . . . . . . . . . . . 100 8.2.9 The level 507451/2 . . . . . . . . . . . . . . . . . . . . . 100 2
8.3 Hyperfine structure studies of Praseodymium . . . . . . . 122 8.3.1 Blend situation and discovery of the level 2911111/2 122 8.3.2 Blending lines 5675.321 and 5675.279 and discovery of the new level 30560.917/2 . . . . . . . . . . . . 124 8.3.3 The new level 3204119/2 . . . . . . . . . . . . . . . . . 127 8.3.4 The levels 3100517/2 and 31005o13/2 . . . . . . . . . . . 128 8.3.5 The level 324029/2 . . . . . . . . . . . . . . . . . . . . . 129 8.3.6 The level 3233615/2 . . . . . . . . . . . . . . . . . . . . 130 8.3.7 The level 25909o17/2 . . . . . . . . . . . . . . . . . . . . 132
3
1
Abstract
This work is experimentally based on laser spectroscopic investigation of spectral lines of free metal atoms using fluorescence detection. In Fourier transform spectra many lines of Ta I and Ta II are unclassified. In case of Ta I lines some of the involved levels are unknown and in case of Ta II, moreover, either the hyperfine constants of most of the levels are not precisely known or some involved levels are unknown. At first main emphasis was given to the classification of Ta I lines and on the discovery of new levels of Ta I. Beside laser induced fluorescence spectroscopy the analysis of spectral lines extracted from already recorded FT spectra using computer programs (Fitter and Classification programs) was carried out. The magnetic hyperfine structure constant ‘A’ and electric quadrupole interaction constant ‘B’ of 200 levels of Ta II were determined. More than 600 lines of Ta I and Ta II were classified either by direct laser excitation, or by resultant fluorescence lines. Eight new levels of Ta II were discovered, which belong to still unknown configurations; all these levels are high lying even parity levels except one with odd parity. 25 new levels of Ta I were also discovered. In this work the hyperfine structures of Pr I and Pr II lines were also investigated. More than 400 lines of Pr were classified either by direct laser excitation or through fluorescence lines. 75 new levels of Pr I were also discovered.
Kurzfassung: Diese Arbeit beruht experimentell auf der laserspektroskopischen Untersuchung der Spektrallinien freier Metall-Atome mittels Fluoreszenz detektion. In vorliegenden Fourier-Transformations-Spektren sind viele der aufscheinenden Ta I - Linien nicht klassifiziert. In vielen Fällen sind die an den Übergängen beteiligten Niveaus nicht bekannt. Bei den Ta II — Linien bestand zusätzlich die Schwierigkeit, daß für die meisten der bereits bekannten Niveaus auch die Hyperfeinstrukturkonstanten erst ermittelt werden mußten, und zusätzlich neue, nicht bekannte Niveaus an den Übergängen beteiligt sind. Zuerst galt das Hauptinteresse der Klassifikation von Ta I - Linien und dem Auffinden neuer, bislang unbekannter Ta I - Niveaus. Neben laser-induzierter Fluoreszenz wurden auch Informationen direkt aus den Fourier-Spektren gewonnen, zumeist mit Hilfe von Computerprogrammen ("Fitter" und Klassifizierungs programme). Danach wurden die magnetischen Hyperfeinkonstanten A und die elektrischen Quadrupol-Wechselwirkungskonstanten B für etwa 200 Ta II -Niveaus bestimmt. Insgesamt wurden mehr als 600 Ta I - und Ta II - Linien klassifiziert, entweder durch direkte Laser-Anregung, oder durch abgestrahlte Fluoreszenz linien. 8 neue Ta II — Niveaus wurden entdeckt, alle energetisch sehr hoch liegend mit gerader Parität, mit Ausnahme eines Niveaus ungerader Parität. Auch 25 Ta I - Niveaus wurden entdeckt. Untersucht wurde auch die Hyperfeinstruktur von Pr I - und Pr II - Linien. Hier wurden mehr als 400 Linien klassifiziert, entweder durch direkte Anregung oder laser-induzierte Fluoreszenz. 75 neue Pr I - Niveaus wurden entdeckt.
4
2
Introduction
2.1
Tantalum
Tantalum is a metal with atomic number 73 in the periodic table of chemical elements. The origin of the name comes from the Greek name Tantalos who is the father of Niobe in Greek mythology. Tantalum was discovered by the Swedish chemist Anders Gustaf Ekenberg in 1802. Many scientist thought that it is an allotrope of niobium because of some chemical similarities. In 1866, a Swiss chemist Jean Charles Galissard de Marignac proved that the tantalum and Niobium are two distinct elements. It is a rare, grey, heavy, hard but ductile metal with a high melting point of 3017 0 C. When pure, it is ductile and can be drawn into fine wires, which can be used as a filament for evaporating metals such as Aluminum. Some chemical and physical properties of Tantalum are listed below: Table 1.1: Chemical and Physical properties of Ta. Atomic number Chemical symbol Electro negativity Color
73 Ta 1.5
Atomic weight Periodic place Density
180.9479 d block 16.4 gm/cm3
grey blue
Solid
Ionization potential Thermal conductivity Atomic radius
7.89V
Phase at room temperature Specific heat
[Xe] 4f14 5d3 6s2
Melting point First Ionization energy
3017 o C 728.43 kJ/mol
Electronic Configuration Electrical resistance Boiling Point
57.5 W/mk 143 pm
0.14 J/gm K
13.15 x Ohm cm 5458 o C
10−6
Naturally occurring Tantalum (Ta) has two isotopes, Ta180 and Ta . The latter isotope (Ta181 ) is 99.988 % abundant in nature. More than 20 artificial isotopes of Ta are known to exist. Ta occurs in nature in minerals columbite, tantalite and euxenite. Niobium and Ta concentrates are found in Brazil, Canada, Africa, Australia and Spain. Ta has body centered cubical crystal structure. The chemical reactivity of Ta is very low, even lower than Platinum, but at high temperatures its reactivity increases. However, it forms oxide films on its surface. Ta oxide films are stable and have a good rectifying and dielectric properties. Ta is used to make a variety of alloys with 181
5
desirable properties such as high melting point, high strength, good ductility, etc. Ta is used to make components for chemical plants, nuclear power plants, airplanes and missiles. Ta is completely immune to body liquids and is a nonirritating material. It has, therefore, found wide use in making surgical appliances. It is alloyed with steel to increase steel’s ductility, strength and melting point. Because of good rectifying and dielectric properties of Ta oxide, Tantalum pentaoxide is used to make capacitors and glasses with high index of refraction those are used in camera lenses. It is frequently used as a substitute of Platinum. Scientists at Los Almos have produced a Tantalum Carbide Graphite composite material, which is said to be one of the hardest materials ever made. It is used in cutting edges of high speed machine tools.
2.2
History of spectral and hyperfine investigation of Ta I and Ta II
In 1933 two groups, E. McMillan, N. S. Grace, [1] and J. H. Gisolf, P. O. Zeeman [2] had started the investigation of the hyperfine structure of Ta atom. In the same year Kiess and Kiess already had investigated the spectrum of Ta in detail. They classified 1890 lines out of 2629 lines of Ta. In 1943 T. Schmidt, determined the quadrupole moment of the atomic nucleus of 181 Ta [3]. In 1952 P. F. A. Klinkenberg , G. J. Van Den Berg and J. C. Van Den Bosch investigated Zeeman splitting of Ta I lines in the region 2500-8500A and gave a large number of classification of Ta I lines [4]. In 1952 G. J. Van Den Berg, P. F. A. Klinkenberg and J. C. Van Den Bosch continued their investigation of the Ta I spectrum. They found additionally few ground state levels and a large number of high odd levels [5]. In 1955 T. Kamei studied the hyperfine structure of the spectrum of Ta I by means of a hollow cathode discharge tube and a Fabry Perot etalon, and determined the quadrupole moments of Ta181 [6]. In 1958 C. E. Moore published the summary of the work of Kiess and Kiess 25 years after their first work [7]. In 1962 K. Murakawa studied the quadrupole coupling in the hyperfine structure of spectra of Ta, and obtained the quadrupole moment for the configuration 5d4 6s by spectroscopic means [8]. In 1971 S. Büttgenbach, G. Meisel measured hyperfine structure in the ground states 4 F3/2 , 4 F5/2 , and 4 F7/2 of Ta with an atomic beam magnetic resonance method. They found magnetic dipole interaction constants and electric quadrupole interaction constants for these states with high precision [9]. In 1980 K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber studied hyperfine and Zeeman splittings of low lying atomic levels of Ta using the atomic beam magnetic resonance method. They also determined the value of nuclear electric quadrupole moment 6
more precisely [10]. In 1982 S. Salih, D. W. Duquette, J. E. Lawler found the radiative lifetime of 35 Ta levels using time resolved laser induced fluorescence on an atomic beam [11]. In 1983 D. W. Duquette, D. K. Doughty investigated hyperfine structure of some Ta lines and measured the hyperfine constants using Doppler free spectroscopy using an atomic beam source [12]. In 1991 J. Persson, U. Berzinsh, T. Nilsson, M. Gustafsson, investigated the hyperfine structure of metastable atomic states belonging to the configuration 5d3 6s2 (4 P3/2 and 4 P5/2 ) using high resolution spectroscopy and laser radio frequency double resonance methods. [13] In 1992 A. Wännstöm, D. S. Gough, and P. Hannaford studied the hyperfine structure of Ta I lines using saturated spectroscopy in a sputtered vapor. They determined magnetic hyperfine constants and electric quadrupole constants for 16 levels of Ta I [14]. In 1993 U. Berzinsh, M. Gustafsson, and J. Persson investigated the hyperfine structure of Ta I using laser radio frequency double resonance and high resolution laser spectroscopy on collimated atomic beams. They determined the magnetic dipole and electric quadrupole hyperfine constant of metastable states of Ta I [15]. In 1997 Nisar Ahmad, M. Akram, K.P. Gill, S.P. Asdaq, R.M. Akhtar, M. Saleem, M.A. Baig investigated the hyperfine structure of Ta by optogalvanic spectroscopy for 17 transitions [16] . Recently V. Fivet, P. Palmeri, P. Quinet, É. Biémont, H. L. Xu, S. Svanberg studied the radiative life time and transition probabilities of 14 odd parity Ta I level belonging to the 5d3 6s6p and 5d4 6p configurations using time resolved laser induced fluorescence spectroscopy [17]. In 1990 members of the Institute of Experimental Physics, Technical University of Graz began with hyperfine structures studies via laser spectroscopy in collaboration with the Universität der Bundeswehr in Hamburg, Germany, where since 1983 the hyperfine structure of Ta was investigated by means of classical optical interference spectroscopy and laser spectroscopy [18][19]. In 1995 this collaboration extended to the Technical University Poznan which contributed to the theoretical interpretation of the experimental results. This outstanding collaboration resulted in the discovery of numerous new levels and the electronic shell of Ta was studied almost completely [20]-[29]. The isotope shift of some Ta I lines was also studied in a collaboration between Graz and Hamburg [30]. In 1952 B. M. Brown and D. H. Tomboulin carried out analysis of the hyperfine structure of several ionic lines of Ta and evaluated the hyperfine constants of the levels involved in the transitions. On the basis of their calculations they found the magnetic and quadrupole moments for the tantalum (Ta181 ) nucleus [31]. In 1978 J. F. Wyrat carried out the first semi empirical analysis of the even levels of Ta II [32], he used the levels of C.E. Moore [7] in his computations. In 1990 J. F. Wyrat and J. Balise carried out a parametric analysis of the odd energy levels of some atoms including Ta by means of Slater7
Condon parametric method. The calculations led to the rejection of few previously known levels of the Ta ion. They also revised the J value for some ionic levels, and found 23 additional levels of Ta II [33]. In 1995 D. Dembczynski performed a semi emperical fit of the even levels of Ta I, based on new experimentally discovered levels. He was able to predict energy and hf constants of some missing levels, which influenced the following experimental work [34] . In 2001 D. Messnarz carried out a parametric analysis of the fine structure of even and odd parity levels of Ta of different configurations and predicted some high lying levels of odd parity. He included 74 levels of even parity and 195 levels of odd parity in his calculations. He also accomplished fine structure analysis for ionic levels of Ta of both parities [35]. In 2002 V. O. Zilio and J. C. Pickering published out hyperfine constants of Ta II levels. Using Fourier transform spectra they made computer fits of several hundred lines of Ta II and found the magnetic dipole constants for 88 levels and the electric quadrupole constants for 73 levels [36]. In 2002 M. Eriksson, U. Litzén, G. M. Wahlgren and D. S. Leckrone recorded the spectrum emitted from a hollow cathode lamp with a Fourier transform spectrometer. They analyzed the recorded hyperfine structures of Ta II and measured the center of gravity for 199 lines and the hyperfine constants for 38 even and 97 odd levels of Ta II [37]. In 2003 D. Messnarz and G. H. Guthöhrlein investigated the hyperfine structure of 39 lines of Ta II by means of Doppler limited laser spectroscopy. They measured the hyperfine constants A and B for 22 levels of even parity and 17 levels of odd parity [38]. Recently N. Jaritz presented her thesis on tantalum atom [39], She investigated 2300 spectral transitions. By the analysis of the hyperfine structure of 648 lines she discovered 129 new levels of Ta I. She also carried out semi empirical calculations of the fine structure using the Cowan code [40] and hyperfine constants using program of Kröger [41].
2.3
Praseodymium
Praseodymium is a rare earth element( these consist of lanthanides and actinides) that has the symbol Pr and atomic number 59 in the periodic table. Its atomic weight is 140.9077 and its electronic configuration is [Xe] 4f 3 6s2 . It is soft, silvery, malleable, and ductile. It belongs to the Lanthanide group ( The lanthanide group contains rare earth elements from atomic number 57 to 71). It reacts with oxegen and makes green oxide (Pr6 O11 ). To avoid exposure to air it is stored in oil or sealed in plastic or glass. The name Praseodymium comes from the Greek prasios, meaning green and didymous, meaning twin. It occurs along with other rare-earth elements in a variety of minerals. In 1885, the Austrian chemist C. F. Auer von Welsbach separated didmium into two ele8
ments, Praseodymium and Neodymium. Praseodymium is primarily obtained through an ion exchange process from Monazite sand, a material rich in rare earth elements. Naturally occurring Pr has only one isotope, Pr141 . Two of the radioisotopes of Pr are relatively stable being Pr143 with a half life of 13.57 hours and Pr142 with a half life of about 19 hours. Majority of the radioisotopes of Pr have half lives less 40 seconds. The isotopes of Pr range in atomic weight from 120.955 u (Pr121 ) to 158.955 u (Pr159 ). The primary decay mode before the stable isotope, Pr141 , is electron capture and the primary mode after it is negative beta decay. The primary decay products before Pr141 are element 58 (Cerium) isotopes and the primary products after are element 60 (Neodymium) isotopes. Some of the chemical and physical properties of Pr141 are given here: Table 1.2: Chemical and Physical properties of Pr. Atomic number Chemical symbol Electro negativity Color
59 Pr 1.13
Atomic weight Specific density Density
140.9077 0.19 J/gm K 6.77 gm/cm3
Silvery white
Solid
Ionization potential Thermal conductivity Atomic radius
7.89V
Phase at room temperature Crystal structure
[Xe] 4f3 6s2
Melting point First Ionization energy
935 o C 523.2 kJ/mol
Electronic Configuration Electrical resisistivity Boiling Point
12.5 W/mk 182 pm
Hexagonal
0.7x 10−4 Ohm cm 3520 o C
Praseodymium’s primary use is as an alloying agent with magnesium to create high-strength metals that are used in aircraft engines. Praseodymium also makes up about 5% of Misch metal, a material that is used to make flints for lighters. Praseodymium forms the core of carbon arc lights which are used in the motion picture industry for studio lighting and projector lights. Praseodymium is added to fiber optic cables as a doping agent where it is used as a signal amplifier. Praseodymium salts are used to give glasses and enamels a yellow color. Praseodymium is also a component of didymium glass, which is used to make certain types of welder’s and glass blower’s goggles.
9
2.4
History of studies of fine and hyperfine structure of Pr I and Pr II
In 1929 H. E. White studied the wavelength and frequency separation of fine structure components of 173 spectral lines in Pr II ion [42]. He assigned I = 2.5 to the nucleus of the Pr atom. In 1941 N. Rosen et al. studied the Zeeman effect of Pr lines in the wide range 2400 to 7100 Å. They determined g and J values for 74 Pr II levels from Zeeman patterns of 141 lines. They also found f 3 (4I o ).s −5 I4o as the lowest term of Pr II, and observed that the most strong lines showing hyperfine structure arise from the f 3 s configuration [43]. In 1953 H. Lew investigated the hyperfine structure of the ground state of Pr I by the atomic magnetic resonance method. He determined nuclear spin, total electronic angular momentum and gJ value of ground state. He found 4 I3/2 being the atomic ground state of Pr, he realized the Russel Saunders coupling also leads to this state, which is according to Hund’s rules - the most probable ground state of the configuration 4f 3 6s2 [44]. In 1953 P. Brix further extended the work of White and evaluated the magnetic hyperfine interaction constant for the 6s electron in the configuration 4f 3 (4I)6s. He also calculated the magnetic moment (µ(Pr141 ) = 3.9±0.3 nuclear magnetons) of Pr [45]. In 1955 J. M. Baker and B. Bleany investigated the hyperfine structure of Pr lines and calculated the hyperfine structure constants of the the level involved [46]. In 1960 K. Murakawa investigated the spectrum of Pr I, classified 3 lines and measured their hyperfine structure. He also calculated magnetic moment of Pr [47]. In 1961 Judd and Lindgren made a number of corrections to the simple Lande formula for the g values of levels belonging to the configuration of the type 4f. Their measurements were based on existing experimental data and theoretical calculations based on the processes of interpolation and extrapolation. They found that the ground states of some atoms including Pr I are of the type 4f [48]. In 1962 B. G. Wybourne examined the effect of intermediate coupling on the calculation of nuclear moments of the rare earth elements from the analysis of hyperfine structure. He found that the interaction of the electron spin moments of 4f electrons with the nuclear magnetic moment is very sensitive to the form of the coupling. He presented calculation for Pr141 and Ho165 [49]. In 1962 Y. C. Amado et al. studied the hyperfine structure of the short living (19 hours) isotope (Pr142 ) of praseodymium in the ground state 4 I9/2 by atomic beam magnetic resonance method. They calculated the splitting factor, nuclear spin, electric quadrupole and magnetic dipole hyperfine constants, and nuclear moment and quadrupole moment for this isotope of Pr [50]. In 1964 N. J. Spector calculated energy parameters for the 4f 2 6s and 4f 2 6p electronic configurations of Pr ions [51]. J. Reader and J. Sugar in 1964, studied the nuclear 10
moment of Pr141 from the hyperfine structure of doubly ionized Pr. They calculated the probability density of the 6s electron at the nucleus and the quantum difference for the configurations 4f 2 6s and 4f 2 7s. By the application of the Goudsmit-Fermi-Segrè formula they calculated a value 4.09±.06 nm for nuclear moment of Pr141 [52]. In 1982 R. M. Macfarlane, D. P. Burum, and R. M. Shelby also studied the magnetic moment of Pr141 [53]. In 1989 A. Ginibre studied the fine and hyperfine structure of singly ionized Pr by Fourier transform spectroscopy. Based on her high resolution data in the range 2783-27920 cm−1 , she found new energy levels of the odd configuration 4f 2 5d6p and of the mixed even configurations 4f 2 5d2 , 4f 2 5d 6s, and 4f 3 6p. She also found the energy, J value and hyperfine structure splittings for these levels [54]. In 1990 H. Iimura, Y. Nakahara, S. Ichikawa, K. Kotani, M. Wakasugi and T. Horiguchi studied the hyperfine structure of Pr ion (Pr II) by means of collinear laser ion beam spectroscopy. They measured the magnetic dipole and electric quadrupole constants for the transition involved in their studies [55]. In 1991 Kim studied the hyperfine structure of doubly ionized Pr [56]. In 1994 H. Iimura, Y. Nakahara, S. Ichikawa, M. Kubota and T. Horiguchi measured the magnetic moment and electric quadrupole moment of a Pr isotope (Pr143 ) by means laser ion beam spectroscopy [57]. In 2000 Maosheng et al, investigated the atomic spectra of singly ionized Pr and neodymium by means of collinear laser ion beam spectroscopy. They measured the hyperfine structure of atomic transition in the wavelength range 560 to 590 nm [58].
11
3
Atomic Structure
The resolution of electromagnetic radiation into its frequency or wavelength components is called its spectrum. In spectroscopy the main emphasize is always on to get a spectral resolution of as high as possible. The first spectrum was observed by Newton. 100 years later Wollaston and Fraunhofer observed the Fraunhofer lines, the dark absorption lines of the spectrum of the sun light. Excited atoms, when relaxing to their ground state, emit electromagnetic radiation. To know the exact phenomenon behind the emission of these electromagnetic radiation scientist investigated the properties and structure of atoms and molecules. J. J. Thomson, Dalton, Rutherford, Bohr, Sommerfeld, Schrödinger, Dirac were few well known physicists who made their contributions in the understanding. Bohr explained in his semi classical theory the stability and discrete energy states of the hydrogen atom. Hydrogen was known to emit few series of lines (Lyman, Balmer, Paschen, Brackett and Pfund series). The most probable lines belong to the Lyman series but the Balmer series was discovered first because of its appearance in the visible region. Exact explanation of emission and absorption of electromagnetic radiations remained a bit ambiguous until quantum mechanics came into its full swing. The reason was very obvious that the emission and absorption of electromagnetic radiation are quantum mechanical phenomena. With the development of high resolution apparatus it is today possible to investigate very fine details of emission and absorption spectrum.
3.1
Element of atomic structure
In classical mechanics the equation of motion is given by Newton’s law dp (1) dt The quantum mechanical analogous to this equation is the Schrödinger equation. F=
HΨ(r, ϑ, ϕ)=EΨ(r, ϑ, ϕ)
(2)
is called Hamiltonian, It is an eigen value equation. The operator H and Ψ(r, ϑ, ϕ) is called eigen function or wave function. It contains the detailed knowledge of the quantum mechanical system. By proper application of the operator details of particular properties of the system can be obtained. For example the operation of Hamiltonian on the eigen function Ψ(r, ϑ, ϕ) gives the total energy of the system. Thus,
12
is also called total energy operator; in simple systhe Hamiltonian H tems it is the sum of kinetic energy and potential energy operators. For a one particle system it is given by 2 2 ∇ + V (r) (3) 2m The first term is the kinetic energy operator and the second term is the potential energy operator. The Schrödinger equation can be used to study the characteristics of any quantum mechanical system. In case of atomic and molecular systems the spherical symmetry allows one to use spherical coordinates in this equation. The exact solution of the Schrödinger equation is very difficult because of the complex nature of this differential equation. However, for some simple systems exact solutions are possible. Otherwise numerical solutions or some approximations are used. One of such approximation is variable separation technique, here one can assume that various motions associated with the systems can be decoupled (like in Born Openheimer approximation applied to molecules). Using this approximation to the atomic system the eigen function can be written as the product of a radial part associated with the radial motion and an angular part associated with its angular momentum, i.e. H= −
Ψ(r, ϑ, ϕ)=R(r)Y (ϑ, ϕ)
(4)
The Schrödinger equation can now be written as a set of two equations (
p2r l(l + 1) Ze2 + − )R(r) = ER(r) 2m 2mr2 r
(5)
L2 Y (ϑ, ϕ) = l(l + 1)Y (ϑ, ϕ)
(6)
where L2 is the total orbital angular momentum operator squared and Y (ϑ, ϕ) is the angular part of the wavefunction. Mathematically, the solution for Y (ϑ, ϕ) are spherical harmonics. Eq. 6 can further be separated into two equations one in ϑ other in ϕ. The solutions of these equations give a discrete set of energy values. The atomic system becomes more and more complex as the atomic number increases. The increasing atomic number increases the numbers of electrons in the orbit around the nucleus, inter particle forces become more and more complex. The energy is also modified, this requires to modify the Hamiltonian of the system, too. For a system of N electrons one can write the Hamiltonian as the sum of Hamiltonians for each electron, some correction terms are also necessary to obtain the exact value of the energy:
13
2 2 ∇ + V (ri )) + some correction terms i 2m i These correction terms arise mainly due to interactions of electron with other electrons, electrons with the nucleus, orbital motion with spin motions. These terms may be considered as the perturbations to the sum of kinetic and potential energies of all electrons. One can write Hamiltonian for N electron system as H = Σ(−
H = Ho + Hee + Hr + HD + Hso
(7)
Where 2 Ho is core Hamiltonian Σ(− 2m ∇2i + V (ri )) i Hee is the Hamiltonian representing electrostatic interaction between electrons Hr is the relativistic Hamiltonian HD is the Darwin Hamiltonian Hso is the Hamiltonian representing the spin orbit interaction 3.1.1
Electron-electron interaction
The electrons, having the same charge, have the characteristics to oppose other electrons to keep them away at a distance to maintain an equilibrium state in the atomic system. The electrons which are close to the nucleus also see the full charge of the nucleus and shield the nucleus in such a way that the outer electrons can not see the full charge of the nucleus. This shielding effect contributes to the total energy of the atomic system and is given by the Hamiltonian Ze2 i rij
(10)
The solution can be expressed in two further matrix elements known as Coulomb or Direct integral ’J(i, j)’ and the Exchange integral
14
’K(i, j)’. The Coulomb integral is written as J(i, j) = Σak (i, j)F k (i, j) k
(11)
where ak (i, j) is the product of matrix elements of spherical harmonics, and F k (i, j) is given by k
F (i, j) =
∞ ∞ 0 0
k e2 r< [Pi (r1 )]2 [Pj (r2 )]2 dr1 dr2 k+1 r>
(12)
The exchange integral is given by K(i, j) = Σbk (i, j)Gk (i, j) k
(13)
where bk (i, j) are similar constants like ak (i, j) and Gk (i, j) is given by k
G (i, j) =
∞ ∞ 0 0
k e2 r< P (r )Pj (r2 )Pi (r2 )Pj (r1 )dr1 dr2 k+1 i 1 r>
(14)
• The radial integrals F k (i, j) and Gk (i, j) are both positive and are known as Slater-Condon parameters. • For equivalent electrons F k (i, j) = Gk (i, j) • The coefficients ak (i, j) and bk (i, j) have non vanishing values only for a few values of k so that sum J(i, j)+ K(i, j) reduce to a small number of terms. 3.1.2
Relativistic term
This term appears in the expansion of the relativistic energy
Here
p2 p4 (m2 c2 )2 + p2 c2 = m2 c4 + − 3 2 2m 8m c
(15)
p4 (16) 8m3 c2 It is the first order relativistic correction to the energy. It is of the order of 0.1 cm−1 . Hr = −
3.1.3
Darwin term
It results in a shift of the s states and of the order of less than 0.1 cm−1 , and is given by HD = (
e2 )∇.E 8m2 c2
15
(17)
3.1.4
Spin orbit interaction
The total Hamiltonian does not commute with the total orbital angular momentum (L) and the total spin angular momentum of the electrons (S). However, it commutes with the resultant angular momentum (J). The energy of the isolated atom does not depend on the orientation of the total angular momentum. As a result, the degeneracy associated with an energy level corresponding to a given L and S is partly removed by the spin orbit interaction. The spin orbit interaction energy is given by the following Hamiltonian: − →− → Hso = ξ(r) L . S
(18)
The total angular momentum is the vector sum of the spin and orbital angular momenta − → − → − → J = L+S
(19)
− →− → − → − → − → − → J 2 = J . J = ( L + S ).( L + S )
(20)
− →− → J 2 = L2 + S 2 + 2 L . S
(21)
− →− → (J 2 − L2 − S 2 ) L.S = 2
(22)
So
(J 2 − L2 − S 2 ) 2 The interaction energy is given by Hso = ξ(r)
∆Eso =< Ψ|ξ(r)
(J 2 − L2 − S 2 ) |Ψ > 2
∆Eso =< ξ(r) > [J(J + 1) − L(L + 1) − S(S + 1)]
(23)
(24)
(25)
where < ξ(r)> is called fine structure splitting constant. It depends on electronic configuration and on S and L and is given by < ξ(r) > ∝ < Ψ|
1 |Ψ > r3
• The possible values of J are |L − S|, |L − S| + 1, ......L + S 16
(26)
• The selection rules for dipole transition is J = 0, ±1 • each term splits into (2s +1) term if S < L or into (2L +1) is S > L. • The total width of splitting between L + S and L − S for L > S is 2 < ξ(r) > S(2L + 1) and for S > L it is 2 < ξ(r) > L(2S + 1). • The fine structure splitting constant may be positive or negative which result in normal and inverted multiplets. • The separation between adjacent fine structure components is given by ∆E = E(J) − E(J − 1) =< ξ(r) > J
(27)
This is known as Lande interval rule. The energy splitting does not depend on MJ ; this means that the energy of an isolated atom can not depend on orientation of its total angular momentum J in space. It can be shown that Σ
(2J + 1)∆EJ = 0
|L−S|≤J≤(L+S)
(28)
This means the center of gravity of the multiplet is Σ(2J + 1)EJ E =
j
Σ(2J + 1)
(29)
j
This energy coincides with the energy of the unsplitted term. The spin orbit interaction is the largest effect and is responsible for the atomic fine structure. This fine structure splitting is of the order of 10-1000 cm−1 . Since the contributions of the relativistic and Darwin terms are not very pronounced as compared to others interactions, hence for a system of N electrons one can write the Hamiltonian H as follows H = Ho + H1 + H2
(30)
where H1 represents interaction of electrons with other electrons and H2 represents the spin orbit interaction. The relative effects of H1 and H2 depend on the atomic number Z. For a lighter atom (for small Z value) H2 is small compared to H1 and H2 is considered as perturbation. For heavy atoms (for large Z value) H1 is small and it is considered as perturbation.
17
3.2
Properties of the eigen function of an N electron system
The electrons are indistinguishable particles, this means the Hamiltonian must be invariant under the interchange of spatial and spin coordinates of any two electrons. Since the electrons are Fermions this means the eigen function of a system of N electrons must be antisymmetric or the electrons in an atom do follow Pauli’s principle. Since the general Hamiltonian is invariant under inversion, so the eigen function must have a definite parity or in other words, the parity is a good quantum number for an atomic state.
3.3
Coupling of angular momenta 2
The Hamiltonian H1 = ( Σ Ze rij ) does not commute with li but it commutes with L and S where L = Σli and S = Σsi . i.e. i
i
[H, L] = 0 and [H, S] = 0
(31)
[H , L + S ] = [H , J ]= 0
(32)
− → − → − → J = L + S
(33)
hence where
− → J is total angular momentum of the atomic system. − → − → The Hamiltonian H2 = Σξ i li .si does not commute with L and S , − → − → − → → but it commutes with j i = l i + − s i where j i is the total angular − → momentum of the ith electron. Since [ H , j i ]= 0,
where
− → − → [H , Σji ] = [H , J ] = 0
(34)
− → − → J =Σ ji
(35)
The coupling scheme given by eq. 33 is called LS coupling or Russell Sunders coupling. This coupling applies when Coulomb interaction energy of electrons is much greater than the spin-orbit interaction energy. In this case li and si are conserved separately. The coupling scheme given in eq. 35 applies when spin orbit interaction energy is greater than Coulomb interaction energy. This coupling scheme is known as j-j coupling.
3.4
Central field approximation
In general H1 is too large to be considered as small perturbation. The solution to this problem, the center field approximation, is proposed
18
by Hartree and Slater. An electron is considered moving in an effective potential which represents the attraction of the nucleus and the average effect of the repulsive interaction between this electron and all other electrons. The central field approximation leads to a classification of gross structure of energy of an atom by configurations.
3.5
Electron configuration
The energy of an atom is specified by the electron configuration given by the quantum numbers n and l of the electrons. The values of n and l are usually indicated by writing n as number and l as letter. The configuration of the ground state is called ground configuration and all other configurations are called excited configurations. For example 1s2 2s2 2p2 is the ground state configuration of the carbon atom, and 1s2 2s 2p3 is one of its excited state configurations. Highly excited states overlap each other, in such case the configuration is given by the mixture of all overlapping configurations. This situation is called configuration mixing or configuration interaction. Since the parity is a good quantum number, configuration mixing takes place only within configuration of same parity.
19
4
Hyperfine structure
With the use of interferometric methods and suitable light sources a very fine structure of the spectra of atoms and molecules can be observed. This further splitting of energy levels is of the order of 0.001 to 1 cm−1 and is called hyperfine splitting or hyperfine structure. The hyperfine structure is explained in terms of properties of the nucleus other than its charge. Each nucleon has an intrinsic spin 12 and may take part in orbital motion of the nucleus. The nucleus has a total angular momentum which is the resultant of spins and angular momenta of all the nucleons which is known as ‘nuclear spin’. The associated quantum number is denoted by I and is called nuclear spin quantum number. ‘I’ may have integral or half integral values the nucleus is then is Bosonic or Fermionic respectively. The atoms, whose nuclei have even number of nucleons, have in most cases I = 0 and show no hyperfine structure. The nucleus may have electromagnetic multipole moments. The multipole moments ( 2k pole moments) which do not vanish are (1) the magnetic moments for odd k and (2) the electric moments for even k. where k > 0. A nucleus of spin quantum number I can not have a multipole moment of order 2k where k > 2I. Usually we deal with the two lowest orders of interaction, i.e. for k= 1 and 2. k=1 corresponds to magnetic dipole interaction and k = 2 corresponds to electric quadrupole interaction. These electromagnetic moments interact with the electromagnetic field produced by electron cloud at the nucleus.
4.1
Magnetic dipole interaction
A nucleus has nuclear magnetic moment µI associated with its angular momentum which is given by µI = gi µN I
(36)
Where the dimensionless factor gi is called nuclear g factor or nuclear Lande factor, µN is analogous to Bohr’s magneton and is often called nuclear magneton. µN = µB /1836 = 5.05082x10−27 J/T
(37)
The interaction of the nuclear magnetic moment µN with the av− → erage magnetic field B produced by the electrons is treated as small perturbation to the energy state of the atoms. This interaction energy is given by the Hamiltonian − → → Hµ = −− µ N.B 20
(38)
The magnetic field produced by the electrons at the site of the nucleus is proportional to the total angular momentum J and is directed along the axis of rotation. − → − → BαJ
(39)
Eq. 38 can be written as →− → µ ∝ −− H I .J →− → µ = A− H I .J
(40) (41)
where, ‘A’ is magnetic dipole interaction constant. It is the product of nuclear and electronic quantities. The energy contribution is calculated by Eµ =< ψ(r, θ, φ)|Hµ|ψ(r, θ, φ) > Eµ =< ψ(r, θ, φ)|AI.J|ψ(r, θ, φ) >
(42) (43)
The total angular momentum of the atom is the vector sum of angular momenta of electrons and the nucleus. It is denoted by F and is given by − → − → − → F = I +J
(44)
− →− → F 2 = I2 + J 2 + 2 I . J
(45)
− →− → (F 2 − I 2 − J 2 ) I .J = 2
(46)
A Eµ = ( )[F (F + 1) − I(I + 1) − J(J − 1)] or 2
(47)
Eµ = AC/2
(48)
C = F (F + 1) − I(I + 1) − J(J − 1)
(49)
∆Eµ (F, F − 1) = Eµ (F ) − Eµ (F − 1) = A(J)F
(50)
The eq.43 gives
where The Landé interval rule also holds for magnetic hyperfine structure i.e.
where
21
− → µI < B > A(J) = IJ
(51)
− → gI µI < B > A(J) = 1836J
(52)
(i) The possible values of F are | I — J |, | I — J | + 1, . . . . . . I + J. (ii) The number of hyperfine structure components corresponding to a fine structure levels is the smaller of the number (2 J + 1) and ( 2 I + 1). These components are called hyperfine structure multiplets. (iii) The total width of splitting between level J+I and | J - I | is ∆W = AI(2J + 1) for J > I and it is ∆W = AJ(2I + 1) for J < I (iv) The total width of splitting is largest for an unpaired ’s’ electron. (v) The electric dipole selection rule for F is ∆F = 0, ±1 (vi) The transition form F = 0 to F = 0 is forbidden. (vii) The separation between two adjacent hf levels is proportional to the larger F value of the two levels.
4.2
Electric quadrupole interaction
The quadrupole moment Q of a nucleus is a measure of the departure of the mean distribution of the nuclear charge from spherical symmetry. Q = 0 , spherically symmetric distribution ( e.g. a sphere) Q > 0 , prolongated ellipsoidal distribution ( e.g. a football) Q < 0 , Oblate distribution ( e.g. door knob) A non spherical symmetric distribution will acquire an energy in a magnetic field. This quadrupole interaction gives rise to an electric hyperfine structure. The conventional definition of Q is Q =< I, I|r2 (3cos2 θ − 1)|I, I >
(53)
1 ∂2 φ VQ = ( ) < J, J| 2 |J, J > e ∂z
(54)
Since Q is a tensor, , one need to choose a proper coordinate system (i.e. the principle axes system) to make off diagonal or mixed product elements zero. The average gradient of the electric field produced by the electrons at the place of the nucleus is defined by
22
The quadrupole interaction causes a shift in the hyperfine levels given by
EQ = (
eQ 6(I.J)2 + 3I.J − 2IJ(I + 1))(J + 1) ) < ∂ 2 φ/∂z 2 > [ ] 4 IJ(2I − 1)(2J − 1)
(55)
Classically this energy is given by eQ ) < ∂ 2 φ/∂z 2 > (3cos2 θ − 1)/2 (56) 4 Here θ is the angle between I and J which are the principle axes for nuclear and electric systems. EQ = (
2(I.J) = C = [F (F + 1) − I(I + 1) − J(J + 1)]
(57)
Eq. 56 can be written in terms of C EQ = (
3 C(C + 1) − 2I(I + 1)J(J + 1) eQ ) < ∂ 2 φ/∂z 2 > [ 2 ] 4 IJ(2J − 1)(2I − 1)
(58)
B 32 C(C + 1) − 2I(I + 1)J(J + 1) [ ] 4 IJ(2J − 1)(2I − 1)
(59)
EQ =
where B is called electric quadrupole hyperfine constants or simple electric hyperfine constant, and is given by B = eQ < ∂ 2 φ/∂z 2 >
(60)
(i) For ’s’ terms electron charge distribution is spherically symmetric , and it makes < ∂ 2 φ/∂z 2 >= o, Hence for ’s’ terms the electric hyperfine constant "B" is zero (ii) The electric hyperfine constant is zero for I < 1 and for J < 1 (iii) B is zero for atoms having even number of protons and even number of neutrons. The total splitting of hyperfine levels due to magnetic dipole and electric quadrupole interactions is given by ∆E =
AC B 3 C(C + 1) − 2I(I + 1)J(J + 1) + [2 ] 2 4 IJ(2I − 1)(2J − 1)
(61)
Quadrupole interaction gives rise to a departure from interval rule because its dependence on F is different than that of the magnetic dipole interaction. The hyperfine levels are independent of quantum number MF and are (2 F +1 ) fold degenerate. This degeneracy can be removed by Zeeman effect.
23
4.3
The tensor operator formalism of hyperfine structure
The matrix element of the scalar product of two tensor operators T(k) and U(k) may be written as Hhf s = Σ < JIF |T (k) .U (k) |JIF >
(62)
k≥1
where T(k) is an irreducible tensor operator, which gives the effect of the electrons and U(k) is an irreducible tensor, which represents the effect of the nucleus. Ramsey [59] has shown that the number of possible multiplets (2k poles) nuclear moments are strictly restricted. Non vanishing magnetic moments are magnetic moments for odd k and electric moments for even k. The term with k=1 in eq. 62 represents the magnetic dipole interaction and term with k=1 represents the electric quadrupole interaction. Since hyperfine splitting is very small compared to the fine structure splitting, the Hamiltonian, of eq. 62 can be treated as small perturbation. We are interested only in first two terms of right hand side of eq. 62. The higher terms in the expansion can be neglected because of very small contributions. The matrix elements of the scalar product T(k) . U(k) in the coupled form is given in[60][61]. Hhf s = Σ (−1)J+I+F k≥1
J I
I J
F k
< J||T (k) ||J >< I||U (k) ||I >
(63)
The quantity in the curly bracket is a 6j symbol. The matrix elements on the right hand side are called reduced matrix elements. The product of reduced matrix elements in eq. 63 is given by a constant similar to the hyperfine constant. This constant is given by Ak (J) =< JJ|T (k) |JJ >< II|U (k) |II >
(64)
Using the Wigner Eckart theorem, above equation can be written in reduced matrix elements
Ak (J) =
J −J
k 0
J J
I −I
k 0
I < J||T(k) ||J >< I||U(k) ||I > I
(65)
Now the eq. 62 can be written in terms of constant Ak (J) and the energy splitting is given by
∆Ehf s = Σ (−1)J+I+F k≥1
J I
I J
F k
J −J
k 0
J J
−1
I −I
k 0
I I
−1
Ak (J)
(66) The constant A1 (J) and A2 (J) are related to hyperfine constants A(J) and B(J) by the equations 24
A1 (J) = hJIA(J) A2 (J) =
hB(J) 4
(67) (68)
Using 3j and 6j values in equation 66 the expression of the hyperfine structure energy is obtained as ∆Ehf s = where again
3 C(C + 1) − 2I(I + 1)J(J + 1) hB(J) C hA(J) + 2 2 IJ(2I − 1)(2J − 1) 4
C = F (F + 1) − I(I + 1) − J(J + 1)
4.4
(69)
(70)
Experimental determination of hyperfine constants
The hyperfine interaction energy has two parts in above equation, the first part is the magnetic interaction energy and second is the electrostatic interaction energy. This equation can also be written as ∆E = αhA1 (J) + βhA2 (J)
(71)
where α and β are called Casimir factors and are functions of F and J for a given atom of nuclear angular momentum I, and are given by following equations C 1 α = [F (F + 1) − I(I + 1) − J(J + 1)] = 2 2 and β=
3 4 C(C
+ 1) − I(I + 1)J(J + 1) 2IJ(2I − 1)(2J − 1)
(72)
(73)
The transition between two different hyperfine levels follows the selection rules ∆F = 0, ±1 and ∆J = 0, ±1. The transition between two hyperfine levels each having F = 0 is forbidden. The parities of both levels should be different. Each allowed transition represents a component of the hyperfine structure pattern of a spectral line. The frequency of a component is given by ν = ν c + αo (Fo, Jo , I)Ao + β o (Fo, Jo , I)Bo − αu (Fu, Ju , I)Au + β u (Fu, Ju , I)Bu (74) ν c is the energy difference between fine structure levels. The upper level is labelled by the letter ’o’ (German word ’oben’, means upper) 25
and lower level is labelled by the letter ’u’ (German word ’unten’, means lower). Apart from ν c , the eq. 74 contains Ao , Bo , Au and Bu as unknown quantities. Thus, for experimental determination of hf constants from a given spectrum, it is necessary to identify the quantum numbers of at least 5 hf components and to measure their (absolute or relative) positions. If one can identify more than 5 components, a least square method has to be used. The relative intensities of the individual hyperfine components are given by[62], I(Fo −→ Fu ) =
(2Fo + 1)(2Fu + 1) 2I + 1
26
Jo Fu
Fo Ju
I 1
2
(75)
5
Laser Spectroscopy
The discovery of the laser as coherent, monochromatic light source opened doors for scientists especially working with spectroscopy. The conventional incoherent light sources were replaced by laser because of its many advantages over the conventional sources. Some of the advantages of laser are listed below: 1. It is coherent and monochromatic. 2. It has small divergence. 3. It has large spectral power density. 4. It has the possibility of continuously tuning of the wavelength. 5. It is useful for high resolution spectroscopy. Lasers may be divided into (i) fixed wavelength lasers (e.g. gas laser) (ii) multiline fixed wavelength lasers (e.g. Ar ion laser), and tunable lasers (e.g. dye laser). The difference between fixed wavelength lasers and tunable lasers is only the tuning range which is narrow for fixed wavelength laser and broader for tunable laser. In this work continuously tuning of the laser wavelength was needed, so the ring dye laser was used through out this work.
5.1
Ring dye laser
The setup of a ring dye laser is shown in the fig.1. The dye in the flowing jet is the lasing medium. An intense laser beam from a pump laser (Argon ion laser) produces population inversion in the dye. The dye jet is oriented at Brewester angle to have 100 % transmission for a proper polarized component of the laser light. The mirrors M1, M2, M3, M4 recirculate the photons from stimulated emission through the dye within the resonant cavity. The transmissivity of output mirror M4 depends on the type of the dye. To maintain single frequency operation in the dye laser is more complicated than in an Argon ion laser. The reasons are (i) in a dye laser a large number of modes of oscillations are possible, and (ii) beside the lasing in single longitudinal mode we also want to change the frequency continuously. Tuning is achieved in steps. Several frequency selective elements are usually necessary to narrow sufficiently the output frequency. Single longitudinal oscillation and frequency scanning is achieved by the combination of birefringent filter (BRF), thick etalon (scanning etalon) and thin etalon. Every optical element has its remarkable contribution to force the laser to operate in single mode. The cavity has a large number of oscillation modes, BRF and thick and thin etalons select one of these modes and cause than a single mode operation. A frequency shift of the selected mode is achieved by a Brewester angled tuning plate. The Brewester plate is mounted on 27
Figure 1: Tunable single mode ring dye laser (Coherent, Inc.) a small galvodrive so that tuning can be controlled with an applied voltage. Thin and thick etalons have to follow this tuning. The fig.?? shows the transmission curves of the optical elements and how the single mode operation is reached. The alignment and stability of the etalons are critical. If there is any drift then unfavored modes become favored ones, and the output frequency changes suddenly. This is called ’mode hopping’. Mode hopping may arise by thermal fluctuations, turbulence in the dye jet, presence of microbubbles in the dye jet etc. For establishing a small width of the output frequency, the resonator length has to be actively stabilized with the help of reference cavity. To achieve active stabilization the mirror M1 is mounted on PZT. Using an error signal generated by comparison of the output frequency with the reference cavity a feed back circuit acts on the PZT mirror and the galvo drive of the Brewester plate to compensate the fluctuations that would otherwise broaden the line width of the laser or shift the laser frequency. A suppression of the unwanted direction of light circulating in the resonator can be achieved with an optical diode inside the resonator. It consists of a Fararday rotator and a birefringent crystal, which allows the laser light to pass in one direction with less losses. Thus
28
ν
Figure 2: Transmission curves of BRF and thick and thin etalons in tunable dye laser there is no standing wave formed in the laser cavity and within the dye medium. Therefore the phenomenon of spatial hole burning does not occur. Because of this single mode operation becomes easier and higher output power is reached since the whole active material contributes to the laser output.
5.2
Absorption spectroscopy
A tunable laser is very useful for measuring the absorption of a sample as a function of the wavelength. In this case the laser replaces radiation sources for conventional absorption spectroscopy as well as the monochromator in the spectrometer. The Doppler broadening caused by the thermal motion of atoms or molecules limits the achievable resolution. Laser with a comparatively large time averaged line width are employed in the determination of energy level structure without regard to the finer details. Two photon absorption spectroscopy, optogalvanic spectroscopy, optical double resonance and level crossing spectroscopy are few examples of Doppler limited laser absorption spectroscopy. In Doppler free high resolution spectroscopy extremely narrow band single mode lasers are utilized. The collimated atomic beam spectroscopy and saturation spectroscopy are the examples of the Doppler free absorption spectroscopy. The saturation spectroscopy is based on nonlinear spectroscopic techniques. In the following sections some of the Doppler limited and the 29
Doppler free techniques are outlined. 5.2.1
Two photon spectroscopy
It is possible for an atom or molecule to absorb two or more photons simultaneously. An atom makes a transition from its ground state(energy E1 ) to an excited state after absorbing a photon of frequency ν 1 .In this excited state the atom may absorb another photon of frequency ν 2 to reach to further high lying excited state having an energy E2 . The difference of energies of ground and final excited states is given by E2 − E1 = h(ν 1 + ν 2 )
(76)
These two photons may be absorbed from a single laser beam passing through the absorbing sample or they may be provided by two or more beams from one or several lasers. The first order Doppler shift in one absorption is exactly cancelled by the corresponding shift in the second absorption, if absorption takes place from two counterpropagating beams, for this condition ν 1 = ν 2 = ν. v v E2 − E1 = hν(1 + ) + hν(1 − ) = 2hν (77) c c Theoretically the width of this resonance is of the same order of magnitude as the natural line width. All irradiated atoms can contribute to the signal and not just a certain velocity group as in case of saturation spectroscopy. The main characteristics of two photon spectroscopy: 1. Excited levels can be reached via two photon transitions that are parity forbidden by single photon excitation. 2. The final state may have an excitation energy in the far UV, while the incident light beam has a frequency in the near UV or Blue region, 3. By proper combination of participating photons, it is possible to eliminate momentum transfer between electromagnetic fields and atoms or molecules, this allows one to get Doppler free spectrum. However the cross section of two photon absorption is usually very small compared to that of a direct transition, this make this process not of general use. 5.2.2
Spectroscopy with a collimated atomic beam
In a high vacuum apparatus a well collimated atomic beam is made to absorb laser light in perpendicular direction. In this case the Doppler width is reduced by the collimation ratio ε (one reaches without difficulty ε > 100) and very small absorption width of atoms is absorbed.
30
High resolution spectroscopy can be performed by irradiating such beam at right angles with a narrow band, single mode laser. D. A. Jackson and H. Kuhn [63] have had used atomic beams long before the invention of lasers. In their work the absorption was analyzed by means of a high resolution Fabry Perot interferometer. The first application of atomic or molecular beams in laser spectroscopy was described S. Ezekiel and R. Weiss [64]. Main characteristics of atomic beam spectroscopy: (i) An atomic beam can be produced essentially for any element. (ii) The Doppler width is reduced appreciably. With a collimation ratio of 100 a typical residual broadening of 5 MHz is obtained. (iii) The number of collisions and collisional broadening is reduced. Since all atoms have almost same velocity, there occurs very few collisions than in the gas at equivalent pressure. (iv) Fluorescence light radiates in 4π steradians and very few of them reach the photodetector. It is possible by using deflection of the trajectories of the atomic beam that each atom affected by laser light contribute to the output signal. Detection of the interaction of an atomic beam with a laser beam (i) Detection by fluorescence: The most direct way to study the optical resonance is to observe fluorescence light, released after excitation. (ii) Detection by photoionization: Here the atomic beam interacts simultaneously with a narrow band laser and an intense laser. The narrow band laser brings the atoms to an excited state and an intense laser, having sufficient energy, ionizes the atoms in excited states. The photoelectrons or the ions are detected in an electron detector [65]. This process has been demonstrated for isotopes separation [66]. (iii) Detection of recoil atoms: When an atom absorbs a photon, the momentum of the photon is transferred to the atom. As a result the atom is deflected from the beam. In the de-excitation process the recoil the momentum transferred either is cancelled (stimulated emission) or is transferred to the atomic beam (spontaneous emission). The latter results in spread and broadening of atomic beam. The deflection of an atomic beam was first demonstrated by R. Frish in 1933 [67]. A. Ashkin [68] proposed to use this technique for isotopes separation. P. Jacquinet et al. [69] first time recorded the hyperfine structure by beam deflection for the sodium D lines. (iv) Detection by magnetic deflection: The first application of the magnetic resonance principle was made with the introduction of atomic beam magnetic resonance technique by I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch in 1938 [70]. They discovered that any change in magnetic sub levels of an atom in the atomic beam can be detected by a change in the deflection of the beam in an inhomogeneous magnetic field. In 1952 I. I. Rabi
31
[71] suggested that this technique could be used in the study excited states if atoms are illuminated resonantly in the interaction region. He also suggested that this method could be used to study isotope shifts. In 1965 Marrus [72] used Rabi’s arrangement and by using the change in magnetic sub levels of ground state he detected and measured optical transitions.
5.2.3
Saturation spectroscopy
If an absorption vapor is irradiated by an intense laser beam at resonance frequency corresponding to the excitation energy of a transition between ground state N1 and excited state N2 , the atoms may be excited faster than they return back to the ground state by spontaneous emission or collisional coupling. The ground state becomes significantly depopulated or in other words excitation reaches its saturation. This phenomenon is called saturation. The high resolution laser spectroscopy based on this phenomenon is called saturation laser spectroscopy. If the spectral line is inhomogeneously broadened the laser interacts only with particular atoms which have certain velocity given by the Doppler effect. If the laser has sufficient intensity it burns a hole in the Maxwell velocity distribution of the ground state atoms. Bennett and Lamb recognized that the narrow resonances that appeared at the center of inhomogeneous broadened line interacting with counterpropagating laser beam resulted from a ‘hole’ burnt in the Maxwell Boltzman velocity distribution. The hole burnt by the intense laser is called W. R. Bennet hole or W. E. Lamb dip [73][74]. The width of the hole also depends on natural and collisional broadening of the resonance line. If an identical laser beam is allowed to pass through the discharge in opposite direction it would burn a hole at a central → velocity -− υ . If the laser can be scanned over the Doppler profile of the resonance line the central frequency ν o can be identified from the point at which one laser beam passes through the hole burnt by the other. A beam splitter and a couple of mirrors are arranged to send the two beams through the absorption column in opposite directions. One of the beams with higher intensity is called saturation beam or pump beam or bleacher. The other laser beam, relatively weaker, is called detection beam or probe beam. When the laser is tuned to the line center, the probe beam detects the hole burnt by the other beam and its transmission is increased. The lock in amplifier records the amplitude of the ac component that can be obtained when the saturation beam is switched on and off with the frequency of the chopper wheel used. Away from the line center the two beams interact with 32
two different velocity groups of atoms so the transmission of the probe beam does not depend on presence of the saturation beam. However at line center the transmission of the probe beam strongly depends on the saturation beam which burns a hole and therefore an ac signal is obtained at the frequency of the chopper. A detector recording the intensity of the probe beam records a sharp increase in the signal at each hyperfine component even when the entire hyperfine pattern is within the Doppler profile [75]. The first saturation spectroscopy experiments using a tunable narrow band laser were performed by T. W. Hänsch, A. L. Shawlow et al. [76] and by C. Borde [77]. The saturation spectroscopy is discussed in detail in [78]. The total LIF intensity is proportional to · Laser intensity · Number density in the initial sate · Einstein coefficient for absorption, and · Quantum yield ( ratio of the number of photons to the number of photons absorbed) In our experimental setup we have used saturation technique when the intensity of the LIF signal was not sufficient enough to record the hyperfine structure. The laser intensity and quantum yield is increased by sending the laser light back to the discharge sample using a high reflectivity mirror.
5.2.4
Laser induced fluorescence spectroscopy
In laser induced fluorescence spectroscopy, laser light of suitable wavelength is irradiated to an absorbing sample. In our experiment we used a dischrage containing carrier gas atoms and ions and atoms of the species to be investigated. The laser light is absorbed by the atoms and ions in the discharge sample, and then they emit radiation of various wavelengths including that of laser light, when the excited atom is relaxing to lower states. This phenomenon is called laser induced fluorescence. The emission spectrum provides information for both qualitative and quantitative measurements. It is also the most direct way to observe optical resonance. If an atom in the ground or an excited state Ei absorbs a laser photon of suitable wavelength, it lifts the atom to the energy state Ef . The population of this excited state is increased, and the excited atom relaxes via several processes. Fluorescence is one of these processes and results in the emission of light. The energy levels are characterized by a set of parameters, namely, the energy, parity, total angular momentum and nuclear spin quantum number I. If I is greater than zero, further parameters are as33
signed to the levels which are two hyperfine constants and the Lande ‘g’ factor. The set of these parameter acts as a finger print of the level. If a sufficiently high lying level is excited by a laser light it decays to a number of lower lying states, according to dipole allowed transitions, and emits a number of fluorescence lines. Each LIF signal mirrors the excitation probability when the frequency of the light driving the transition is tuned over the resonance. The strength of a LIF signal is determined by the branching ratio of the upper excited level. The hyperfine transition of the LIF lines does not play any role, since the monochromator selecting one LIF line does not resolve the hfs of this line, but acts only as a filter to suppress other lines of the discharge. The observed fluorescence lines can further be divided: (i) Fluorescence with positive LIF signal: These are the fluorescence lines which appear as decay from the upper level of the excited transition. In fig.3 E3 is an upper level, whose population is increased when atoms in state E2 absorb resonance laser light of wavelength λ23 . The level subsequently decays to the levels E4 and E5 by emitting fluorescence light of wavelengths λ34 , λ35 . If now the laser light is intensity modulated by a chopper wheel and phase sensitive detection (a Lock in amplifier) is used, the maximum signal appears at a certain phase between chopper and amplifier. Since the LIF signal increases when the laser is on, we call this a positive phase, or shortly a positive fluorescence. (ii) Negative Fluorescence: If the lower level is high lying compared to very low lying levels, this level decays to the further low lying levels and also emit fluorescence light. Such emission line is known as negative fluorescence. In fig.3 lower level E2 can decay to another level E1 . In the resonance excitation from E2 to E3 some of the atoms decay to the ground state and emit fluorescence light of wavelength λ12 . The population of E2 is diminished when the laser is on. This fluorescence is registered with 180o phase shift compared to (i). (iii) Impact or collision coupling: In some cases two or more excited levels lie very close to each other. The probability of impact or collision process is always there because of thermal motion. The atoms transfer their population during this impact process to the atoms of closely lying excited states, which subsequently decay and emit fluorescence light. In fig.3 the excited level E3 lies very close to another excited state E6 . The energy of atoms in state E3 is transferred to the atoms of
34
excited state E6 . The atoms relax to the energy state E7 by emitting fluorescence light of wavelength λ67 Impact coupling Chopper wheel
E3
E6
+ve fluorescence Due to impact coupling λ67
λ23 Laser light
λ35 E2
λ12
λ34
E7 +ve fluorescence E5 Signal increases
+ve fluorescence E4 -ve fluorescence E1
when laser is on
Signal decreases when laser is on
Figure 3: The figure shows the positive and negative fluorescences and impact coupling In all three cases the observed hyperfine structure is the structure of the excited transition. Advantages of LIF Blend situation: Sometimes more than one level is excited simultaneously (i.e. both lines lie in the scan range of laser), both levels then show LIF. This is known as blend situation. Two or more blend lines can be detected separately. The hyperfine structure of each line can be recorded separately by detecting the corresponding fluorescence line. The two recorded structures show the different hyperfine structure of the blend lines. The role of Positive LIF: If an unknown level is excited by resonance laser light and positive fluorescence is observed, the energy of the unknown upper level E3 can be calculated by combining the wave numbers of exciting and fluorescence lines. A further laser spectroscopic excitation confirms the ‘new level’.
35
The role of negative LIF: In practice, Negative LIF is observed only when the probability of decay with λ12 is very high. The lower level can be easily recognized by this negative fluorescence line, which is usually an already classified line. Thus, it is possible to identify the level E2 . By adding the wavenumbers of resonance line and level E2 , the energy of the upper level E3 can be calculated. To confirm this level another laser excitation is done. 5.2.5
Optogalvanic spectroscopy
When the wavelength of a laser beam, passing through an electrical discharge, is tuned to a particular resonance transition, a significant change in the populations of ground and excited state takes place. This alters the electrical properties (impedance, current etc.) of an electrical discharge. This occurs due to reasonable probability of collisions and ionization of high lying levels compared with low lying levels. This effect is known as optogalvanic effect. The technique which utilizes this effect is called Optogalvanic spectroscopy. The Optogalvanic effect was first observed by F. M. Penning[79]. He observed a change in the impedance of a neon discharge when it was irradiated by an adjacent neon discharge. Similar observations were made by C. Kenty[80] and by K. W. Meissner and W. F. Miller[81]. R. B. Green, R. A. Keller, G. C. Luther, P. K. Schenck, and J. C. Travis [82] used the optogalvanic effect with the tunable dye laser for spectroscopic measurements. The fig. 4 is the standard arrangement for optogalvanic spectroscopy.
Figure 4: Experimental arrangement of optogalvanic spectroscopy[83] 36
There are several processes occurring in the discharge which may contribute to the ionization process with in the atom. Some of them are given below: (i) Direct Ionization by electron impact on atom ’A’ A + e− → A+ + 2e−
(78)
A + e− → A∗ + e− , A∗ + e− → A+ + 2e−
(79)
A + B ∗ → A∗ + B + ∆E
(80)
A∗ + B ∗ → A+ + B + e−
(81)
This process dominates at low pressures. (ii) Two step ionization or multistep ionization
In noble gases this process is particularly important if excited states are metastable states. There are some processes which involve collisions between states. (iii) Excitation transfer: An atom ’A’ in ground state collides with an atom ’B’ in excited state, as a result ’A’ goes into excited state and ’B’ relaxes to the ground state.
(ii) Metastable collisions: two atoms in metastable states collide, one of the atom absorbs sufficient energy and becomes ionized.
The discharge current changes when the laser beam passing through a discharge is tuned to an optical transition. This current change ∆I can be measured as an ac voltage, ∆V = R∆I over a ballast resistance ‘R’ by chopping the laser intensity. This ac voltage is directly fed into a lock in amplifier to record the optogalvanic effect. Following are the advantages of optogalvanic spectroscopy: (i) The experimental setup is very simple. It does not require a monochromator and a photomultiplier tube or photodiode detector to obtain the spectra because the discharge itself acts as a resonant detector. (ii) To measure the hyperfine structure of a particular transition only the knowledge of exciting wavelength is necessary. However a substantial disadvantage exists in relation to unwanted current change. The gas discharge must burn calmly to obtain an acceptable signal to noise ratio. The optogalvanic signal has nothing to do with the fluorescence light, hence nothing can be said about the levels involved in the transition. Of course the excitation probability and thus the hf structure of the excited transition are mirrored in the OG signal.
37
Application of Optogalvanic effect • Determination of the hyperfine constants by exciting classified lines. • When exciting an unclassified line, OG signal can help in recording the hf structure of the line, and to place the laser frequency when later searching for LIF lines. • To study the collision process and ionization probabilities in a gas discharge. • This technique can be used for wavelength calibration in laser spectroscopy [84]. • The study of Rydberg states is also possible by optogalvanic spectroscopy [85]. • It is very efficient for the investigation of Autoionizing levels [86]. • The optogalvanic signals may be used for laser frequency stabilization [87][88]
5.3
Line broadening mechanisms
The spectral lines emitted and absorbed by an atom or molecule are not strictly monochromatic because of some physical phenomena which broadens the spectral line. The line broadening occurs due to finite life time of the excited state, random motions of atoms, and collisions. These broadenings are respectively called natural, Doppler, and collision or pressure broadenings. Line broadening can be homogeneous and inhomogeneous. If the probability of absorption or emission of radiations is same for all atoms in a (discharge) sample this broadens the line profile in the same way, the effect is called homogeneous broadening. Natural broadening and pressure broadenings are examples of homogeneous broadening. If the probability of absorption or emission of radiations is not same for all atoms, this line broadens inhomogeneously. The Doppler broadenings is an example of inhomogeneous broadening. The line broadening mechanisms have been discussed in [89]-[93]. The importance of any line broadening is measured by its full width at half maximum (FWHM) and is called line width or half width of spectral line. 5.3.1
Natural broadening
The population of the excited state at any time is given by N (t) = N (0)e−t/τ 38
(82)
where τ is called mean natural life time of the state and it depends on the transition rate for spontaneous emission. The life time τ i in the state ‘i’ is given by τi = Σ j
1 Aij
(83)
where Aij is the transition rate for spontaneous emission from state with energy Ei to state Ej . The uncertainty principle requires that the levels can not be infinitely narrow. The spread is given by h (84) ∆t where ∆t is the uncertainty in time associated with finding the atom in that particular state and is given by mean life time τ of the state. The corresponding frequency spread is given by ∆E=
∆Ei = ∆Ci =
h τi
(85)
In general the life time of a highly excited state is longer than that of lower lying state. The ground state has infinitely long life time. Hence ν i is negligible for ground and metastable states. Any dipole allowed transition from excited state ‘i’ to another excited state ‘j’ is the sum of the line widths of both the states and is given by ∆vij = vi + vj
(86)
The life time of excited states is of the order 10−6 to 10−9 sec. Hence a transition from such state to the ground state will have a line width of 0.1 to 100 MHz. A similar situation exists in absorption; the absorption line is broadened due to finite life time of the excited state. This line width is called natural line width and the phenomenon is called natural line broadening. The line width is small in infrared and micro wave regions Aij ∝ ν 3 . The profile function of the spectral line broadened by natural broadening is given by I(ν) = Io
(ν
1 4πτ 1 2 − ν o )2 + ( 4πτ )
(87)
where ν o is resonant frequency, where the intensity is maximum i.e. I = Io . The intensity function I(ν) is known as Lorentzian line shape function.
39
I
ν
Figure 5: Line profile of a spectral line showing half intensity points 5.3.2
Doppler broadening
The random motions of the atoms give rise to Doppler effect which broadens the spectral line. The resulting broadening is called Doppler broadening. The Doppler shift is not the same for all atoms because of random directions and magnitudes of motions of atoms. The atoms moving at non relativistic speed will emit the light of frequency υx ) (88) c where υ x is the component of velocity of atoms in the direction of interacting electromagnetic radiations, and ν o is the resonant frequency. If the atoms are in thermal equilibrium at temperature T, their velocity follows a Maxwellian velocity distribution, which is given as ν = ν o (1 +
ni (ν x )dν x =
Ni −( vvxp )2 √ e dν x υp π
(89)
where Ni is the density of the population of atoms in energy state Ei 1 2 and υp = ( 2kT m ) is the most probable velocity of atoms. The numbers of atoms in the frequency range ν and ν +dν is given by ni (υ x )dυx =
o 2 Ni cν o −[c( ν−v υ o vp )] √ e dυ x υp π
(90)
The intensity I(ν) of light emitted or absorbed in the frequency interval ν and ν + dν near resonant frequency ν o is given by 40
I(ν) = Io exp[−
Mc2 ν − ν o 2 ( ) ] 2RT νo
(91)
The intensity profile of Doppler broadened spectral line follows a Gaussian distribution with the central frequency ν o . Half intensity points are found as: 1 M c2 ν 1/2 − ν o 2 Iν = Io = Io exp[− ( ) ] 2 2RT νo
√ M c2 ν 1/2 − ν o ln 2= ( ) 2RT νo
(92) (93)
which gives ∆ν D
2ν o = 2(ν 1/2 −ν o ) = c
2RT ln 2 M
(94)
The quantity ∆ν D is called Doppler width.
T −7 ∆ν D = 7.16x10 ν o per sec (95) M R = NA K K = Boltzman constant M = atomic mass, and c = speed of light in vacuum (i) The Doppler width is proportional to the central frequency ν o . The lower the frequency, the lower the Doppler width; hence a red spectral line smaller than one in violet or ultraviolet region under the same conditions. (ii) The Doppler width is proportional to the square root of the temperature. The Doppler width is smaller at reduced temperature. Therefore for higher resolution the hollow cathode discharges are cooled with water or liquid air. (iii) The Doppler width is inversely proportional to the square root of the atomic or molecular mass. The Doppler width can be reduced by a further order of magnitude by using atomic and ion beam experiments, where a well collimated atomic or ionic beam interacts at right angle with the laser beam. 5.3.3
Collisional broadening
An excited atom can not only relax to the ground state by spontaneous emission but also release its excitation energy to another atom in an impact. Its life time is therefore shortened and the line is broadened. Since with increasing pressure the collision frequency
41
increases this is known as pressure broadening or collisional broadening. The collisional broadening is actually the result of inelastic collision between atoms. It is very prominent in plasmas and gas discharges because of the long range Coulomb interaction between charged particles. The collisional broadening produces a Lorentzian profile, the same as that of natural broadening. But it is of increased width. In order to avoid pressure broadening, the pressure in the spectral source should be kept low. By changing the pressure and observing the corresponding change in line width the information about the collisions occurring in the gas can be obtained. The collisions which have large impact parameter cause noticeable line broadening but can also shift the line center. The collisional broadening in called Lorentz broadening if collisions occur between different kinds of atoms and is called Holtsmark broadening if collisions occur between same kind of atoms. 5.3.4
Stark broadening
If collision occurs between ions and electrons, an additional line broadening takes place due to strong electric field experienced by atoms during collisions. This is called Stark broadening. 5.3.5
Saturation broadening
The line width also increases when the atom is interacting with a strong radiation field. This is normally called saturation broadening. If a gas or vapor is irradiated by a laser of sufficiently high intensity, operating at near resonant frequency, atoms can be excited faster than they return by spontaneous emission or collisions. This significantly changes the population of atomic states, and leads to saturation broadening. The saturation broadening is also called power broadening. The saturation broadening is different for homogeneously and inhomogeneously broadened spectral lines. 5.3.6
Combined line profile
The different broadening mechanisms can not be observed separately in the experiment. However, one can reduce the effects of particular line broadening, e.g. reduced pressure decreases the pressure broadening, reduced temperature decreases the Doppler broadening, and weakening the intensity of the laser light decreases the saturation broadening. It is not possible to isolate a spectral line from all broadenings. The total contribution of all types of broadenings can be represented by the single line profile which is the convolution of all type of line broadening profiles. i.e. 42
I(ν) = IN (ν) ∗ ID (ν) ∗ IP (ν) ∗ IS (ν)
(96)
IV (ν) = IG (ν) ∗ IL (ν)
(97)
where IN (ν), ID (ν), IP (ν), IS (ν) are the line profiles of natural, Doppler, pressure and saturation line broadenings, respectively. I(ν) is neither Lorentzian nor Gaussian because the line profiles are not all the same. Collisional broadening and natural broadening together give a Lorentzian line profile, while Doppler line broadening gives a Gaussian line profile. Saturation broadening may be Lorentzian or Gaussian. Hence, the line profile of the total line broadening is obtained by folding all line profiles. The resulting line profile is a convolution of Lorentzian and Gaussian functions, and is known as Voigt profile.
where IL (ν) is the total Lorentzian line profile, IG (ν) is the total Gaussian line profile, and IV (ν) is the Voigt profile In our work we observed that the line profile is determined mainly by a Gaussian line profile, because the most transitions had small probability of excitation, so they show no saturation broadening. However, in some cases, where the probability of excitation was very high, saturation effects did play their role and we observed a Voigt profile. The Doppler line width observed in our work was between 600-900 MHz.
43
6
Experimental setup
Every spectroscopy experiment has basically three main parts (i) a suitable source of light for absorption and emission spectra (ii) the discharge sample whose spectrum has to be investigated, and (iii) the detector for emitted and absorbed light by discharge sample.
6.1
Hollow cathode lamp
The first hollow cathode lamp was originally used by Schüler[94][95], it however had one anode. Paschen made a hollow cathode with the cathode inside two anodes[96]. Feldmann was the first who introduced a discharge with a clear path through the electrodes[97], Miyazaki et al. modified his discharge assembly by placing the hollow cathode between two hollow anodes[98]. A similar lamp was developed by Behrens and Guthöhrlein et al. [99][100]. The cathode may be made of the material to be excited, if it is a metal with suitable physical properties. Other materials may be place inside a hollow cathode. The cathode containers should not or only very little contribute to the discharge. The suitable cathode containers may be made up of copper or aluminium etc. Since the discharge is wholly confined inside the cathode, the efficiency of the excitation is high. In our experiment, we investigated the hyperfine structure of tantalum and praseodymium. The hollow cathode was made of a hollow cylinder of tantalum or praseodymium. The inner diameter of the tantalum cathode was 3 mm, and it had a length of 15 mm. The inner diameter of the praseodymium cathode lamp was 1.5-2.5 mm and its length was 12-15 mm, the inner most material of the praseodymium cathode lamp consisted of a metallic praseodymium rod with the central bore. The complete cathode lamp is presented in the fig.6. Two anodes are placed at both ends of the cathode. The anodes are mounted on a ceramic holder to avoid their contact with the cathode. The separation between anode and cathode was 0.75 mm. The anodes, the cathode and the ceramic parts had coaxial hole of almost same diameter. The whole arrangement was installed in a brass tube, which is capsulated in a glass tube that extended to both ends and forms the actual discharge container. The ends of glass tube are sealed by the two circular quartz glass plates. The quartz glass is used in order to allow the ultraviolet fluorescence light to emerge from the cathode lamp. These quartz glass plates actually act as windows of the hollow cathode lamp. Once the cathode assembly is installed in the discharge container, it is pumped out overnight to create a good vacuum. The Argon or Neon gas (or mixture of both) is filled in the cathode lamp at a typical 44
Figure 6: Hollow cathode lamp; HK... Hollow cathode, H...Valve, F...Quartzglass window, A...Anode connection lead, D... ’O’ ring
Figure 7: Vacuum system: HKL...Hollow cathode lamp, H1-H2... Glass shut-off valves, S1-S2... sliding valve, V1-V7... Valves, KF1-KF2... Cooling traps, M... Manometer, P... two-stage rotary vane pump, G... Gas inlet, Ne... Storage vessel for neon, Ar...Storage vessel for Argon
45
gas pressure of approximately 1.5 mbar for tantalum cathode lamp and less than 1 mbar for praseodymium cathode lamp. The cathode current was held constant at a value between 50 - 60 mA. The ionized gas is accelerated and strikes with cathode material and produces free atoms of tantalum and praseodymium. This is known as cathode sputtering. Cathode sputtering produces a cloud of free atoms in ground and excited states, the population of ground and excited state is considerable. Ionic levels are occupied to a smaller amount. It has been seen especially in case of praseodymium, reduced gas pressure below 0.5 mbar increases the population of ionic levels considerably. The Doppler width of the hyperfine components is reduced by cooling the discharge surroundings with liquid nitrogen.
6.2
Measurements
The dyes Rhodamine 6G, Rhodamine 110, DCM, Stilbene 1, and Stilbene 3 were used to produce dye laser radiations used in this work. The wavelength regions of different dyes are shown below: Dye lase working range / nm Rhodamine 6G 650 - 595 Rhodamine 110 540 - 570 Stilbene 1 410 - 440 Stilbene 3 420 - 450 DCM 630 - 690 The experimental setup is illustrated in fig.8. The single line Argon ion laser, operating between 5.5- 7.5 watts was used to pump the dye laser. The lasing action in dye laser produces laser light which has a certain range of wavelength depending on the type of dye used for lasing. By adjusting different optical elements the laser can be set to any wavelength or frequency within this spectral range. This single mode laser light falls on beam splitter M1, the laser beam 2 further splits into two beams by beam splitter B1. The laser beam 4 is fed to a λ− meter to read the wavelength of the laser beam. The other beam 3 further splits into two beam 5 and 6 by beam splitter B2. The laser beam 5 is fed to spectrum analyzer which displays the waveform on an oscilloscope. The laser beam 6, enters in a temperature stabilized Fabry Perot interferometer. The laser beam 1 is chopped periodically and passes through lenses L1 and L2, falls through mirror M6, which has a small transparent hole at its center which allows laser light to pass through it. The laser is made to pass exactly through the central hole of hollow cathode lamp, where it interacts with the cathode plasma. If the energy of laser light is exactly matching the difference of energies of two levels the resonance condition is fulfilled, provided the selection rules are not violated. The fluorescence light is emitted when atoms relax to the ground state, and a strong fluorescence signal may be 46
obtained if the ground state is sufficiently populated. This fluorescence light, with the combination of mirror M6 and lenses L3 and L4, is made to enter in the monochromator (grating monochromator with 1200 lines/mm). A photomultiplier mounted at the other end of the monochromator detects the fluorescence signal and converts it into a photocurrent, which is then fed to a lock-in-amplifier, whose reference frequency is the chopper frequency.
Chopper frequ.
Chopper frequ.
Figure 8: Experimental setup In order to analyze the hyperfine spectrum of a line, the frequency distances between different hyperfine components must be known exactly. This is done by the marker etalon, which gives equidistant frequency marks parallel to the hyperfine structure signal. Both signals are recorded simultaneously electronically on a computer for further evaluation and, for documentation on strip chart recorder. The recorded signal is then linearized. The distance between consecutive transmission maxima depends on the region of the spectrum, in blue region it is 149.6 MHz, in the red region it is 197.6 MHz, and in the yellow region it is 149.6 MHz. Because of the reading precision of the monochromator, the measured wavelength of fluorescence signal may have an uncertainty of 47
˚ Sometimes it is necessary to determine the wavelength of the ±2A. LIF light with higher accuracy. Especially when one of the fluorescence signals lie in the accessible range of our dye laser, it is good to know the exact wavelength for a second excitation of the level. For this purpose, a second chopper in front of the input window of the monochromator is used to modulate the whole emitted radiation of the hollow cathode lamp. The output of the photomultiplier tube is then also the input for a second lock in amplifier, with the frequency of the second chopper as its reference frequency. The laser light is set on the highest component of the excited transition, and the ˚ and the whole grating monochromator is scanned over several 10A. fluorescence light as well as LIF signal is recorded simultaneously on separate traces. Comparison with FT spectra gives the wavelength ˚ of LIF line with an accuracy of ±.05A.
6.3
Spectrum
The experimental determination of the energy levels of any atom or ion is best done by the investigation of its spectral lines. In order to receive the information about the electron shell of atoms or ions, one examines the light emitted by these atoms or ions. The atoms or ions emit electromagnetic radiation if they are excited. In order to bring the atom to an excited state energy is needed. This necessary energy can be supplied to the atoms or ions thermally (by heating), electrically (by discharge phenomenon) or by impact with other electrons. Another possibility is excitation by absorption of light, for which the resonance condition ∆E = hν has to be fulfilled. The life time of the excited state is usually short and atoms do relax to their ground state by emitting electromagnetic radiation of discrete frequencies. This electromagnetic radiation is resolved into its components when they pass through a suitable apparatus. These discrete spectra are usually seen in the form of distribution of intensity over frequency or wavelength. If the spectral line has sufficient intensity and if the apparatus which analyses the emitted light has high resolution the intensity maxima of spectral line show a hyperfine structure. Every element emits its own characteristics spectra, which is known as finger print of that atom. In order to get sufficient knowledge about the electron shell, one has to examine numerous spectral transitions. To study a wide range of wavelengths of the emitted light, a highly resolved spectra in that wavelength range is needed. Since in our group in Graz is working on investigation of Ta hyperfine structure since 1990, we have obtained and worked with some spectra of Tantalum, which show many lines of atoms and ions in a broad range from
48
UV to far infra red. These are grating spectra on photo plates and Fourier transform spectra. 6.3.1
Grating spectra of Ta on photo plates
At the beginning of studies of hyperfine structure of Ta at the institute of experimental physics, Graz, the Ta-spectra on photo plates were used. These spectra were taken up at the University of Poznan by B. Arcimowicz. The photoplates were exposed several times, once with the light of an Ar-Ta hollow cathode lamp and then with Ar-Fe hollow cathode lamp. The second exposure is just to get a reference spectrum to calibrate the Tantalum lines. For a systematic investigation the center of gravity wavelengths of lines were determined from the spectrum on the photoplates with a Comparator. These spectra contain lines of both atomic and ionic tantalum. All the lines which were not listed in the reference are considered as new lines. In the work of N. Jaritz such lines are indicated by the label ’nl’ (new line). 6.3.2
Fourier transform spectra
High resolution FT spectra have been recorded using the FT spectrometer at Imperial College (JCP) and Kitt Peak (RE). These spec˚ up to 50000 A. ˚ The resolution is limited tra cover the range of 2000 A by the Doppler width of the lines, and the majority of the hyperfine structures are at least partly resolved, allowing the identification of the transition if the hyperfine constants of the involved levels are known. In the UV and visible spectral region water cooled hollow cathode lamps were used with Ar as buffer gas. The diameter of the hollow cathode was typically 8 mm, the Ar gas pressure 2 mbar, and the current 300 mA. These spectra have been wave number calibrated by means of a set of interferometrically measured standard Ar wave numbers. In the IR region, an electrodeless high frequency discharge in flowing He and T aCl5 vapor was used. The T aCl5 molecules were completely dissociated, so only lines of He, Cl and Ta lines were observed in these spectra. The lines of He and Cl both were broad showing no hyperfine structure, while line of Ta showing hyperfine structures. The wave number calibration was accomplished using a reference T a/N e hollow cathode . The Ne lines were used to calibrate the hollow cathode spectrum and the resulting accurate wavelengths of Ta lines were then used to calibrate the spectrum of the electrodeless discharge, some portion of FT spectra are shown in fig. 22. The line 3738.46 is not prominent in FT spectrum (ii). This line was new and unclassified. The signal to noise ratio was good in FT spectrum (i). The new level 50256o11/2 was discovered by fitting this line. In FT spectrum (i) the ionic lines are prominent. Some of the important features of FT spectra are listed below: 49
1. FT spectrum is obtained in digitalized form. 2. FT spectra show a high resolution. 3. FT spectra can display a large spectral range. 4. The position of the hyperfine components in FT spectra is very accurate. It is however may a disadvantage of FT spectra that it is hard to find a light source that emits weak lines with sufficient intensity.
3736.759 Ta I
3738.229 Ta I
50 Relative Intensity
3738.46 Ta I
3736.12 Ta II
3738.024 Ta I 3737.43 Ta I 3737.43 Ta I
0 3739
3738
3737
3736 Wavelength /Å
(i)
Ta II 3738.888 Ar
3736.759 Ta I
50 3738.229 Ta I
3736.12 Ta II
Relative Intensity 0 3739
3737.49 Ta II
3738
3737 (ii)
3736 Wavelength /Å
Figure 9: Same portion from two different FT spectra obtained from two different sources (i) high frequency discharge of He and T aCl5 (ii) hollow cathode lamp with Ar − T a.
50
7
Computer programs
In this work some important computer programs were used. The ’classification program’ was used to handle the huge amount of data of Tantalum and Prseodymium, ’the fitter program’ was used to obtain the best fit of experimentally recorded hyperfine structures or hyperfine structures of lines extracted from FT spectra, and ’the Origin macro’ was used to extract the hyperfine structure of a line from FT spectra.
7.1
Classification of spectral lines by means of their hyperfine structure
The tantalum and praseodymium atoms and ions have a huge number of spectral lines. To organize such a large number of lines of any atom or ion is very difficult without a proper program. The classification program which classifies spectral lines by means of their hyperfine structure was written by L. Windholz ( Institute of experimental physics, Graz, Austria)[101]. The viewer version is also available on internet. This program is can be used for any element. We used the same program for Tantalum and Praseodymium. The program can simultaneously be used for atomic or ionic lines or both. This program uses three data files, (i) a level file for atoms, which contains all known levels of atomic states (ii) a level file for ions, which contains all known levels of the first ionic state of the atom , and (iii) the wavelength file, which contains all known lines whether classified or unclassified. The wavelength table has more than 12000 entries in the following format. 4820.512, 30, , , ,31270.87 ,8.5 ,o, 512 , —, *Z05-,10531.98 ,8.5 ,e, 546v , - , *Be99,(Pr I) Z05-08-20 a5798.145 The first entry is line wavelength in Å in air, next four entries are intensities from different sources. If the line is classified the next entries are the energy, angular momentum, parity, A and B values and comment about the upper level. Then the next entries are for lower levels in the same order as for the upper level. Finally, it is possible to comment the lines, for example to give excitation wavelengths and so on. This program has the ability to deal with a large number of spectral lines and levels. At present the wavelength file of Tantalum contains more than 10000 lines, and wavelength file of praseodymium contains more than 17000 lines. The classification program opens a window that is separated into two separate parts, each small window has a graphic field, where the hyperfine structure of the line is displayed. The left side of the window shows the center of gravity wavelength of a spectral line, the wave numbers, if it is classified, the angular momenta, the hyperfine 51
constants of upper and lower levels, and remarks against each level. This remark usually displays the name/s of the person or group who discovered the level. The center of gravity wavelength is converted in the wave number by using the dispersion formula of Peck and Reeder [102]. The difference of upper and lower wave numbers is also displayed, which is again converted into wavelength by the Peck and Reeder formula. The difference of calculated wave number and center of gravity wave number is also displayed, which helps to understand how accurately the wave numbers of upper or lower levels are known. This window also displays the wavelengths of previous and next lines. The graphic field displays the hyperfine structure of the line. The other side of the main window displays all possible suggestion for classification of the line, it displays both atomic as well as ionic transitions. If one only wants to see atomic or ionic transition, one can suppress other transition by using the one of the options, search atomic transitions, ionic transitions, or both transitions. The graphic field of this window also shows the hyperfine structure of the suggested transition. Fig. 10 shows the classification of the line 3089.75 Å, both possible suggested transitions and their hyperfine structure.
Figure 10: The right classification of the line 3089.75 Å is shown in both windows and some other suggestion are shown on the right window by classification program. Some of the important features of the program are (i) one can easily move to previous or next line using the buttons prev or next respectively. (ii) out of thousand lines one can select any line through the button ’Go to lambda’. (iii) A new line can be added to the wavelength list (in wavelength file) without opening the actual file using ’insert line’ button. (iv) The already entered wavelength of the line and its parameters can be edited directly using ’change entry’ button. The ’change entry’ 52
and ’insert line’ buttons opens a window, where one can enter some important things related to the line. For example, the intensity of the line, the source of the line, any comment like " new level involved" etc, atomic or ionic line, seen as fluorescence or excited using laser, etc. can be entered in the wavelength list again without opening the file. This is a comfortable way to access this huge file. The edited entries are also displayed in the left window. (v) The save button allows one to save all the changes made. (vi) One can quickly move to beginning or end of the file. (vii) One can easily shrink or expand the hyperfine structure through a scale button. (viii) The Doppler width of the spectral line can be changed. (ix) One can browse through all lines belonging to the same level. (x) The program has the option to show all lines having the same comment. (xi) The lines having intensity greater than a certain value can be selected. (xii) It displays interesting current parameter e.g. the total no. of levels in level the list, the total number of lines in wavelength list, etc. (xiii) Without opening the level list, it is possible to see the all entries in the atomic or ionic level lists. (xiv) The atomic or ionic level list can be sorted according to angular momenta and hyperfine constants, or according to energy. (xv) The program displays all even and odd levels separately. (xvi) It displays the list of all possible transition from upper level or possible transitions to a lower level. (xvii) It displays positive as well as negative fluorescence lines. (xvii) Working with the program if the level list is updated, the changes can be activated easily by reloading the level list. (xviii) A hypothetical new level can be found based on the actual line or fluorescence lines observed during an experiment. (xix) A sub program window can be activated, which converts the wavelength into wave number, or wave number into wavelength automatically using Peck and Reeder dispersion formula. It also displays the difference between two wavelengths in wave number or difference between two wave numbers in terms of wavelength. (xx) The details of the hyperfine structure of suggested and classified lines can be seen. 7.1.1
Simulation program
The classification program also has another subprogram, which simulates the hyperfine structure of the classified or unclassified line. If the line is classified, it automatically takes the hyperfine constants and J values of the levels involved in the transition, and displays the 53
hyperfine structure of the line. The classification suggestion can be accepted if the hyperfine structure of simulation program matches either with the laser spectroscopically recorded structure of the same line, or with a well resolved hyperfine structure in a FT spectra. The simulation program shows an alert if the selection rules are violated. The Doppler width and nuclear spin can also be changed in the simulation program, if needed. If the line is still unclassified and its FT spectrum shows a well resolved hyperfine structure (or a laser spectroscopic hyperfine structure is recorded), with the help of this routine one can simulate the hyperfine structure of the line and approximate values of the hyperfine constants are obtained, which serve as starting values in the fitter program for further evaluation. Fig. 11 shows the simulation of the line 3608.758 Å, the simulated curve overlaps the hyperfine structure extracted from FT spectra.
Figure 11: Simulation of the line 3608.758 Å and its hyperfine structure taken from a FT spectrum.
7.1.2
Finding a new level by combination of the wave numbers
If our classification program does not show any suggestion for an unclassified line, it is clear that at least one unknown level is involved in the transition. This unknown level can be found using the wave number of the unclassified line. The basic principle is the same as given in Ritz combination principle. To start with the search we assume a certain parity of the new and unknown level, e.g. odd parity. Then from the list of the even levels, the level with the lowest energy is taken and the wave number of the unclassified line is added. This gives the energy of a hypothetical new level in wave numbers. Then the wave numbers of all other unclassified lines from the line 54
list are added to other even level energies. If the energy obtained in this way coincides, with in a given uncertainty, with the energy of the hypothetical new level then the even levels with wavelength are displayed. This procedure is then repeated for the next higher even level. In this way a number of hypothetical levels are calculated. The J- value of these hypothetical levels can be easily found by the selection rules. The next step is to simulate the investigated unclassified line by fixing the A- and B values of the lower even level. If a simulation is impossible then the hypothetical level is rejected. If the simulation is possible, then the A and B values of the hypothetical level are estimated. To make sure that the hypothetical level really does exist, other unclassified lines which appear as decay from the hypothetical level, are taken, and their simulated hyperfine structures are compared with the corresponding hyperfine structures in FT spectra. If one or more hyperfine structures are identical then the level existence is confirmed. If no odd level fulfils this condition, the above procedure is repeated assuming that the hypothetical level now has even parity. Initially the upper level wave number limit was set to 75000 cm−1 for Ta II. After the discovery some new levels with energy greater than 75000 cm−1 , the upper level limit was increased. The line 3286.118 with a relative intensity of 40 was unclassified and had a well resolved hyperfine structure in the FT spectrum. A new level 75048.39 cm−1 with even parity was found. The simulation gave J = 3, and the hyperfine constants A = 740 MHz and B = -1200 MHz. The list of all possible transitions from this new level showed some unclassified lines. To confirm this level, and to see whether these unclassified lines are explained by this new level or not, the hfs of the lines can be treated. Using the predicted hyperfine constants of the new level and the hyperfine constants of already known lower levels the hyperfine structure of each line was predicted and compared with the hyperfine structure of the corresponding lines in the FT spectra. An excellent matching between the simulated hfs and the hfs in FT spectra was found, which not only confirmed the new level, but also made possible to classify these unclassified lines. Fig. 12 shows the simulated hfs and corresponding hfs in FT spectra.
7.1.3
Determination of a new level by fluorescence lines
If an unclassified line is excited by laser light and some fluorescence lines are observed, a new level energy can also be found using the information obtained from laser spectroscopy. The fluorescence lines are fed in the search procedure through a window which accept the fluorescence lines observed during the experiment. The search procedure is again based on Ritz combination principle. It is a bit different 55
Figure 12: Comparison of simulated hyperfine structures and hyperfine structures from FT spectra for classification of unclassified lines as decay from the level 750483 cm−1 .
Figure 13: The Ta II line, 3286.1 Å, which led to the discovery of the new level 750483 cm−1
56
from the above method in a sense that it only uses the current line and lines from the data base in a certain wavelength range around the observed fluorescence lines. 7.1.4
Determination of a new level by analysis of the hyperfine structure
Sometimes it is possible to have an idea about the transition by looking at the hyperfine structure of an unclassified line, The hyperfine constants of the unknown upper and known lower level are then found by simulation. Then a lower level is searched in the level list with hyperfine constants close to the pair obtained by simulation. If the simulation is perfect the lower level can be obtained from the list. The addition of the center of gravity wavenumber of the line and wavenumber of the lower level gives the energy of the upper unknown level. After introducing this level in the level list, the transition list from this level generated by the classification program is investigated to see if some other unclassified lines are also decay channels from this level. If this occurs its hyperfine structure verifies whether this unclassified line is a real decay from this level. If this is so, this confirms the new level.
N ew lev el U n c lassifie d L in e lea d in g T o d isc o v e ry O f n e w lev e l
L o w er lev e l id e n tified b y A , B v alu es A n o th e r k n o w n lev el
Figure 14: Example of finding a new level by analyzing the hyperfine constants of the levels
57
7.1.5
Classification of unclassified lines by its hyperfine structure
The classification program gives the suggestions for unclassified line, sometimes it shows more than one suggestion. A graphic field displays the hyperfine structure of each suggestion, and the unclassified line can be classified if the line shows the same hyperfine structure in the FT spectrum and corresponding peaks also coincide. The line 5418.87 Å is a line in FT spectrum with sufficient signal to noise ratio. During this work this line was found in a FT spectrum and it was seen that this line was not known before and is obviously unclassified. This line was inserted in the classification program, and few suggestions were displayed by the program. One of the suggestions had the similar hyperfine structure so it was considered that the line had the suggested classification. Later a laser spectroscopic excitation further confirmed this classification. Hundreds of lines are classified in this way by our group. In fig. 15 the structure of the line 5418.87 Å is shown. The two different overlapped traces are portions of two different FT spectra. The ripple ocurrs due to the Fourier transform of a very strong line in the neighbourhood ( 5419.19 Å, which has a relative intensity of 1700 ).
R e la tiv e In te n s ity
W a v e le n g th /Å
Figure 15: The line 5418.87 Å is shown in the FT spectra. It is a result of decay from the level 550809/2 , this level was discovered by our group.
7.2
Fitter program
The laser spectroscopic investigation allows us to record the hyperfine structure of the lines in digital form on a computer for further evaluation of hyperfine constants and center of gravity wavenumber of 58
the line. The hyperfine structures are recorded as intensity distribution function of the tuned laser frequency. The hyperfine structures in FT spectra are also intensity distributions of the frequency. To evaluate the hyperfine constants and center of gravity of a laser spectroscopically recorded line or of a line extracted from FT spectra the fitter program, especially designed for this purpose, is used. This program was designed at Hamburg, Germany[103]. In order to evaluate the physical information contained in the recorded hyperfine structure, a mathematical model of intensity distribution is computed which best fits an already recorded intensity distribution ’I’ recorded as a function of time (equidistant time intervals ). This function has to be converted in a function of frequency by means of the marker etalon. Due to scanning behavior of the laser, these points have not a constant frequency spacing. By a linearization the program converts the measured spectrum I(t) in a spectrum I(ν) with points now equally spaced in frequency. The reason is that mathematical least square routine are much simpler and faster for equal spacing of data points. The positions of the individual component results with the help of Casimir factors and hyperfine structure constants, by the following equation ν = ν c + αo Ao + β o Bo − αu Au + β u Bu
(98)
→ ESS= Σ[Iν (k) − Iν (ν k , − a )]2
(99)
The intensity of each component is introduced theoretically by the intensity formula given in last article of the chapter three, using 6j symbols. The mathematical model contains the physical boundary conditions as parameters. The model is developed by the variation of these parameters gradually according to the method of least square errors or Gauss-Newton procedures.
The function ESS is the squared error sum , Iν (k) is the measured → intensity at a given frequency point ν k and Iν (ν k , − a ) is the calculated → intensity at the corresponding position, and the vector − a is a set of fit parameter. The above equation can be expanded using Taylor series and a number of nonlinear, inhomogeneous equations are obtained. The number of such equations are exactly equal to the number of → parameters in vector − a . The solution of these equation is obtained in such a way that the deviation form measured intensity becomes less and less, and the solution also gives a new set of parameters of → vector − a . This new vector is used as start value for next iteration, and this procedure is repeated until an abort criterion is reached. The important parameters in this fit procedures are hyperfine constants of lower and upper levels, the frequency of a certain hyperfine component, the half width of the components, and the underground intensity. 59
Obviously the number of parameters is reduced by fixing some values ( e.g. if one of the levels involved in the transition is known one can fix the hyperfine constants of this level and the total number of parameters is reduced by 2, or if one knows the half width, it could be fixed and the number of parameters is reduced by 1). Saturation effects may change the relative intensity of some hyperfine components. In this case various component coupled together in the fit procedure. The fitter program can be used for 2 or more isotopes simultaneously, or if two or more hyperfine structures are overlapped, to fit all lines together. Figs. 16, 17, 18 show the fit of a single line, two lines overlapping their hyperfine structures and three lines blending. L-Start in A = 5774.08109 L-Fluores. in A = 6185
Güte = 50.8397 Skalierung = 1.6564
Bestfitsituation: C:\fitter\spek\arb\P054019.bf
I = 5/2, Jo = 13/2, Ju = 11/2, L-Luft = 5772.375 A Ao = 627.83, Bo = 0.00, Au = 1009.20, Bu = 0.00 (in MHz)
1.0 0.9 0.8
normierte Intensität
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
2500
5000
S 7500 10000 Offsetfrequenz in MHz
12500
15000
17500
Figure 16: The best fit of the unblended Praseodymium line 5772.375 Å.
60
L-Start in A = 3220.588646 L-Fluores. in A = 1.0
Güte = 23.0572 Skalierung = 0.8221
Bestfitsituation: C:\fitter\spek\arb\3219_5e.bf
I = 7/2, Jo = 7/2, Ju = 7/2, L-Luft = 3219.624 A Ao = 655.00, Bo = -329.00, Au = 333.00, Bu = 1196.00 (in MHz) I = 7/2, Jo = 7/2, Ju = 9/2, L-Luft = 3219.571 A Ao = 509.00, Bo = 282.00, Au = 1084.00, Bu = -2701.00 (in MHz)
0.9 0.8
normierte Intensität
0.7 0.6 0.5 0.4 0.3 0.2 0.1
0
0
5000
S 10000
15000
S 20000 25000 Offsetfrequenz in MHz
30000
35000
40000
Figure 17: Fitting of two Ta I lines 3219.624 and 3219.571
L-Start in A = 3093.998571 L-Fluores. in A = 1.0
Güte = 49.2273 Skalierung = 2.4952
Bestfitsituation: C:\fitter\spek\arb\3093_0.bf
I = 7/2, Jo = 2, Ju = 3, L-Luft = 3093.006 A Ao = -610.00, Bo = 714.00, Au = 1940.00, Bu = 300.00 (in MHz) I = 7/2, Jo = 9/2, Ju = 9/2, L-Luft = 3092.987 A Ao = 117.00, Bo = 4188.00, Au = 256.00, Bu = -650.00 (in MHz) I = 7/2, Jo = 5, Ju = 4, L-Luft = 3093.071 A Ao = 335.00, Bo = -50.00, Au = 220.00, Bu = -350.00 (in MHz)
0.9 0.8
normierte Intensität
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
S 10000
20000
S S 30000 40000 Offsetfrequenz in MHz
50000
60000
Figure 18: Blend situation and best fit of three lines 3093.006, 3092.987, 3093.071
61
7.3
Origin Macro
The new Ta II high lying levels are found by the investigation of unclassified lines appearing in the FT spectra. To obtain the best fit of the a line using the fitter program, the input file for this program was the hyperfine structure extracted from FT spectra. To extract the hyperfine structure form the FT spectra, a subroutine was written by N. Jaritz which works with the custom button of "origin". It extracts the intensity distribution of the hyperfine structure in a data file.
62
8
Experimental results and discussion
My LIF experiments led to new data on the hyperfine structure of Ta:I and Pr:I, besides I determined the hyperfine structure constants of Ta:II levels evaluating already recorded FT spectra. The hyperfine constants of most of the Ta:II levels are not yet known and some constants available in the literature turned out to be not accurate. The hyperfine constants of 200 levels are determined in this work. These hyperfine constants are shown in two separate tables, one for the even levels and the other for the odd levels. The values of the hyperfine constants are also compared with previous data of Zilio, Erikson and Messnarz. Professor Windholz has already investigated FT spectra in detail. He found hundreds of new lines both of the tantalum atom and the ion, which were not mentioned in previously published tantalum line lists. He classified many lines by their hyperfine structure using our classification and simulation programs. He put a remark ’ new level involved’ if no suggestion was possible for a line. Some of the lines had a very good signal to noise ratio, the best fit could be obtained for such lines. Once the best fit or simulation of a line is possible, the energy of the upper level can be found after the identification of the lower level via its hyperfine constants. Eight new levels of tantalum are discovered in this work by fitting of lines with good signal to noise ratio. All new levels are shown in the table of new levels of tantalum II. More than 70 unclassified lines were classified after discovery of new levels of Ta II.
8.1
Classification of Ta II lines, determination of hyperfine constants of Tantalum II levels
The FT spectra, recorded from two different light sources containing tantalum atoms, contain more than 1000 lines which are partially resolved with respect to their hyperfine structures. There are hundreds of lines which are still unclassified. Most of them are in the UV region and belong to the Ta II spectrum. The classification can be done via the wave numbers of the lines and by their hyperfine structures, but in most cases our classification program either shows no suggestion or the hyperfine structure of the suggested classification does not match. It is obvious that the energy levels of the electronic shell of Ta II are still not completely known. Besides laser induced fluorescence spectroscopy, we also tried to discover these unknown levels by an analysis of the FT spectra. Most of the lines have a very small hyperfine splitting, which is masked by the Doppler width of the line. So the hyperfine structure is not clearly pronounced in the spectra. Few of these lines have very good signal to noise ratio, which is needed to get a good fit of the line. A problem when fitting the hf structure is that we always have to locate the position of the highest 63
component of the hyperfine structure. If the line pattern is partly masked by Doppler width of the line it is almost impossible to get reliable hyperfine constants from fitting the line. In the figs. 19, 20 and 21 three possible fits of the line 3769.9 Å are shown. This line was classified after the discovery of the new level, 752942 , of Ta II. This was a 2-1 transition, so we fitted the line with J0 = 2 and Ju = 1. In fig. 19 the fit is obtained by varying all four hyperfine constants. The quality of the fit is 46.6. In the second fit all hyperfine constants are again varied but the relative position of the highest intensity component is changed. The quality of fit is 47.3. In fig. 21 the best fit is obtained by fixing the hyperfine constants of the lower level (Au , Bu ). This is possible if one level of the transition is already identified and when its hf constants are known. The quality of fit in this case is 46.8. The difference of the qualities is not large. The third fit belongs to the actual transition. This example shows that, if the line is masked by the Doppler width of the line, it is purely accidental where one places the highest intensity component. Thus, reliable values of the hyperfine constants can not be found even the quality of the fit is high. Otherwise, for identifying at least one level of the transition one needs reliable constants, thus, the identification of one level of the transition via its A/B pair is not possible. The situation can be made slightly better, if one of the levels involved is already identified then the number of variables is reduced by 2, and it is possible to use the known hyperfine constants of one of the levels. The results of the three fit are shown in the following table. Table 7.1: The results of the three fits of the line 3769.918 Å. ˚ Jo λ/A Ao Bo Doppler Quality Ju Au Bu Highest MHz MHz width of fit MHz MHz com-
3769.9
2
123
970
2119
46.64
1
44
593
ponent 7000
3769.9
2
46
306
2011
47.31
1
205
720
5000
3769.9
2
-57
-1404
2131
46.79
1
-61
430
5000
The situation discussed before is not suitable to find a new level of Ta II. The reasons are: (i) Its hard to decide which lower level is involved in the transition. (ii) To try all possible lower levels too much time is needed. (iii) In some cases it is not sure that the observed structure belongs to one line or it is a blend of two or more lines. (iv) In some cases the signal to noise ratio is not good, and the quality of the fit is mainly limited by noise and not by the model 64
Figure 19: Fit of the line 3769.9, all four hyperfine constants are treated as free parameters. The highest intensity component is set to 7000 MHz. function used. However, the above treated situation is well suited to find the hyperfine constants of the upper level, if one of the suggestions is the real transition explaining the line. The hyperfine constants of many levels of Ta II were found in this way. Again a serious problem occurs, if both levels involved in the transition have unknown hyperfine constants.
8.1.1
Determination of the hyperfine constants of the Ta II level 39758o5
If the signal to noise ratio is good and the splitting of the hyperfine structure is larger than the Doppler width, the structure is well resolved. It is easy to decide the position of the highest intensity component. A good fit can be obtained easily even if the line is blended with another (e.g. Ta I) line and their hyperfine structures overlap. The hyperfine constants of the level 39758o5 are found by fitting one of its decay lines, 3330.99Å. This line has a relative intensity of 300 but is blended with the Ta I line 3331.009Å, which has a relative intensity of 436. Both lines have a very good signal to noise ratio. The Ta I line is already classified and the hyperfine constants of both levels are 65
Figure 20: Fit of the line 3769.9Å, all four hyperfine constants are set free. The highest intensity component is set to 5000 MHz
Figure 21: Fit of the line 3769.9Å, the hyperfine constants of the lower level are fixed. The highest intensity component is set to 5000MHz.
66
L-Start in A = 3332.077813 L-Fluores. in A = 1.0
Güte = 39.4740 Skalierung = 1.8477
Bestfitsituation: D:\FITTER\spek\arb\3331_0e.bf
I = 7/2, Jo = 9/2, Ju = 7/2, L-Luft = 3331.005 A Ao = 1030.00, Bo = 1962.00, Au = 1148.00, Bu = -312.00 (in MHz) I = 7/2, Jo = 5, Ju = 4, L-Luft = 3330.995 A Ao = 1526.17, Bo = -26.09, Au = 303.00, Bu = 1680.00 (in MHz)
0.9 0.8
Ta I
Ta II
normierte Intensität
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
10000
20000
S S 30000 Offsetfrequenz in MHz
40000
50000
Figure 22: Fit of the line 3330.999Å, which is blended with the Ta I line 3331.009Å. well known. The Ta II line was classified and the hyperfine constants of the lower level are known. In the input file of the fit program the hyperfine constants of both levels of Ta I and of the lower level of Ta II are fixed. The fit was possible with quality of 38, and the hyperfine constants of the level the 39758o5 are found. The hyperfine constants of this level are shown in the following table. Table 7.2: The best fit result of the blend lines 3330.9 Å and 3331 Å.
Line Å 3330.9 3331.0
Jo 5 4.5
To cm−1 39758 42247
Ao MHz 1529 1030
Bo MHz 457 1962
Ju 4 3.5
Tu cm−1 9746 12234
Au MHz 307 1148
Bu MHz -2124 -312
The fig. 22 shows the best fit of the two blend lines.
8.1.2
The level 771964
The level 771964 was discovered when the line 3235.135Å was fitted. It has a well resolved structure of relatively high intensity. So it was believed that the fit would give good results. It is always difficult to
67
L-Start in A = 3236.130634 Bestfitsituation: C:\fitter\spek\arb\3235_1e.bf L-Fluores. in A= 1.0
Güte = 71.6409 Skalierung = 1.9823
I = 7/2, Jo = 4, Ju = 5, L-Luft = 3235.126 A Ao = 409.70, Bo = -1135.87, Au = 672.24, Bu = -255.54 (in MHz)
0.9 0.8
normierte Intensität
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
5000
10000
S 15000 20000 Offsetfrequenz in MHz
25000
30000
Figure 23: Best fit of the line 3235.135 which led to the discovery of the level 77196 decide how the starting values of hyperfine constants should be chosen, and which set of J values is involved. To overcome this problem various combinations of J values were tried. The highest quality of the fit was obtained with the combination Jo =5 and Ju =4. The quality of the fit was 71. For the lower level we got hyperfine constants Au =672 MHz and Bu = -255 MHz. Then in the level list of known Ta II levels a level with these hyperfine constants was searched. One of the levels, 46295o5 , had Au =674 MHz and Bu = -190 MHz. Assuming this as the lower level of the transition, the upper level energy was found by adding the wave numbers of lower level and the center of gravity of the line 3235.135 Å. The energy of the new level is 77196.89 cm−1 . The fit was repeated with Au and Bu fixed to obtain the final value Ao and Bo . This level 77196.89 cm−1 was introduced in the level list. Our classification program showed then the list of all possible transitions from the new level. It was revealed that some unclassified lines were explained by the introduction of this new level. Then the expected hyperfine structures generated by our classification program were compared with the hyperfine structure of these lines in the FT spectra. The hyperfine structures were in good agreement. Some of the lines which appeared as decay from this level had also relatively 68
77196
3667.4 3614.2
49937
3552.4
3480.1
49055
49536 3403.6
48470
3341.7
47825 3329.2
47280 3273.2
3235.1 47169
46645
3065.5
46295 2970.6
44585
2804.8
43544
2669.1 41554 39743
Figure 24: The lines classified after the discovery of the level 771964. high intensities. So a good fit was also possible for those transitions when fixing the hyperfine constants of the lower level. Then the average value of the hyperfine constants of the new level was obtained. It is shown in the table of new levels. The combinations from the new level are shown in detail in the fig. 24. 8.1.3
The level 752942
The level 752942 was discovered by the fitting three lines, 3639.42 Å, 3514.7 Å and 3091.741 Å. All three lines have partially resolved hyperfine structures in the FT spectra and were unclassified. Various combinations of angular momenta were tried to fit the line 3639.42 Å, the best quality, 12.6 was obtained with Jo = 2 and Ju = 3. For the hyperfine constants of the lower level we got Au = 922 MHz and Bu = -70 MHz. The level list of Ta II has a level with energy 47825.449o3 cm−1 and A/B values close to these figures. This energy was added to the center of gravity wave number (27469.064 cm−1 ) of the line 3639.42 Å. The new level was found to have the energy 75294.513 cm−1 . After introduction of this level in the level list possible decays from this level explained some unclassified lines. The Two lines mentioned before were also in the combination list. They had very good signal to noise ratio and a fit could be obtained. Both these lines were fitted separately. The best fits are shown in the figs. 26, 27. The results of fitting these three lines are shown in the following 69
Figure 25: The best fit of the line 3514.7 Å.
Figure 26: The best fit of the line 3639.422 Å
70
New level Steps to new level determ ination
1. Determination of J, A, B of lower and Upper level form sim ulation of hyperfine structure 2. Identification of lower by hyperfine constants 3. Finding energy of new level by adding wavenum bers of lower and unclassified line 4. T est if the new level explain at least one m ore unclassified line
U nclassified line leading to discovery of new level
Lower level identified by A, B values
Another known level
Figure 27: The best fit of the line 3091.735 Å table: Table 7.3: The results of the best fit of three 75294 cm−1 . wave Jo Ao Bo DW Quality length Å MHz MHz MHz 3514.71 2 -66 -1104 2611 31.24 3639.42 2 -53 -726 2517 12.63 3091.74 2 -48 -1081 2509 9.59
lines of the new level Ju
Au
Bu
2 3 3
MHz 1111 910 980
MHz -1875 -530 -850
To obtain the final value of Ao , Bo the weighted average was taken. The relative intensity of each line in the FT spectra and the quality of the fit were taken as weight. The average values obtained in this way are Ao = - 63 (15) MHz. and Bo = -1050 MHz for the new level 752942 . After the discovery of this level, more than 15 unclassified lines could be explained with respect to their wavenumbers and hf patterns. 8.1.4
The level 769233
The level was discovered from fitting the line 2872.636 Å. This line was unclassified, so all four hyperfine constants were varied, and the line was fitted assuming different combinations Jo − Ju . The best fit gave Jo = 3, Ao = 2513 MHz, Bo = -1745 MHz, Ju = 4, Au = 1065 MHz, Bu = -912 MHz. The center of gravity wave number is 71
L-Start in A = 2873.535461 Bestfitsituation: D:\FITTER\spek\arb\2872_6e.bf L-Fluores. in A= 1.0
Güte = 10.2638 Skalierung = 0.5555
I = 7/2, Jo = 3, Ju = 4, L-Luft = 2872.632 A Ao = 2441.88, Bo = -64.33, Au = 1007.00, Bu = 939.00 (in MHz)
0.9 0.8 0.7
normierte Intensität
0.6 0.5 0.4 0.3 0.2 0.1 0
0
5000
10000
S 15000 20000 Offsetfrequenz in MHz
25000
30000
35000
Figure 28: The fitting of the previously unclassified line 2872.632Å. The Signal to noise ratio was not very good 34801.069 cm−1 . The level list of Ta II was searched for a lower level with Au = 1065 MHz, and indeed one of the odd levels, 42122o4 had Ao = 1007 MHz. Assuming this as lower level of the transition, the new level was found by adding the center of gravity wave number to it. The new level has the energy 76923.95 cm−1 . More accurate values of hyperfine constants of new level were found by fixing hyperfine constants of lower level 42122o4 . The best fit is shown in the fig. 28. The new level was introduced in the level list of Ta II. Using the classification program a list of possible transitions from this level was generated. It could be seen that two unclassified lines were in the combination list of this new level. These two lines are 2943.394 Å and 3175.984 Å. The simulations of the hyperfine structure of both lines, and the corresponding predicted hyperfine structure in the FT spectra were identical, which is a sufficient proof of the existence of the new level. The simulation of these two line and their overlap with the hyperfine structure from FT spectra are shown in the figs. 29, 30. 8.1.5
The level 777275
The line 3597.404Å was an unclassified line of Ta II and has partially resolved structure in FT spectra but it was a blend with another
72
N e w le v e l S t e p s t o n e w le v e l d e t e r m in a t i o n
1 . D e t e r m in a t io n o f J , A , B o f lo w e r a n d U p p e r le v e l f o r m s im u la t i o n o f h y p e r f i n e s t r u c t u r e 2 . I d e n t if ic a t i o n o f lo w e r b y h y p e r f in e c o n s t a n t s 3 . F i n d i n g e n e r g y o f n e w le v e l b y a d d in g w a v e n u m b e r s o f lo w e r a n d u n c l a s s if ie d li n e 4 . T e s t if t h e n e w le v e l e x p l a in a t le a s t o n e m o r e u n c la s s if ie d lin e
U n c la s s if ie d lin e le a d in g t o d is c o v e r y o f n e w le v e l
L o w e r le v e l i d e n t i f i e d b y A , B v a lu e s
A n o t h e r k n o w n le v e l
Figure 29: The simulation of the hyperfine structure of the 2943.394Å overlapping with the hyperfine structure of the same line from FT spectra
Figure 30: The simulation of the hyperfine structure of the 3175.984Å overlapping with the hyperfine structure of the same line from FT spectra
73
Figure 31: The best fit of the line 3597.404 Å, this line is a blend of two Ta II lines. classified Ta II line, 3597.358 Å. In order to fit this line a blend situation fit was tried. One of the lines in the blend was the decay from 722251 to 44434o0 . The hyperfine constants of these levels were fixed, the hyperfine constants of the unclassified line were varied and the best fit was obtained. On the basis of this result the lower level of the unclassified line was identified from the level list and its wave number was added to the center of gravity wave number of the unclassified line. A new level, 77727.755 cm−1 was discovered. This level explains additionally four unclassified lines, these lines are given in the table 7.5. The simulation of these lines were used to confirm the hyperfine constants of the new level and then an average value of the hyperfine constants was calculated. 8.1.6
The level 789665
The level 789665 was discovered from the fitting of the unclassified Ta II line 3278.148 Å. The line had a good signal to noise ratio, a relative intensity of 46, and its hf structure was resolved sufficiently enough, so the best fit could be obtained. Various combinations of J values were tried, finally the best fit with Jo =5 and Ju = 4 was obtained. The lower level’s hyperfine constants were determined as Au =750 MHz and Bu = 1171 MHz. One of the levels in the level list of Ta II had Au =713 MHz. The wave number of this level, 48470.391
74
Figure 32: The discovery of the level 789665 through the best fit of the line 3278.146 Å cm−1 , and the center of gravity wave number, 30496.24 cm−1 , of the line 3278.148 Å were added to get the wave number of the new upper level, 78966.63 cm−1 . The new level explained some unclassified lines. Up till now this is the highest lying level of Ta II. The hyperfine constants of this level are also computed from others lines, which gave an average value shown in the table 7.4. The decay lines from this level are shown in the list of newly classified lines of Ta II. The fig. 32 shows the best fit of the line 3278.148 Å. 8.1.7
The level 65329o1
The hyperfine structure of the line 2992.692Å in the FT spectra indicated that it might be 1-0 or 0-1 transition. Then the fitting was done with J0 =1 and Ju =0. The best fit gave Ao / B0 = 1338 / -280 MHz for upper level and obviously Au /Bu = 0/ 0 for lower level. The center of gravity wave number 33405.043 cm−1 , and the quality of fit 36.48. The fig. 33 shows the best fit. To find new upper levels all levels with A/B = 0/0 were tried and several new hypothetical upper levels were calculated. The level 65329.043 cm−1 was obtained by adding the center of gravity wave number 33405.043 cm−1 and lower level wave number 31924 cm−1 . This new level was introduced by Wyrat [32]. The list of possible
75
Figure 33: The best fit of the line 2992.692 Å combinations from this new level showed a line 2862.566 which was a bit away from an unclassified line 2862.494Å. Fortunately this line had good signal to noise ratio and could be fitted well. I tried to get the best fit for this line. The best fit is shown below. The fitting of the line 2862.494Å gave Ao /Bo = 1334/-401MHz for upper level and Au / Bu = -231 / -188MHz, for lower level and a center of gravity wave number = 34924.373 cm−1 . The A / B values of the upper level were similar, within some uncertainty, with those obtained in fitting 2992.692Å. This made sure that both lines were the result of a decay from the same level 65329. After subtracting the center of gravity wave number 34924.373 cm−1 from the wave number of the new upper level, I got 30404.67 cm−1 , Kiess [?] has already given a level 30405.61 cm−1 . There was a difference of almost 1 cm−1 . To calculated a better wavenumber of the this new level I took the Kiess level as lower level (30405.61 cm−1 ) and added the center of gravity wave number of the line 2862.494 Å which was 34924.373 cm−1 . I got the new level at 65329.983 cm−1 . To get exact value of the lower level of the decay line 2992.692Å from this level, the center of gravity wave number 33405.043 cm−1 was subtracted from 65329.983 cm−1 . The exact value of the lower level turned out to be 31924.94 cm−1 . The average values of hf constants of the new level 65329.983 cm−1 are A / B = 1336 (2) / -350 (70)MHz. 76
Figure 34: The best fit of the line 2862.494Å 8.1.8
The new line 2948.679Å
During the fitting of this line it appeared that the known and unclassified line 2968.686 Å was blend of two lines, thus the line was fitted as a blend. One of the lines was assumed to be the decay from the upper level 750483 to the lower level 41144o2 , the hyperfine constants of these levels were fixed when fitting. The other line was the transition from 66930o1 , to the lower level 330272 . The hyperfine constants of the upper level were not known so they were varied in the fitting process. A quality of fit 46.99 was obtained in the fitting of this unclassified line. The output file generated by the fitter program yielded the center of gravity wave numbers of both lines in the blend. The two lines have center of gravity wave lengths 2948.679 Å and 2948.69 Å. Hence the 2948.679Å is a new line. 8.1.9
The new line 3093.006 Å
The line 3093.082Å was already known but unclassified. In the determination of the hyperfine constants of the level 68936o2 , it was found that this level has a decay possibility to the lower level 366143 , the wavelength of the corresponding line was close to 3093.082Å. There was another possible decay from the upper level 789665 to the lower level 46645o4 , but it was hard to decide which decay classifies this line. The hyperfine structures of both lines were not exactly matching with line structure in FT spectra. It looked that these two lines are over-
77
Figure 35: The new line 2948.679 Å of Ta II, which blends with another Ta II line 2948.69 Å lapping their hyperfine structures, the width of the decay line from 789665 was short (0.397 cm−1 ) and that from 68936o2 , was large (2.031 cm−1 ). The unclassified line did not look so wide in the FT spectrum. Because one classified Ta I line is also blending with the decay line from 68936o2 , the other side of the Ta I line in the FT spectrum has two small peaks (see fig. 36 ) which were not classified and are not given in any data base of Ta lines, so it looked promising that the line with largest splitting is blending with one Ta I and another line of Ta II. Since almost all hyperfine constants were known, all the hyperfine constants were kept fixed and best fit of 3 blending lines was obtained. The best fit gave a quality of 49.22. The fig. 37 shows the result of the best fit. The splitting of the line is more than 60000 MHz which is almost 2.031 cm−1 . It also shows the two other lines. Ta I line had very good signal to noise ratio and a relative intensity of 275. The output file gave center of gravity wave numbers and wavelengths of all three lines, one was already classified Ta I line, the second (3093.08 cm−1 ) was an unclassified line which is now classified as decay form 789665 , and the third line which is a new line (3093.006 cm−1 ) and is classified as the decay from the level 68936o2 .
78
Figure 36: The hfs of three blended lines extracted from Fourier transform spectra. The line 3093.006 Å has large splitting and it overlaps to the hfs of two lines, one Ta I and other Ta II line.
Figure 37: The best fit of the three overlapping lines. The lines 3093.006 Å and 3093.071 Å are Ta II lines and 3092.987 Å is a Ta I line.
79
2995.608
2995.575 2995.557
2995.459
Figure 38: The best fit of three overlapping lines which led to the classification of the line 2955.608 Å 8.1.10
The classification of the line 2955.608 Å
The line 2955.575 Å and 2955.459 Å are classified lines of Ta II and Ta I respectively, both have well resolved hyperfine structure in FT spectrum. The line 2955.608 Å was a new and unclassified line of Ta II, it has a single peak and is adjacent to the classified line of Ta I. Our classification program did not show any suggestion for this line and it was thought some unknown level might be involved in the transition. Looking at the hyperfine structure of the three lineblend it looked that the line 2955.609Å might have an extended hyperfine structure rather than a single peak structure. The line 2955.557Å was then inserted in our data base, and the classification program showed one suggestion for this line, the hyperfine constants of both levels were known. The best fit for three blended lines was accomplished with a quality of more than 13. The excellent fitting justified the assumption that the lines are blending. So the unclassified line 2955.608Å is now classified as the transition from 70439o3 to 366143 . The center of gravity wavelength is 2955.557 Å. The fig. 38 shows the best fit of the three lines.
80
Table 7.4: New levels of Ta II. Angular momentum 1 3 2 3 4 5 2 5
Parity Odd Even Even Even Even Even Even Even
Energy cm-1 65329.983(.233) 75048.391(.200) 75294.428(.200) 76923.950(.200) 77196.890(.200) 77727.250(.200) 78657.350(.200) 78966.631(.200)
A MHz 1336(2) 740(30) -30(20) 2436(15) 410(30) -115(10) 340(20) 335(10)
B MHz -350(70) -1200(500) -1500(200) -450(300) -1100(200) -750(200) -500(300) -50(600)
Table 7.5: The classification of Ta II lines via simulation. Wavelength In Angstrom 2555.650 2669.199 2683.224 2770.333 2804.811 2828.576 2872.636 2911.158 2943.394 2955.786 2970.686 2984.736 2991.038 3004.555 3036.282 3020.112 3039.072 3065.502 3091.741 3101.849 3141.191 3148.692 3155.084 3174.871 3175.984 3210.706 3215.723 3216.368 3220.388 3235.135 3278.148 3284.823
Signal to noise ratio 3 6 4 4 8 37 13 4 8 10 23 7 10 30 20 4 13 53 13 17 4 5 34 26 11 314 17 7 6 83 46 6
Even parity Jo 2 4 5 3 4 5 3 5 3 2 4 3 2 3 3 5 3 4 2 2 2 2 5 2 3 5 2 5 3 4 5 2
Even parity Energy/ cm-1 75294.428 77196.890 78966.631 75048.391 77196.890 39758.765 76923.950 78966.631 76923.950 78657.350 77196.890 75048.391 78657.350 75048.391 75048.391 77727.750 75048.391 77196.890 75294.428 75294.428 78657.350 75294.428 78966.631 78657.350 76923.95 78966.631 75294.428 77727.750 75048.391 77196.890 78966.631 78657.350
81
Odd parity Ju 2 4 5 3 3 4 4 4 3 3 3 3 1 4 4 4 2 5 3 2 3 3 4 3 2 4 1 4 4 5 4 2
Odd parity Energy/ cm-1 36177.194 39743.630 41708.992 38962.375 41554.386 4415.764 42122.933 44626.051 42959.625 44835.230 43544.489 41554.386 45233.850 41755.291 42122.933 44626.051 42153.286 44585.330 42959.625 43064.948 46831.390 43544.489 47280.883 47169.138 45446.776 47829.770 44206.320 46645.810 44005.221 46295.070 48470.391 48223.110
Wavelength In Angstrom 3286.118 3308.868 3325.651 3329.292 3330.999 3341.730 3342.252 3403.691 3480.107 3488.054 3512.327 3514.710 3519.783 3527.234 3542.963 3552.437 3597.404 3600.308 3609.276 3614.206 3630.879 3637.085 3639.429 3667.451 3672.320 3673.674 3769.923 3692.882 3695.331 3726.762 3881.149 3897.86 3905.108 3961.681 4012.043 4037.098 4127.574 4181.593 4437.763 4605.981
Signal to noise ratio 40 12 5 9 300 46 69 30 14 10 10 56 64 8 104 120 15 80 62 42 37 22 20 93 4 23 30 10 15 22 6 13 18 8 14 4 6 14 3 8
Even parity Jo 3 3 2 4 5 4 5 4 4 3 2 2 3 2 3 4 5 3 2 4 3 5 2 4 3 5 2 2 5 3 2 2 5 5 5 2 2 5 5 3
Even parity Energy/ cm-1 75048.391 75048.391 75294.450 77196.890 39758.765 77196.890 78966.631 77196.890 77196.890 75048.391 75294.428 75294.428 75048.391 78657.350 75048.391 77196.890 77727.750 75048.391 75294.428 77196.890 75048.391 78966.631 75294.428 77196.89 75048.391 78966.631 75924.428 75294.428 39758.765 75048.391 75294.428 75294.450 39758.765 77727.750 78966.631 75294.428 75294.428 39758.765 39758.765 75048.391
82
Odd parity Ju 4 3 1 3 4 4 5 3 4 2 3 2 4 3 3 5 4 4 1 3 2 4 3 4 3 5 1 2 4 2 3 3 5 4 5 1 3 4 4 4
Odd parity Energy/ cm-1 44626.051 44835.230 45233.850 47169.138 9746.375 47280.883 49055.180 47825.449 48470.391 46387.280 46831.390 46850.690 46645.810 50314.430 46831.390 49055.180 49937.771 47280.883 47596.020 49536.203 47514.610 51479.860 47825.449 49937.771 47825.449 51753.700 48776.360 48223.110 12705.402 48223.110 49536.203 49646.600 14158.510 52492.980 54048.810 50531.170 51073.880 15851.120 17231.220 53343.560
Table 7.6: The hyperfine constants of Even levels of Ta II.
Eriksson et al.
J 1 2 3 2 4 1 2 5 3 2 4 1 3 2 3 4 5 4 1 2 5 4 2 3 1 3 4 2 4 1 6 5 4 2 3 2 4 2 1 3 5
Energy / cm-1 0 1031.418 2642.306 3180.142 4415.764 5330.82 5657.949 6186.72 6831.441 9690.489 9746.375 10713.3 11767.262 11875.518 12435.85 12705.402 12830.94 12966.02 13475.4 13560.282 14158.51 14205.53 14494.873 14581.064 14627.75 15726.107 15851.12 17168.5 17231.22 17375.11 17982 18186.04 18493.67 18500.6 18553.83 22928.62 23082.7 23294.7 23406.14 23620.36 24226.2
Zilio and Pickering
D. Messnarz and This work Guthohrlein A in A in MHz B in MHz A in MHz B in MHz MHz B in MHz A in MHz B in MHz -2348.1 -360 -2346 -660 -2348(8) -542(20) 1065.3 150 1032 450 573.3 300 1030(15) -555(70) 1500 -1200 1365 -750 1361(10) -598(90) 573 1470 591 390 581(1) 492(30) 1422 -1320 1416 -750 1408(10) -737(185) 1030.5 450 975 360 996(18) 406(110) 1503 -870 1449 -690 1452(6) -987(250) 1656 -1260 1455 1410 1447(6) -1400(140) 489 2400 354 1350 370(9) 1000(180) 1350 -1410 1248 -810 1249.8 -1182 1251(11) -1194(100) 180 0 303 1680 303(10) 1680(300) 5045.7 -90 4961(10) 212(90) -615 -540 -588 750 -586.8 729 -584(4) 740(90) 1842 -2700 1962 1650 1923.3 -1620 1919(3) -1695(10) 2010 2100 1932 1970(7) 1888(200) -525 -1590 -510 3062 -504.9 2133 -505(6) 2060(260) 135(30) 230(100) 1500 1486(20) 2399(200) -390 2100 -480.3 726 -484(4) 741(20) 660 540 766.5 -1095 766(2) -1174(10) 1410 2850 1478(6) 2270(480) -160(20) -1100(200) -270 0 -270 450 -242(6) 610(80) -579 420 -690 -696(7) -451(40) -330 210 1650 -600 -1713(5) -514(50) -1278 690 -90 2400 -128.7 -579 -130(30) -405(100) -600 0 -660 990 -619.5 645 -617(4) 558(180) 1710 0 1590 -300 1515.9 -423 1514(30) -421(40) -960 900 -330(14) 250(500) -1410 1800 -2166(20) -772(30) 852 600 1300(15) 2000(1000) 0 0 744(10) -730(200) -210 -330 -460.2 -510 -460(10) -650(100) -1260 0 -1398.9 1866 -1401(5) 1974(100) 2160 1500 1956.3 -846 1955(15) -784(18) -711.6 516 -775(20) 576(100) -360 3600 250(30) 475(100) 420 1800 317.1 -1002 456(10) 1080(400) 3840.6 -534 3822(8) -800(30) 630(10) 350(30) -750 0 130(10) 4000(200)
83
Eriksson et al.
J 4
D. Messnarz and This work Guthohrlein Energy / A in cm-1 A in MHz B in MHz A in MHz B in MHz MHz B in MHz A in MHz B in MHz 24432.78 755.4 2706 702(1) 3426(300)
3 4 5 6 1 3 2 4 2 5 3 4 3 2 4 3 2 3 4 3 1 2
24869.61 25385.49 25413.95 26010.7 26234.6 26928.09 28044.14 28165.4 29843.58 30349.93 30624.09 31267.1 31531.7 34879 35151.35 36614 37274.31 40369.15 40904.37 43606.36 72225.2 72786.79
1866
Zilio and Pickering
0
1830
0
1530
0
84
306.3
1809
-12
411
765(20) 2600(900) 651(50) -1651(600) 300(20) 450(500) 287(20) 1870(50) -12(50)
400(100)
245(20) 441(50) 85(20) 767(10) -750(10) 260(40) 370(30) 265 (40) 1940(40) -30(20) 250(100) -13(10) 300(100) 430(2) 1344(15)
563(100) 1128(600) -1100(200) -200(500) -750(100) 0(500) 1080(300) -1575(500) 1500(500) -960(100) 575(400) -728(80) -1090(350)
Table 7.7: The hyperfine constants of odd levels of Ta II. Eriksson et al.
J
Zilio and Pickering
D. Messnarz and Guthohrlein
Energy/ cm-1 A in MHz B in MHz A in MHz B in MHz A in MHz
2
29256.897
3
32318.44
1
900
-549.3
This work
B in MHz
A in MHz
B in MHz
1011
-547(8)
976(70)
531
1403(6)
540(200)
-351 -1924(1)
-357(10)
-450
450
-546 1410
420
1404
33706.39
-1923
-330
-1911
-420
-1925.4
2
33715.32
660
-1050
663
-1500
3
36113.09
1536
1560
1540.2
2
36177.194
471
2370
462
3
36763.759
1290
-600
1263
-1350
1261.8
-1356 1261(10)
1
36987.724
2225.1
-60
2220
27
2216.4
-75 2214(10)
-73(10)
2
37230.738
1251
120
1242
1254(4)
-315(30)
1119
652(8)
-1315(200)
1540(1)
1057(40)
460(6)
1800(200) -1299(200)
3
38270.63
2
38515.698
600
720
591
90
1
38535.375
-1617
-330
-1617
-360
3
38962.375
1116
-180
1074
-360
3
39295.954
1104
1380
969
2250
4
39743.63
1068
-1920
951
-1050
2
40233.632
1920
-1020
1884
-900
1878.3
1
40304.775
732
-960
612
-750
584.4
2
41144.93
699
360
681
1
41355.06
1989
0
3
41554.386
750
840
738
5
41708.992
918
-1140
912
450
4
41775.291
960
2070
882
4
42122.933
1113
1680
1017
2
42153.286
60
540
12
3
42959.625
996
-120
975
2
43064.9948
1242
-420
1023
0
3
43544.489
231
930
183
960
184(5)
720(40)
1
43553.87
2445
-300
2487
-300
2486(2)
-257(50)
4
44005.221
1110
-1290
930
300
914(4)
210(90)
1
44206.32
921
-270
1200
-1500
880(17)
-954(20)
2
44259.2
1275
-810
1260
-1500
1246(8)
-790(95)
3
44430.433
270
0
690
3080
685(4)
954(80)
5
44585.29
1230
0
1026
390
1006(25)
903(100)
4
44626.051
1080
-690
1080
1800
1079(15)
461(130)
3
44835.23
423
480
390
0
304(4)
1321(40)
1
45233.85
1263.9
-540
1260
-810
1288(3)
-812(100)
85
588.3 -1624.2 974.7
-6
-347(10)
420(30)
576(23)
125(150)
-393 -1622(4)
-433(30)
1069(5)
-517(150)
975(6)
2000(100)
950 (9)
-1140(90)
1965
-636 1878(20)
-873(150)
-780
584(10)
-700(70)
689(10)
72(80)
3377(11)
265(100)
741.6
450
742(5)
454(200)
921.6
510
914(5)
434(0)
1950
886(5)
1853(60)
1740
1007(8)
939(250)
750
12(4)
372(100)
980(10)
-850(100)
1042(5)
-400(80)
1041
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Eriksson et al.
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Zilio and Pickering
D. Messnarz and Guthohrlein
Energy/ cm-1 A in MHz B in MHz A in MHz B in MHz A in MHz
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This work A in MHz
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944(5)
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2
45446.776
990
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1
46174.63
1680
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1680
1689(16)
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5
46295.07
720
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660
240
674(3)
-190(100)
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46387.28
1968
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375
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46831.39
324
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1830
105
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370(7)
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819
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336(100)
1
47596.02
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445(50)
3
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942
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910(90)
530(300)
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2700
144
3081
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3000(150)
4
48162.1
990
3750
1020(12)
3715(200)
226.2
1128
-201
306(11)
-459(300)
-1830 1111(40)
-1875(90)
115(1)
1070(100)
2
48223.11
1266
0
1113(30)
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4
48470.391
984
210
750
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710(15)
1900(300)
2
48666.55
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1860
285(20)
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431(100)
3
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1320
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1290
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1272(150)
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5
49055.18
567
240
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210
430(20)
375(200)
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49080.44
78
390
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750
-41(20)
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49536.203
858
-2190
745(20)
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49592.9
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2910
3
49646.6
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170(20)
500(400)
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387
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1034(300)
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621(10)
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1278
0
705(10)
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51753.7
375
2580
185(10)
2244(200)
3
52121.22
30
-840
570(3)
2761(200)
1
52155.76
-390
-1230
258(50)
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4
52492.98
900
1920
937(20)
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3
52580.41
1353
-720
1340(10)
1000(200)
1
52824.53
-960
-990
-1100(10)
-250(200)
6
52846.28
470(10)
3377(2000)
2
53010.95
440(10)
-200(100)
540
1260
210
330
-150
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Zilio and Pickering
D. Messnarz and Guthohrlein
Energy/ cm-1 A in MHz B in MHz A in MHz B in MHz A in MHz
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5
53234.65
593(10)
1853(200)
2
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0(200)
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516
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600(200)
5
54048.81
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54648.81
261
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56987.88
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564
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565(100)
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253(100)
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735(100)
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Energy/ cm
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-1
Zilio and Pickering
D. Messnarz and Guthohrlein
A in MHz B in MHz A in MHz B in MHz A in MHz
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347(100)
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720(20)
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65495.18
330(10)
300(100)
3
65657.89
185(100)
-402(500)
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66469.26
340(40)
290(200)
5
66610.27
-192(10)
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1
66930.35
657(10)
916(100)
5
66985.23
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850(300)
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67499.21
1600(100)
100(100)
3
67777
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68299.8
920(10)
1940(200)
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68313.77
590(10)
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712(100)
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70064.31
520(20)
136(50)
3
70439.52
378(20)
-1190(100)
360
510
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B in MHz
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4530
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88
8.2
Classification of Ta I lines, determination of new levels of Tantalum I levels
In this work, twenty five new levels of Ta I were discovered. More than 500 new and known unclassified lines were classified via simulation of the hyperfine strcutures, direct laser transition, and fluorescence detection. As an example the discoveries of few new levels of Ta I are discussed here. 8.2.1
The level 445733/2
The line 3676.890Å was a known but unclassified, and surely new level was hidden. The relative intensity of this line in the FT spectrum was 210, it had a well resolved hyperfine structure indicated that levels with lower J values are involved in the transition. The best fit with a quality greater than 20 was obtained with the combination Jo =1.5 and Ju =1.5. The best fit is shown in the fig. 39.
Figure 39: The best fit of the line 3676.89Å, through which the level 44573.8393/2 was discovered. The level 17384o3/2 was identified as the lower level of the transition from the hyperfine constants determined by the fit procedure. The center of gravity wave number of the line was added to the lower level to get a hypothetical upper level, which was 44573.8393/2 . After introducing this level in the level list of Ta I, the list of possible transitions from this level showed that we could classify another un-
89
Figure 40: The best fit of the line 3834.877Å, a decay from the level 44573.8393/2 . classified line, 3834.878 Å . The best fit of this line was also obtained. The fig. 40 shows the fit results. The hyperfine constants obtained when fitting this second line were similar to the values belonging to the levels of the suggested transition. We then further tried to excite this new level. The line 4271.162Å was another decay line from our hypothetical level. By tuning the laser in the neighborhood of this line we were able to see both lines 3676.89 Å and 3834.878 Å, as fluorescence lines. This confirmed our hypothetical level to be really existing. 8.2.2
The level 50256o11/2
The level 50256o11/2 was discovered when fitting the unclassified line 3738.460Å. This line has relative intensities 2 and 21 in two different FT spectra. In one of the FT spectra the hyperfine structure was well resolved, every peak was standing alone. Various combinations of upper and lower J values were tried, finally the best fit was obtained with the combination Jo =11/2 and Ju =13/2. The magnetic hyperfine constant of the lower level was found to be 941 MHz. One of the levels in the Ta I level list has Au =965 MHz. The wave number of the center of gravity of the line was added to the wave number of the lower level 23514.92313/2 . The new hypothetical odd parity level was found to have the energy 50256.303 90
Figure 41: The best fit of the line 3738.460 Å which is a decay of new level 50256o11/2 .
91
Figure 42: The best fit of the line 2844.751 Å cm−1 . Thus we proceed if the transition list from this new level would explain other unclassified lines. It turned out that three lines in the combination list had similar hyperfine structures in the simulation program and the FT spectra. This confirmed the new level. One of the lines, 2844.751 Å, had a relative intensity of 30. The best fit for this line was obtained by fixing the hyperfine constants of the lower level and the hyperfine constants of the new level were found again. The magnetic hyperfine constants of the upper level were approximately the same as obtained in the fitting of the line 3738.46Å. The best fit is shown in the fig. 42. The line 3794.93Å also had partially resolved hyperfine structure in the FT spectra. The simulated hyperfine structure and the its hyperfine structure from FT spectra are shown in the fig. 43. 8.2.3
The level 514231/2
The line 3858.229A was an unclassified line of Ta I with the relative intensity of 62. Such a high intensity usually gives very good quality of fit. The hyperfine structure had small splitting with just two peaks, such a hyperfine structure usually belong to small J values. With Jo =Ju =1/2 the fitting was excellent with a fit quality of 47. The lower level of the transition was identified easily by the Au value obtained from the fitting. The fit was repeated by fixing the
92
Figure 43: Simulation of the line 3794.93 Å
Figure 44: The best fit of the line 3858.229 Å. The level 514231/2 was discovered from the hyperfine constants obtained from the best fit.
93
Figure 45: the best fit of the line 3380.975 Å hyperfine constants of the lower level to get more accurate values of the hyperfine constants of the upper level. The upper level has hyperfine constants Ao =-756 MHz and Bu =0. This level also explains one other unclassified line, 3380.975 Å. It also had suitable signal to noise ratio, the best fit for this line was also obtained by fixing the hyperfine constant of the lower level. The hyperfine constant Ao was again found to be close to -756 MHz. Both the lines explained by this level are new lines discovered by N. Jaritz. The best fit of the line 3380.975 Å is shown in the fig. 45. 8.2.4
The level 536413/2
The line 3723.807Å was a new unclassified line of Ta I marked by N. Jaritz in her work, it had a relative intensity of 3 in one FT Spectrum, in other FT spectrum it was 33. Since it was an unclassified line, and up to now an unknown level was involved in the transition. The fit with Jo =3/2 and Ju =5/2 was the best with a quality of 12. The best fit gave the value of 1032 MHz for Au . The search of a lower level with Au in the neighborhood of 1032 MHz led to the level 26794o5/2 which has Au =1035 MHz and Bu =712 MHz. Then these values of hyperfine constants were used as fixed parameters and the fitting was repeated to obtain more reliable values for the hyperfine constants of the new level. The hyperfine constants 94
Figure 46: The best fit of the line 3723.807 Å. for the new level were found to be Ao =1315 MHz and Bo = -48 MHz. The energy of the new level was found by adding the wave numbers of the lower level and the center of gravity wavenumber of the line. The new level, with the energy 53641.382 cm−1 , was introduced in the level list of the Ta I. Then the list of the possible combinations of the new level was generated by the classification program. Every possible line was investigated by comparing its suggested hyperfine pattern in the graphic field of the classification program and the corresponding hyperfine pattern in the FT spectra. One of the lines 3432.523 Å had a good signal to noise ratio but it portion of the structure was disturbed due to blending with the line 3432.614Å. However, most of the hyperfine structure was well resolved. This resolved portion was similar to the hyperfine structure in the graphic field. To make further sure the classification the peak position was compared and also the hyperfine structures were overlapped. The overlapping was very good. The discovery of this level explains four further unclassified lines of Ta I. The new level also explains another line, 3733.20 Å. This line is a new line of Ta I and it is blending with the classified line 3733.713Å of Ta I.
95
Figure 47: Simulation of the line 3432.614 Å 8.2.5
The level 545287/2
The line 3383.5 Å has the relative intensity of 23 in its FT spectrum. The hyperfine structure is a single peak with two small wings on each side. It looked initially that it is a blend of two lines, but first I tried to fit the structure by assuming it as single hyperfine pattern. With a combination of Jo = Ju =7/2 the best fit with a quality of 20 was obtained. A hypothetical level was found after identification of the lower level via the hyperfine constants of the lower level from the best fit. The addition of the wavenumbers gave 54528 cm−1 .To confirm the new level the list of possible combination from this level was generated by the classification program. It was found that the unclassified lines 3895.02 Å and 3077.8 Å could be explained by this level. By further investigation of the combination list it was found that it explains two further unclassified lines(3604.64 Å and 3787.63 Å) which were recorded on a photographic plate. The center of gravity wavelengths of these lines were not accurately known. The new center of gravity wavelengths are 3604.69 Å and 3787.585 Å. In addition to the explanation of unclassified lines, the new level also explains two new lines, 3492.246 Å and 3969.496 Å, which were discovered in one of the available FT spectrum. The best fit of the line 3383.5Å is shown in the fig. 48. 8.2.6
The level 54616o7/2
The line 3138.29 Å was an unclassified Ta I line. It had a relative intensity of 18 in the FT spectrum. The resolution of the hyperfine structure of the line was good. A simulation of the line with different 96
Figure 48: The best fit of the line 3383.5 Å J combinations was tried. The best simulation was possible with the combination Jo = Ju =7/2. Through the initial simulation Au was found to be 389. The lower level 227617/2 has Au =348. Assuming this level as the lower level of the transition, the new level energy was calculated by the addition of wave numbers of the lower level and the center of gravity of the line. The new level 54616o3/2 showed the unclassified line 3324.579Å as one of its decay scheme. The hyperfine structure displayed in the graphic field was compared with the hyperfine structure of the line in FT spectrum, they were similar in structure. Then the portion of the FT spectrum showing the hyperfine structure of the line is cut using the origin macro and overlapped with the simulated hyperfine structure; the overlapping was good. This confirmed the new level. 8.2.7
The level 56957o13/2
The line 3231.635 Å is a known but unclassified line. This line had in the FT spectrum had a structure which looks like a blend of two or more lines. N. Jaritz and L. Windholz realized that this line is a blend. So they introduced another line 3231.694 Å as a new line of Ta I in the line list. This line was also an unclassified line. A part of the hyperfine structure of this new line had a good signal to noise ratio 97
Figure 49: Simulation of the line 3138.29
Figure 50: Simulation of the line 3324.579 Å
98
Figure 51: The best fit of the line 3231.635, which is a blended line. and good resolution. But some portion of it overlaps the hyperfine structure of the line 3231.635Å. Nevertheless it was possible to get a simulated hyperfine structure of the new line. In fitting procedure the fitting can be done only for a desired range. One has to mention the range of fitting in the finite interval line of the program. The fitting was done only for the well resolved portion of the line. The fit with various J combinations had the same quality of fit. Every fit was investigated and an identification of the lower level was tried. Finally the lower level 26022.739 with even parity and Ju =11/2 was identified as the lower level of the transition. Addition of the center of gravity wave number to the wave number of the lower level gave the energy 56957.329 cm−1 . By looking at the combination list of this level it was revealed that one strong line, 3640.788 Å is given in the combination list. The suggested hyperfine structure and the hyperfine structure in the FT spectrum were in good agreement. The best fit for this line was then obtained, too. This confirmed the hyperfine constants of the new level and also confirmed the new level. One more unclassified line, 2389.152 Å was also explained by the new level. The discovery of this level and it now known hyperfine structure leads to the conclusion that the line 3231.635Å might be the blend of three Ta I lines. The new line may have center of gravity wavelength 3231.608Å.
99
Figure 52: The best fit of the line 3640.788 Å 8.2.8
The level 58562o9/2
The level 58562o9/2 was discovered via the unclassified line 3072.298Å. This line has a well resolved hyperfine structure in the FT spectrum, however, the signal to noise ratio is not very good. I decided to simulate the hyperfine structure of the line. The simulation is shown in the fig. 53. The lower level is identified by the hyperfine constant of the lower level in the simulation procedure. The energy of the upper level was found by adding wave numbers of the center of gravity of the line and of the lower level. The new level has odd parity, Jo =9/2, and the energy is 58562.209 cm−1 . The new level also explains two further unclassified lines. One of the line was also simulated, the simulation is shown in the fig. 54. 8.2.9
The level 507451/2
The level 50745.2541/2 was discovered via fitting the line 3215.8Å. The line 3215.8Å was a new line marked by N. Jaritz and was unclassified. The signal to noise ratio was good enough to obtain a good fit. The best fit with the combination Jo =0.5 Ju =1.5 gave Ao =837 MHZ, Bo =0, Au =643 MHz and Bu =-270 MHz. The lower level was identified from Au and the center of gravity wavenumber of the line was added to it. The new level was found to 100
Figure 53: Simulation of the line 3072.298 Å
Figure 54: Simulation of the line 3439.72 Å
101
Figure 55: The best fit of the line 3215.8 Å have an energy 50745.254 cm−1 . The new level explained two more unclassified lines, 3335.3 Å and 3962.0 Å. These two lines also had good signal to noise ratios, the best fits for them were also obtained, and then the average value of the hyperfine constants of the new level were calculated. Table 7.8: The results of 507451/2 . wave length Jo Ao Å - MHz 3215.8 0.5 837 3335.3 0.5 843 3962.0 0.5 839
the best fits of three lines of the level Bo MHz 0 0 0
DW MHz 1800 1644 1372
Quality 12.1 16.98 9.5
Ju 1.5 1.5 0.5
Au MHz 643 225 89
Bu MHz -270 -250 0
The new level 50745.2541/2 has Ao =840(4) MHz and Bo =0(20) MHz. The discovery of new level also led to the discovery of two new lines of Ta I. The new lines 3649.949Å and 3844.147Å are decays from the new level. The figs. 56 and 57 show the best fit of the lines 3335.3 Å and 3962 Å.
102
Figure 56: The best fit of the line 3335.3 Å
Figure 57: The best fit of the line 3962 Å
103
Table 7.9. New levels of Ta I. Angular Momentum 1.5 4.5 3.5 2.5 1.5 1.5 2.5 2.5 1.5 5.5 2.5 0.5 1.5 2.5 3.5 3.5 3.5 4.5 4.5 6.5 2.5 0.5 4.5 5.5 5.5
Parity EVEN EVEN ODD ODD ODD ODD ODD EVEN ODD ODD ODD EVEN EVEN ODD EVEN ODD EVEN ODD ODD ODD ODD EVEN ODD ODD ODD
Energy cm-1 44573.839(.2) 55938.150(.2) 55260.620(.2) 53172.700(.2) 52842.290(.2) 50313.270(.2) 53236.090(.2) 54199.700(.2) 47650.710(.2) 50256303(.2) 51329.450(.2) 51423.950(.2) 53641.382(.2) 53418.020(.2) 54528.490(.2) 54616.540(.2) 54631.990(.2) 57160.570(.2) 58562.209(.2) 56957.329(.2) 53816.039(.2) 50745.254(.2) 52838.770(.2) 55961.780(.2) 56998.480(.2)
A MHz -1376(10) 1330(15) 620(10) 362(10) 452(10) 1014(15) 490(20) 549(10) 1867(50) 454(10) -60(20) -760(20) 1315(20) 652(10) 556(5) 614(10) 1025(10) 445(10) 340(10) 254(20) 330(20) 840(10) 460(10) 335(10) 220(10)
B MHz -176(50) -550(40) -520(50) -270(50) 327(50) 0(50) 0(100) 128(50) -67(100) 2300(50) -50(50) 0 -47(50) 516(50) -560(40) 404(20) 85(50) 470(40) 1320(50) 4005(500) -220(50) 0 0(50) 800(100) 544(50)
Table 7.10: The classification of Ta I lines via simulation. Wavelength In Angstrom 2434.741 2389.152 2526.664 2603.576 2650.009 2669.594 2793.29 2844.751
Signal to Noise ratio 2 10 9 5 19 32 5 30
Even parity Jo 2.5 6.5 4.5 2.5 5.5 4.5 3.5 5.5
Even parity Energy/ cm-1 9253.453 15114.28 10690.42 9253.453 15114.28 15391.02 17383.173 15114.28
Odd parity Ju 1.5 5.5 5.5 1.5 4.5 4.5 2.5 5.5
Odd parity Energy/ cm-1 50313.27.27 56957.33 50256.3 47650.71 52838.77 52838.77 53172.7 50256.3
3002.05 3057.451 3072.298
2 8
1.5 0.5 5.5
53641.38 20144.81 26022.74
0.5 1.5 4.5
20340.41 52842.29 58562.21
3077.826
-
3.5
54528.49
2.5
22047.45
3105.36 3138.29 3145.316
10 4
1.5 3.5 4.5
21623.02 22761.28 25376.469
1.5 3.5 4.5
53816.04 54616.54 57160.57
104
Wavelength In Angstrom 2434.741 2389.152 2526.664 2603.576 2650.009 2669.594 2793.29 2844.751
Signal to Noise ratio 2 10 9 5 19 32 5 30
Even parity Jo 2.5 6.5 4.5 2.5 5.5 4.5 3.5 5.5
Even parity Energy/ cm-1 9253.453 15114.28 10690.42 9253.453 15114.28 15391.02 17383.173 15114.28
Odd parity Ju 1.5 5.5 5.5 1.5 4.5 4.5 2.5 5.5
Odd parity Energy/ cm-1 50313.27.27 56957.33 50256.3 47650.71 52838.77 52838.77 53172.7 50256.3
3002.05 3057.451 3072.298
2 2 8
1.5 0.5 5.5
53641.38 20144.81 26022.74
0.5 1.5 4.5
20340.41 52842.29 58562.21
3077.826
2
3.5
54528.49
2.5
22047.45
3105.36 3138.29 3145.316 3149.002 3155.139 3162.333 3168.68 3189.105 3202.229 3215.803 3231.694 3232.252 3254.855 3255.831
2 10 4 6 11 2 12 13 4 6 4 10 7 7
1.5 3.5 4.5 1.5 4.5 2.5 2.5 4.5 2.5 0.5 6.5 4.5 2.5 3.5
21623.02 22761.28 25376.469 15903.818 21153.4 21623.018 21623.018 23912.929 21623.018 50745.25 26022.74 55938.15 24545.202 54631.99
1.5 3.5 4.5 1.5 4.5 2.5 2.5 3.5 1.5 1.5 5.5 5.5 3.5 3.5
53816.04 54616.54 57160.57 47650.71 52838.77 53236.09 53172.7 55260.62 52842.29 19657.8 56957.33 25008.899 55260.62 23926.716
3256.007 3268.597 3268.597 3285.68 3287.302
2 6 5 5 10
4.5 4.5 4.5 2.5 3.5
23912.93 25376.469 25375.47 17224.462 22761.279
3.5 4.5 5.5 1.5 2.5
54616.54 57160.57 55961.78 47650.71 53172.7
3287.432 3289.264 3296.133 3302.32 3324.579 3335.385 3338.117 3342.89 3345.293 3365.308 3380.975 3383.511 3393.38 3408.519
2 3 4 4 10 14 5 4 3 3 6 4 15 8
5.5 1.5 1.5 2.5 2.5 0.5 3.5 2.5 4.5 2.5 0.5 3.5 2.5 2.5
22428.65 22842.851 22842.851 54199.7 24546.2 50745.25 21381.052 23512.447 25376.469 21623.018 51423.95 54528.49 54199.7 23512.447
4.5 2.5 2.5 3.5 3.5 3.5 2.5 2.5 3.5 2.5 1.5 3.5 1.5 1.5
52838.77 53236.09 53172.7 23926.716 54616.54 20772.36 51329.45 53417.92 55260.62 51329.45 21855.12 24981.88 24739.06 52842.29
105
Wavelength In Angstrom 3432.523
Signal to Noise ratio 15
Even parity Jo 1.5
Even parity Energy/ cm-1 53641.38
Odd parity Ju 0.5
Odd parity Energy/ cm-1 24516.76
3435.09 3439.72 3455.365 3459.614 3482.642 3495.246 3507.772
4 3 16 4 21 6 7
4.5 5.5 1.5 1.5 3.5 3.5 3.5
21153.4 29498.6 21381.052 24275.91 54631.99 54528.49 24917.996
5.5 4.5 1.5 2.5 4.5 4.5 2.5
50256.3 58562.21 50313.27 53172.7 25926.383 25926.38 53417.92
3512.661 3518.591 3530.302 3533.047 3550.744 3560.59 3572.92 3585.22 3591.293 3593.898
4 21 12 46 2 15 7 12 6 6
1.5 3.5 3.5 2.5 4.5 0.5 2.5 3.5 3.5 2.5
53641.38 54631.99 24917.996 24546.202 55938.15 22236.014 54199.7 29276.388 54631.99 23512.447
2.5 2.5 2.5 1.5 5.5 1.5 2.5 4.5 2.5 2.5
25181.19 26219.648 53236.09 52842.29 27783.084 50313.27 26219.648 57160.57 26794.812 51329.45
3604.69 3612.795 3624.703 3629.414 3632.185 3634.548 3639.25 3640.788
4 4 12 4 20 60 5 8
3.5 3.5 2.5 2.5 3.5 0.5 1.5 5.5
54528.49 54631.99 25655.493 27715.82 25894.22 20144.81 22842.851 29497.6
2.5 3.5 2.5 3.5 2.5 1.5 1.5 6.5
26794.81 26960.484 53236.09 55260.62 53417.92 47650.71 50313.27 56957.33
3649.949 3656.352 3664.849 3676.891 3677.209 3679.279 3716.315 3716.625 3723.811 3733.713 3738.46
3 33 7 40 10 27 4 23 3 5 2
0.5 3.5 3.5 1.5 2.5 4.5 2.5 3.5 1.5 1.5 6.5
50745.25 25894.22 25894.22 44573.84 25655.493 55938.15 27715.82 54631.99 53641.38 53641.38 23514.92
0.5 2.5 2.5 1.5 1.5 4.5 3.5 4.5 2.5 0.5 5.5
23355.42 53236.09 53172.7 17384.69 52842.29 28766.644 54616.54 27733.511 26794.81 26866.05 50256.3
3761.142 3772.784
41 29
1.5 3.5
44573.84 54631.99
2.5 2.5
17993.73 28133.941
3787.585 3794.93 3830.574 3834.878
10 3 4 4
3.5 4.5 0.5 1.5
54528.49 23912.93 26743.95 44573.84
2.5 5.5 1.5 0.5
28133.94 50256.3 52842.29 18504.76
3844.147
13
0.5
50745.25
1.5
24739.06
106
Wavelength In Angstrom 3858.232 3865.084 3893.9 3895.027 3962
Signal to Noise ratio 7 39 19 4 2
Even parity Jo 0.5 3.5 2.5 3.5 0.5
Even parity Energy/ cm-1 51423.95 54631.99 25655.493 54528.49 50745.25
Odd parity Ju 0.5 4.5 2.5 2.5 0.5
Odd parity Energy/ cm-1 25512.66 28766.644 51329.45 28862.04 25512.66
3969.496
12
3.5
54528.49
2.5
29343.5
4012.345 4084.36 4179.965 4247.792 4604.257 4783.73 4939.754
36 7 12 6 10 24 12
1.5 2.5 1.5 2.5 2.5 2.5 1.5
44573.84 54199.7 27412.44 54199.7 54199.7 26752.4 27412.44
1.5 3.5 2.5 1.5 2.5 1.5 1.5
19657.8 29722.985 51329.45 30664.684 32486.755 47650.71 47650.71
5031.292 12450.46 15163.57 17000.16 17838.03 18669.7 18810.74 21886.57
10 7 7 10 17 25 17 20
0.5 3.5 3.5 3.5 4.5 1.5 4.5 4.5
51423.95 50532.56 46245.79 46958.11 51394.01 48461.2 51683.81 51394.01
1.5 4.5 4.5 4.5 5.5 1.5 5.5 5.5
31553.88 58562.21 52838.77 52838.77 56998.48 53816.04 56998.48 55961.78
107
TABLE 7.11: The classification of Ta I lines via direct laser excitation. Excitation wavelength/ Å
Even levels Energy/ cm-1 J
4182.693
44461.65
5
20560.32
7
3777.086, 4527.474
4191.151
6049.433
1
29902.27
1
5017.062
4194.627
6068.956
3
29902.27
1
5017.062
Odd levels Energy/ cm-1 J
Fluorescence wavelengths/ Å
4200.916
12966.02
4
36763.76
3
2797.757
4218.4
15114.28
11
38813.34
9
3011.877, 3434.496
4222.88
20144.81
1
43818.65
3
2646.871, 2935.165, 2953.978, 3068.947, 3121.507
4223.481
13560.28
2
37230.74
2
2685.157, 2761.666
4230.838
18493.67
4
42122.93
4
2532.125, 3087.753
4241.648
18553.83
3
42122.93
4
2532.125
4245.85
41539.61
5
17993.73
5
4470.78, 4568.729, 5078.728
4255.608
21623.02
5
45114.73
7
2787.704, 3147.388
4256.59
21623.02
5
45109.37
5
2429.664
4277.25
17383.17
7
40755.89
7
2580.156, 2717.179, 2845.349
4293.21
17224.46
5
40510.39
5
2596.606, 3415.866
4322.512
10950.26
3
34078.46
3
4147.758, 4712.883
4325.702
22428.65
11
45539.8
9
2868.648
4368.066
22761.28
7
45648.31
7
4379.224
15114.28
11
37942.92
9
2781.366, 3095.39 2942.135, 3540.99, 3668.34, 3888.72,4065.31, 4379.22,5954.44, 6443.90,6585.08,6754.20,7125.622
4388.867
22761.28
7
45539.8
9
4395.33
20646.7
7
43391.72
9
2868.648 2535.521, 2646.774, 3057.088, 3208.629, 3327.92, 3535.375
4398.442
2010.134
5
24739.06
3
6455.826
4440.742
17231.22
4
39743.63
4
2694.518
4443.246
21381.05
3
43880.82
5
2504.453
4444.607
14494.87
2
36987.72
1
3042.066, 3804.91
4450.72
13351.55
9
35813.52
11
3311.141
4461.707
45769.74
5
23363.11
5
3599.202, 3759.559
4464.093
13351.55
9
35746.23
7
2963.319
4467.058
21153.4
9
43533.22
7
2526.453, 2636.895
4467.08
10690.42
9
33070.36
11
3642.049
4473.38
22761.28
7
45109.37
5
2560.678
4534.397
0
3
22047.45
5
6256.681
4574.306
0
3
21855.12
3
6332.911
4812.746
0
3
20772.36
3
6790.253
4989.298
2010.134
5
22047.45
5
6256.681
5037.654
2010.134
5
21855.12
3
6332.911
5328.379
2010.134
5
20772.36
3
6790.256
5596.932
24546.2
5
42408.18
3
2357.3, 2474.6, 2751.0, 3061.9, 3265.3, 3384.93
5613.68
25376.47
9
43185.12
11
2661.334
5635.71
10950.26
3
28689.34
3
5640.177
12965.967
5
30590.98
7
5704.303
21153.4
9
38679.18
7
5733.5
21623.02
5
39059.53
5
3484.618 3497.848,3754.511, 4003.69,4685.256,4786.643, 5023.582, 5446.2 2726.288,3450.403,3571.8443872.889,3947.144, 4294.82,4694.406 2559.4, 2698.3, 2848.5, 3030.2, 3437.3, 3556.5, 3806.6, 5429.4, 5655.02
108
Excitation wavelength/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Fluorescence wavelengths/ Å
5747.65
27715.82
5
45109.37
5
2560.678
5753.691
25376.47
9
42751.8
7
5765.67
23512.45
5
40851.65
5
5836.632
26752.4
5
43880.82
5
2577.3, 2692.3, 2984.3, 3025.1, 3172.8, 3275.9, 3653.8 2573.795,2710.127,3237.846,3376.798,3493.441, 3572.236,4007.232,5199.129,5526.26,5551.29 2387.578, 2504.453, 2643.886, 2925.219, 3573.344, 3772.848, 4302.805, 4908.202, 5099.352, 5485.345, 5485.346
5837.269
21381.05
3
38507.61
1
2596.113, 3081.846, 3477.437, 3503.862, 3742.084
5847.587
25655.36
5
42751.8
7
3275.913, 3345.108
5857.005
23912.93
9
40981.77
7
3150.847, 3361.747
5922.507
22761.28
7
39641.34
7
5993.185
44461.65
5
27780.65
7
6101.568
22428.65
11
38813.34
9
2656.579, 2802.069 3692.125, 3777.086, 3954.073, 4030.49, 4220.129, 4291.735 2868.651, 3011.877, 3434.496, 3554.801, 3926.343, 4218.4, 4268.23, 5503.066
6106.328
29276.39
7
45648.31
7
3095.39
6122.864
44461.65
5
28133.94
5
5185.155, 5993.185
6143.99
22236.01
1
38507.61
1
2596.113, 3081.846, 3477.437, 3503.862, 3742.084
6147.078
29276.39
7
45539.8
9
2504.338,2789.788,3001.81,3105.81,4016.039
6157.999
24275.96
3
40510.39
5
6160.009
44918.66
5
28689.34
3
6162.09
25655.49
5
41879.25
5
6161.879
26022.74
11
42247.07
9
2596.6,2735.4,2902.6,3245.2,3381.9,3415.8 3712.9,3957.5,4104.2,4140.2,4209.1,4334.6,4371.1, 4435.6,4637.1,4835.3,5387.9,5453.2 2507.452,2636.671,3107.207,3133.551,3372.34, 3445.704,5443.091 2611.336 ,3072.086 , 3331.0 , 3684.5 , 3722.4 , 4628.2 ,4739.4 ,5044.4 ,5130.4 ,5452.7,5769 , 5925.8
6163.07
9705.35
7
25926.38
9
4551.95
6180.065
26575.22
7
42751.8
7
2577.3, 2692.3, 2984.3, 3025.1, 3172.8
6184.489
27715.82
5
43880.82
5
6194.438
15391.02
9
31530.05
9
6194.71
27412.44
3
43550.8
5
2504.453, 2643.886, 3063.103 3626.607, 3858.581, 4580.675, 5181.164, 5499.474, 6090.016 2295.4,2406.5,2525.3,2667.1,2953.7,2977.5,3066.5, 3094.3,3258,3616,3797.3,3820.4,4364.8,4509.3. 4827.7,4989,5260.4,5889.1
6200.305
25894.22
7
42018
7
2746.678
6204.09
17383.17
7
33497.15
9
3385.046, 3586.291
6212.444
26752.4
5
42844.67
5
2976.1
6212.503
24918
7
41010.12
5
3148.033
6216.334
41594.85
3
25512.66
1
6217.02
21381.05
3
37461.48
1
4459.763 2668.616,3182.569,3184.549,3608.759, 3637.225,3770.906,3894.596,4637.426
6256.681
6068.956
3
22047.45
5
6258.734
17224.46
5
33197.72
7
6262.27
24546.2
5
40510.39
5
6266.395
23514.92
13
39468.66
11
6274.285
24918
7
40851.65
5
6280.505
22761.28
7
38679.18
7
2953.56, 4152.058, 5458.41 2447.1,2573.7,2710.1,2874.1,3163.8,3209.7,3237.8, 3343.3,3376.4,3493.4,4231.2,5551.29,6131.2 2879.734, 3024.102,3397.413,3571.844, 3872.889, 3947.144,4294.82,4694.406,5861.368
6281.388
42501.64
5
26585.98
7
4686.033, 4887.61, 5382.106
6303.113
26743.95
1
42604.76
1
2346.434, 3063.875, 3244.488, 3744.12
4534.397, 4989.29 3205.478,3419.717,3625.229,4175.185,4441.75, 4553.68,5037.734 2467.7,2596.6,2735.4,2902.6,3245.2,3381.9,3415.8 3535.6,3616.3,4062.7,4322.6,5032.8,5226.1,5293.5, 5658.5.5881.4
109
Excitation wavelength/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
6313.388
27715.82
5
43550.8
5
Fluorescence wavelengths/ Å 2295.4,2406.5,2525.3,2667.1,2914.8,3094.3,3258,3616, 3797.3,3820.4,4364.8,4989,5260.4,5586.5,5889.1
6330.113
24546.2
5
40339.33
3
2478.22, 2608.19
6332.911
6068.956
3
21855.12
3
6345.592
27412.44
3
43167.09
3
4574.306, 5037.654 2315.868, 2684.756, 2947.805, 2992.414, 3011.967, 3103.065, 3299.26, 3853.57
6345.987
9759.017
1
25512.66
1
3918.515
6348.338
25894.22
7
41641.97
9
2653.274, 2775.35
6400.566
26022.74
11
41641.97
9
6411.587
24918
7
40510.39
5
6417.9
29116.26
9
44693.41
7
2653.274 2596.6,2735.4,2902.6,3245.2,3381.9,3415.83535.6, 3616.3,4062.7,4322.6,5032.8,5226.1 2342.12,2454.48,2558.59,2820.84,2857.27,2940.05, 2988.69,3079.95,3141.03,3189.706,3411.71,4246.88, 4719.9,4962.07,5055.37
6422.825
37420.29
1
21855.12
3
5285.185
6434.544
9975.837
3
25512.66
1
3918.515
6439.77
15903.82
3
31428.09
5
3180.947, 3398.308, 3640.072, 3942.238, 4602.179
6443.904
22428.65
11
37942.92
9
2942.135, 3092.992
6444.595
20646.7
7
36159.29
7
4178.66
6445.869
23912.93
9
39422.45
9
2957.6
6455.826
9253.453
5
24739.06
3
4398.442
6459.078
21153.4
9
36631.22
9
3712.84, 4294.386
6459.901
9705.35
7
25181.19
5
3970.098
6472.837
21381.05
3
36825.98
5
2714.671, 2871.415
6484.545
29276.39
7
44693.41
7
2857.279, 2940.058, 3079.951, 3189.706
6486.049
10950.26
3
26363.72
3
3792.015
6507.867
43142.5
5
27780.65
7
3975.211, 4171.736, 4256.897, 4815.143, 5054.357
6514.394
11243.66
5
26590.05
3
3759.736
6547.87
12865.97
5
28133.94
5
3553.412
6556.863
15114.28
11
30361.26
11
5082.248, 5877.37
6587.172
21623.02
5
36799.91
7
3206.384, 3689.729, 3911.86
6620.895
20646.7
7
35746.23
7
2963.319, 3318.534, 3839.029
6680.87
43825.98
5
28862.04
5
5305.223
6697.152
29761.71
1
44689.31
3
2861.984, 2879.882, 2963.058, 2989.063
6714.25
29276.39
7
44165.58
7
2986.489
6717.542
30879.72
7
45762.01
9
2490.47, 2772.596, 2850.472
6769.26
30879.72
7
45648.31
7
2791.366, 2905.739, 3095.39
6783.779
17224.46
5
31961.44
5
3127.8,3337.7
6788.968
12234.77
7
26960.48
7
4006.829
6790.253
6049.433
1
20772.36
3
6792.323
24275.96
3
38994.38
3
6808.32
25655.36
5
40339.33
3
6809.77
22842.85
3
37523.59
3
6831.357
25876.05
3
40510.39
5
6838.797
22842.85
3
37461.48
1
4812.746, 5328.379 2563.7,2703.05,3036.2,3361.4,3419.5,3445.1,3564.7, 3602.4,3675.1,3826.1,4329.56,4592.2,5303.6,5755.02, 5965.5,6189.5 2478.22,2608.19,2915.457,2917.116,3215.96,3269.13, 3501.9,3638.8, 4091.2,4325.0,4950.445,5273.2 3176.2,3536.2,3600.6,3762.1,3804.1,3885.1,4054.3, 4624.1,4924.9,5752.3,6193.1.6287.3,6539.4 2467.7,2596.6,2735.4,2902.6,3245.2,3381.9,3415.8 3535.6,3616.3,4062.7,4322.6,5032.8,5226.1,5293.5 2668.616,3182.569,3184.549,3608.759,3637.225, 3770.906
110
Excitation wavelength/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Fluorescence wavelengths/ Å
6852.788
29761.71
1
44350.29
3
3019.663, 3070.663, 3514.371, 4352.427
6853.923
43275.47
3
28689.34
3
6857.63
17383.17
7
31961.44
5
3954.302, 4232.923 3127.8,3337.7,3570.722,3861.03,4402.5,4491.8,4547.1, 4758.0,4825.4,5067.8,5235.3
6946.87
21623.02
5
36014.07
5
2775.875, 3338.485, 4318.796, 5365.939, 6505.499
6964.8
25876.05
3
40230.04
3
2484.956, 2615.659, 2924.453, 2926.453, 3227.312, 3304.375
6981.802
42501.64
5
28182.63
7
7003.609
29276.39
7
43550.8
5
4079.168, 4286.366, 4556.336, 4968.507 2295.4,2406.5,2525.3,2667.1,2977.5,3066.5,3094.3, 3258,3616,3797.3, 3820.4,4364.8,4509.3.4827.7,4989,5260.4,5586.5
7008.296
25376.47
9
39641.34
7
2656.579, 2802.069
7012.252
29276.39
7
43533.22
7
2526.453, 2636.895
111
TABLE 7.12: The classification of Ta I lines via laser induced fluorescence. Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
2295.462
0
3
43550.8
5
6194.71, 6313.388, 7003.609
2315.868
0
3
43167.09
3
6345.592
2342.12
2010.134
5
44693.41
7
6417.9
2346.434
0
3
42604.76
1
6303.113
2357.314
0
3
42408.18
3
5596.932
2387.578
2010.134
5
43880.82
5
5836.632
2406.549
2010.134
5
43550.8
5
6194.71, 6313.388, 7003.609
2429.664
3963.922
7
45109.37
5
4256.59
2447.143
0
3
40851.65
5
6274.285
2454.482
3963.922
7
44693.41
7
6417.9
2467.756
0
3
40510.39
5
6262.27, 6831.357
2474.619
2010.134
5
42408.18
3
5596.932
2478.222
0
3
40339.33
3
6330.113, 6808.32
2484.956
0
3
40230.04
3
6964.8
2490.47
5621.123
9
45762.01
9
6717.542
2504.338
5621.123
9
45539.8
9
6147.078
2504.453
3963.922
7
43880.82
5
4443.246, 5836.632, 6184.489
2507.452
2010.134
5
41879.25
5
6162.09
2525.326
3963.922
7
43550.8
5
6194.71, 6313.388, 7003.609
2526.453
3963.922
7
43533.22
7
4467.058, 7012.252
2532.125
2642.306
3
42122.93
4
4230.838, 4241.648
2535.521
3963.922
7
43391.72
9
4395.33
2558.591
5621.123
9
44693.41
7
6417.9
2559.427
0
3
39059.53
5
5733.5
2560.678
6068.956
3
45109.37
5
4473.38, 5747.65
2563.706
0
3
38994.38
3
6457.361, 6792.323
2573.795
2010.134
5
40851.65
5
5765.67, 6274.285
2577.352
3963.922
7
42751.8
7
5753.691, 6180.065
2580.156
2010.134
5
40755.89
7
4277.25
2596.113
0
3
38507.61
1
5837.269, 6143.99
2596.606
2010.134
5
40510.39
5
4293.21, 6157.999, 6262.27, 6411.587, 6831.587
2608.199
2010.134
5
40339.33
3
6330.113, 6808.32
2611.336
3963.922
7
42247.07
9
6161.879
2615.659
2010.134
5
40230.04
3
6964.8
2636.671
3963.922
7
41879.25
5
6162.09
2636.895
5621.123
9
43533.22
7
4467.058, 7012.252
2643.886
6068.956
3
43880.82
5
5836.632, 6184.489
2646.774
5621.123
9
43391.72
9
4395.33
2646.871
6049.433
1
43818.65
3
4222.88
2653.274
3963.922
7
41641.97
9
6348.338, 6400.566
2656.579
2010.134
5
39641.34
7
5922.507, 7008.296
2661.334
5621.123
9
43185.12
11
5613.68
2667.166
6068.956
3
43550.8
5
6194.71, 6313.388, 7003.609
2668.616
0
3
37461.48
1
6217.02, 6838.797
Excitation wavelength/ Å
112
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
2685.157
0
1
37230.74
4223.481
2692.393
5621.123
9
42751.8
7
5753.691, 6180.065
2694.518
2642.306
3
39743.63
4
4440.742
2694.756
6068.956
3
43167.09
3
6345.592
2698.3
2010.134
5
39059.53
5
5733.5
2703.054
2010.134
5
38994.38
3
6972.323
2710.127
3963.922
7
40851.65
5
5765.67, 6274.285
2714.671
0
3
36825.98
5
6472.837
2717.179
3963.922
7
40755.89
7
4277.25
2726.288
2010.134
5
38679.18
7
5704.303
2735.43
3963.922
7
40510.39
5
6157.999, 6262.27, 6411.587, 6831.587
2746.678
5621.123
9
42018
7
6200.305
2751.033
6068.956
3
42408.18
3
5596.932
2761.666
1031.418
2
37230.74
2
4223.481
2772.596
9705.35
7
45762.01
9
6717.542
2775.35
5621.123
9
41641.97
9
6348.338
2775.875
0
3
36014.07
5
6946.87
2781.366
9705.35
7
45648.31
7
4368.066, 6769.26
2787.704
9253.453
5
45114.73
7
4255.608
2789.788
9705.35
7
45539.8
9
6147.079
2797.757
1031.418
2
36763.76
3
4200.916
2802.069
3963.922
7
39641.34
7
5922.507, 7008.296
2820.843
9253.453
5
44693.41
7
6417.9
2845.349
5621.123
9
40755.89
7
4277.25
2848.522
3963.922
7
39059.53
5
5733.5
2850.472
10690.42
9
45762.01
9
6717.542
2857.279
9705.35
7
44693.41
7
6417.9, 6484.545
2861.984
9759.017
1
44689.31
3
6697.152
2868.648
10690.42
9
45539.8
9
4325.702, 4388.867
2868.651
3963.922
7
38813.34
9
6101.568
2871.415
2010.134
5
36825.98
5
6472.937
2874.149
6068.956
3
40851.65
5
6274.285
2879.734
3963.922
7
38679.18
7
6280.505
2879.882
9975.837
3
44689.31
3
6697.152
2902.624
6068.956
3
40510.39
5
6157.999, 6262.27, 6411.587, 6831.587
2905.739
11243.66
5
45648.31
7
6769.26
2914.81
9253.453
5
43550.8
5
6313.388
2915.457
6049.433
1
40339.33
3
6808.32
2917.116
6068.956
3
40339.33
3
6808.32
2924.779
6049.433
1
40230.04
3
6964.8
2925.219
9705.35
7
43880.82
5
5836.632
2926.453
6068.956
3
40230.04
3
6964.8
2935.165
9759.017
1
43818.65
3
4222.88
2940.058
10690.42
9
44693.41
7
6417.9, 6484.545
2942.135
3963.922
7
37942.92
9
5780.017, 6443.904
2947.805
9253.453
5
43167.09
3
6345.592
2
113
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
2953.56
5621.123
39468.66
11
6266.395
2953.744
9705.35
7
43550.8
5
6194.71
2953.978
9975.837
3
43818.65
3
4222.88
2957.6
5621.123
9
39422.45
9
6445.869
2963.058
10950.26
3
44689.31
3
6697.152
2963.319
2010.134
5
35746.23
7
4464.093, 6620.895, 6850.794
2976.1
9253.453
5
42844.67
5
6212.444
2977.54
9975.837
3
43550.8
5
6194.71, 7003.609
2984.35
9253.453
5
42751.8
7
5753.691, 6180.065
2986.417
10690.42
9
44165.58
7
6714.25
2988.695
11243.66
5
44693.41
7
6417.9
2989.063
11243.66
5
44689.31
3
6697.152
2992.414
9759.017
1
43167.09
3
6345.592
3001.68
12234.77
7
45539.8
9
6147.078
3011.877
5621.123
9
38813.34
9
6101.568, 4218.4
3011.967
9975.837
3
43167.09
3
6345.592
3019.663
11243.66
5
44350.29
3
6852.788
3024.102
5621.123
9
38679.18
7
6280.505
3025.164
9705.35
7
42751.8
7
5753.691, 6180.065
3030.286
6068.956
3
39059.53
5
5733.5
3036.283
6068.956
3
38994.38
3
6972.323
3042.066
4124.88
0
36987.72
1
4444.607
3057.088
10690.42
9
43391.72
9
4395.33
3061.976
9759.017
1
42408.18
3
5596.932
3063.103
11243.66
5
43880.82
5
6184.489
3063.875
9975.837
3
42604.76
1
6303.113
3066.54
10950.26
3
43550.8
5
6194.71, 7003.609
3068.947
11243.66
5
43818.65
3
4222.88
3070.537
11792.15
1
44350.29
3
6852.788
3072.086
9705.35
7
42247.07
9
6161.879
3079.951
12234.77
7
44693.41
7
6417.9, 6484.545
3081.846
6068.956
3
38507.61
1
5837.269, 6143.99
3087.753
9746.375
4
42122.93
4
4230.838
3092.992
5621.123
9
37942.92
9
6443.904
3094.393
11243.66
5
43550.8
5
6194.71, 6313.388, 7003.609
3095.39
13351.55
9
45648.31
7
4368.066, 6106.328, 6769.26
3103.065
10950.26
3
43167.09
3
6345.592
3105.81
13351.55
9
45539.8
9
6147.078
3107.207
9705.35
7
41879.25
5
6162.09
3121.507
11792.15
1
43818.65
3
4222.88
3127.864
0
3
31961.44
5
6783.779, 6857.63
3133.551
9975.837
3
41879.25
5
6162.09
3141.032
12865.97
5
44693.41
7
6417.9
3147.388
13351.55
9
45114.73
7
4255.608
3148.033
9253.453
5
41010.12
5
6212.503
3150.847
9253.453
5
40981.77
7
5857.005
9
114
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
3163.82
9253.453
40851.65
5
6274.285
3172.867
11243.66
5
42751.8
7
5753.691, 6180.065
3176.291
6049.433
1
37523.59
3
6809.77
3180.947
0
3
31428.09
5
6439.77
3182.569
6049.433
1
37461.48
1
6217.02, 6838.797
3184.549
6068.956
3
37461.48
1
6217.02, 6838.797
3189.706
13351.55
9
44693.41
7
6417.9, 6484.545
3205.478
2010.134
5
33197.72
7
6258.734
3206.384
5621.123
9
36799.91
7
6587.172
3208.629
12234.77
7
43391.72
9
4395.33
3209.726
9705.35
7
40851.65
5
6274.285
3215.966
9253.453
5
40339.33
3
6808.32
3227.312
9253.453
5
40230.04
3
6964.8
3237.846
9975.837
3
40851.65
5
5765.67, 6274.285
3244.488
11792.15
1
42604.76
1
6303.113
3245.281
9705.35
7
40510.39
5
6157.999, 6262.27, 6411.587, 6831.587
3258.004
12865.97
5
43550.8
5
6194.71, 6313.388, 7003.609
3265.32
11792.15
1
42408.18
3
5596.932
3269.138
9759.017
1
40339.33
3
6808.32
3275.913
12234.77
7
42751.8
7
5753.691, 5847.587
3292.482
9975.837
3
40339.33
3
6808.32
3299.26
12865.97
5
43167.09
3
6345.592
3299.768
6049.433
1
36345.87
1
6680.53
3304.375
9975.837
3
40230.04
3
6964.8
3311.141
5621.123
9
35813.52
11
4450.72
3318.534
5621.123
9
35746.23
7
6620.895, 6850.794
3327.92
13351.55
9
43391.72
9
4395.33
3331.009
12234.77
7
42247.07
9
6161.879
3337.791
2010.134
5
31961.44
5
6783.779, 6857.63
3338.485
6068.956
3
36014.07
5
6946.87
3343.36
10950.26
3
40851.65
5
6274.285
3345.108
12865.97
5
42751.8
7
5847.587
3361.405
9253.453
5
38994.38
3
6972.323
3361.747
11243.66
5
40981.77
7
5857.005
3372.34
12234.77
7
41879.25
5
6162.09
3376.498
11243.66
5
40851.65
5
5765.67, 6274.285
3381.957
10950.26
3
40510.39
5
6157.999, 6262.27, 6411.587, 6831.587
3384.014
12865.97
5
42408.18
3
5596.932
3385.046
3963.922
7
33497.15
9
6204.09
3397.413
9253.453
5
38679.18
7
6280.505
3398.308
2010.134
5
31428.09
5
6439.77
3411.712
15391.02
9
44693.41
7
6417.9
3415.866
11243.66
5
40510.39
5
4293.21, 6157.999, 6262.27, 6411.587, 6831.587
3419.536
9759.017
1
38994.38
3
6972.323
3419.717
3963.922
7
33197.72
7
6258.734
3434.496
9705.35
7
38813.34
9
6101.568, 4218.4
5
115
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
3437.366
9975.837
3
39059.53
5
5733.5
3445.085
9975.837
3
38994.38
3
6972.323
3445.704
12865.97
5
41879.25
5
6162.09
3450.403
9705.35
7
38679.18
7
5704.303
3477.437
9759.017
1
38507.61
1
5837.269, 6143.99
3484.618
0
3
28689.34
3
5635.71
3493.441
12234.77
7
40851.65
5
5765.67, 6274.285
3497.848
2010.134
5
30590.98
7
5640.177
3501.968
11792.15
1
40339.33
3
6808.32
3503.862
9975.837
3
38507.61
1
5837.269, 6143.99
3514.371
15903.82
3
44350.29
3
6852.788 4395.33
3535.375
15114.28
11
43391.72
9
3535.6
12234.77
7
40510.39
5
3536.292
9253.453
5
37523.59
3
3540.371
9705.35
7
37942.92
9
5780.017
3553.412
0
3
28133.94
5
6547.87
3554.801
10690.42
9
38813.34
9
6101.568
3556.529
10950.26
3
39059.53
5
5733.5
3564.791
10950.26
3
38994.38
3
6972.323
3570.722
3963.922
7
31961.44
5
6857.63
3571.844
10690.42
9
38679.18
7
5704.303, 6280.505
3572.236
12865.97
5
40851.65
5
5765.67
3573.344
15903.82
3
43880.82
5
5836.632
3586.291
5621.123
9
33497.15
9
6204.09
3599.202
45769.74
5
17993.73
5
4461.707
3600.685
9759.017
1
37523.59
3
6809.77
3602.485
11243.66
5
38994.38
3
6972.323
3608.759
9759.017
1
37461.48
1
6217.02, 6838.797
3616.006
15903.82
3
43550.8
5
6194.71, 6313.388, 7003.609
3616.34
12865.97
5
40510.39
5
3625.229
5621.123
9
33197.72
7
6258.734
3626.607
3963.922
7
31530.05
9
6194.438
3637.225
9975.837
3
37461.48
1
6217.02, 6838.797
3638.852
12865.97
5
40339.33
3
6808.32
3640.072
3963.922
7
31428.09
5
6439.77
3642.049
5621.123
9
33070.36
11
4467.08
3643.871
11243.66
5
38679.18
7
5704.303
3653.828
15391.02
9
42751.8
7
5753.691
3668.344
10690.42
9
37942.92
9
5780.017
3675.123
11792.15
1
38994.38
3
6972.323
3684.527
15114.28
11
42247.07
9
6161.879
3689.729
9705.35
7
36799.91
7
6587.172
3692.125
44461.65
5
17384.69
3
5993.185
3712.84
9705.35
7
36631.22
9
6459.078
3712.972
44918.66
5
17993.73
5
6160.009
3722.494
15391.02
9
42247.07
9
6161.879
6157.999, 6262.27, 6831.587 6809.77
6262.27, 6411.587, 6831.587
116
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
3742.084
11792.15
38507.61
5837.269, 6143.99
3744.12
15903.82
3
42604.76
1
6303.113
3747.173
2010.134
5
28689.34
3
5635.71
3754.511
3963.922
7
30590.98
7
5640.177
3759.559
45769.74
5
19178.43
5
4461.707
3759.736
0
3
26590.05
3
6514.394
3760.19
9759.017
1
36345.87
1
6680.53
1
1
3762.104
10950.26
3
37523.59
3
6809.77
3770.906
10950.26
3
37461.48
1
6217.02, 6838.797
3772.848
17383.17
7
43880.82
5
5836.632
3777.086
44461.65
5
17993.73
5
4182.693, 5993.185
3792.015
0
3
26363.72
3
6486.049
3797.399
17224.46
5
43550.8
5
6194.71, 6313.388, 7003.609
3804.109
11243.66
5
37523.59
3
6809.77
3804.91
10713.3
1
36987.72
1
4444.607
3816.648
12865.97
5
39059.53
5
5733.5
3820.426
17383.17
7
43550.8
5
6194.71, 6313.388, 7003.609
3826.167
12865.97
5
38994.38
3
6972.323
3839.029
9705.35
7
35746.23
7
6620.895
3853.57
17224.46
5
43167.09
3
6345.592
3858.581
5621.123
9
31530.05
9
6194.438
3861.031
6068.956
3
31961.44
5
6857.63
3872.889
12865.97
5
38679.18
7
5704.303, 6280.505
3885.195
11792.15
1
37523.59
3
6809.77
3888.726
12234.77
7
37942.92
9
5780.017
3894.596
11792.15
1
37461.48
1
6217.02
3911.86
11243.66
5
36799.91
7
6587.172
3918.515
0
3
25512.66
1
6345.987
3926.343
13351.55
9
38813.34
9
6101.568
3942.238
6068.956
3
31428.09
5
6439.77
3947.144
13351.55
9
38679.18
7
5704.303, 6280.505
3954.073
44461.65
5
19178.43
5
5993.185
3954.302
43275.47
3
17993.73
5
6853.923
3957.591
44918.66
5
19657.8
3
6160.009
3970.098
0
3
25181.19
5
6459.901
3975.211
43142.5
5
17993.73
5
6507.867
4003.697
5621.123
9
30590.98
7
5640.177
4006.829
2010.134
5
26960.48
7
6788.968
4007.232
15903.82
3
40851.65
5
5765.67, 6274.285
4016.039
20646.7
7
45539.8
9
6147.078
4030.49
44461.65
5
19657.8
3
5993.185
4054.391
12865.97
5
37523.59
3
6809.77
4062.796
15903.82
3
40510.39
5
4065.318
13351.55
9
37942.92
9
5780.017
4079.168
42501.64
5
17993.73
5
6981.802
4080.05
11243.66
5
35746.23
7
6850.794
6262.27, 6411.587, 6831.587
117
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
4091.248
15903.82
40339.33
6808.32
4104.23
44918.66
5
20560.32
7
6160.009
4140.268
44918.66
5
20772.36
3
6160.009
4147.758
9975.837
3
34078.46
3
4322.512
4152.058
15391.02
9
39468.66
11
6266.395
4171.736
43142.5
5
19178.43
5
6507.867
4175.185
9253.453
5
33197.72
7
6258.734
4178.66
12234.77
7
36159.29
7
6444.595
4209.175
44918.66
5
21167.6
5
6160.009
4218.4
15114.28
11
38813.34
9
6101.568
4220.129
44461.65
5
20772.36
3
5993.185
4231.219
17224.46
5
40851.65
5
6274.285
4232.923
43275.47
3
19657.8
3
6853.923
4246.887
21153.4
9
44693.41
7
6417.9
4256.897
43142.5
5
19657.8
3
6507.867
4268.23
15391.02
9
38813.34
9
6101.568
4286.366
42501.64
5
19178.43
5
6981.802
4291.735
44461.65
5
21167.6
5
5993.185
4292.82
15391.02
9
38679.18
7
5704.303, 6280.505
4294.386
13351.55
9
36631.22
9
6459.078
4302.805
20646.7
7
43880.82
5
5836.632
4318.796
12865.97
5
36014.07
5
6946.87
4322.681
17383.17
7
40510.39
5
4325.001
17224.46
5
40339.33
3
4329.56
15903.82
3
38994.38
3
6972.323
4334.647
44918.66
5
21855.12
3
6160.009
4352.427
21381.05
3
44350.29
3
6852.788
3
3
6262.27, 6411.587, 6831.587 6808.32
4364.804
20646.7
7
43550.8
5
6194.71, 6313.388, 7003.609
4371.1
44918.66
5
22047.45
5
6160.009
4402.502
9253.453
5
31961.44
5
6857.63
4415.745
6049.433
1
28689.34
3
5635.71
4419.551
6068.956
3
28689.34
3
5635.71
4435.691
44918.66
5
22380.48
7
6160.009
4441.751
10690.42
9
33197.72
7
6258.734
4459.763
41594.85
3
19178.43
5
6216.334
4470.78
41539.61
5
19178.43
5
4245.85
4491.894
9705.35
7
31961.44
5
6857.63
4509.388
21381.05
3
43550.8
5
6194.71, 7003.609
4527.474
44461.65
5
22380.48
7
4182.693
4547.159
9975.837
3
31961.44
5
6857.63
4551.95
3963.922
7
25926.38
9
6163.07
4553.689
11243.66
5
33197.72
7
6258.734
4556.336
42501.64
5
20560.32
7
6981.802
4568.729
41539.61
5
19657.8
3
4245.85
4580.675
9705.35
7
31530.05
9
6194.438
4592.21
17224.46
5
38994.38
3
6972.323
118
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
4602.179
9705.35
7
31428.09
5
6439.77
4624.1
15903.82
3
37523.59
3
6809.77
4628.258
20646.7
7
42247.07
9
6161.879
4637.426
15903.82
3
37461.48
1
6217.02
4637.897
44918.66
5
23363.11
5
6160.009
4685.266
9253.453
5
30590.98
7
5640.177
4686.033
42501.64
5
21167.6
5
6281.388
4694.406
17383.17
7
38679.18
7
5704.303, 6280.505
4712.883
12865.97
5
34078.46
3
5322.512
4719.9
23512.45
5
44693.41
7
6417.9
4739.432
21153.4
9
42247.07
9
6161.879
4758.039
10950.26
3
31961.44
5
6857.63
4768.983
12234.77
7
33197.72
7
6258.734
4786.643
9705.35
7
30590.98
7
5640.177
4797.206
10690.42
9
31530.05
9
6194.438
4815.143
43142.5
5
22380.48
7
6507.867
4825.424
11243.66
5
31961.44
5
6857.63
4827.718
22842.85
3
43550.8
5
6194.71, 7003.609
4835.381
44918.66
5
24243.45
3
6160.009
4887.61
42501.64
5
22047.45
5
6281.388
4908.202
23512.45
5
43880.82
5
5836.632
4923.458
5621.123
9
25926.38
9
6163.07
4924.949
17224.46
5
37523.59
3
6809.77
4950.445
20144.81
1
40339.33
3
6808.32
4962.079
24546.2
5
44693.41
7
6417.9
4968.507
42501.64
5
22380.48
7
6981.802
4989.045
23512.45
5
43550.8
5
6194.71, 6313.388, 7003.609
5017.062
9975.837
3
29902.27
1
4191.151,4194.627
5023.583
10690.42
9
30590.98
7
5640.177
5023.912
43826.01
5
23926.72
7
6680.87
5032.899
20646.7
7
40510.39
5
5037.351
13351.55
9
33197.72
7
6258.734
5044.41
22428.65
11
42247.07
9
6161.879
5054.357
43142.5
5
23363.11
5
6507.867
5055.376
24918
7
44693.41
7
6417.9
5067.867
12234.77
7
31961.44
5
6857.63
5078.728
41539.61
5
21855.12
3
4245.85
5082.249
10690.42
9
30361.26
11
6556.863
5099.352
24275.96
3
43880.82
5
5836.632
5130.488
22761.28
7
42247.07
9
6161.879
5136.469
6049.433
1
25512.66
1
6345.987,6434.544
5141.626
6068.956
3
25512.66
1
6345.987
5143.692
9253.453
5
28689.34
3
5635.71
5181.164
12234.77
7
31530.05
9
6194.438
5185.155
44461.65
5
25181.19
5
6122.864
5199.129
21623.02
5
40851.65
5
5765.67
6262.27, 6411.587, 6831.587
119
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
5226.106
21381.05
3
40510.39
6262.27, 6411.587, 6831.587
5235.383
12865.97
5
31961.44
5
6857.63
5260.429
24546.2
5
43550.8
5
6194.71, 6313.388, 7003.609
5273.274
21381.05
3
40339.33
3
6808.32
5281.062
9759.017
1
28689.34
3
5635.71
5285.185
37420.29
1
18504.76
1
6422.825
5293.063
21623.02
5
40510.39
5
5303.676
20144.81
1
38994.38
3
6972.323
5305.223
43825.98
5
24981.88
7
6680.87
5365.939
17383.17
7
36014.07
5
6946.87
5382.106
42501.64
5
23926.72
7
6281.388
5387.901
44918.66
5
26363.72
3
6160.009
5429.497
20646.7
7
39059.53
5
5733.5
5443.091
23512.45
5
41879.25
5
6162.09
5446.239
12234.77
7
30590.98
7
5640.177
5452.785
23912.93
9
42247.07
9
6161.879
5453.257
44918.66
5
26585.98
7
6160.009
5454.465
44918.66
5
26590.05
3
6160.009
5458.41
21153.4
9
39468.66
11
6266.395
5485.346
25655.49
5
43880.82
5
5836.632
5499.474
13351.55
9
31530.05
9
6194.438
5503.066
20646.7
7
38813.34
9
6101.568
5526.267
22761.28
7
40851.65
5
5765.67
5551.297
22842.85
3
40851.65
5
5765.67, 6274.285
5558.148
25894.22
7
43880.82
5
5836.632
5586.503
25655.36
5
43550.8
5
5632.521
22761.28
7
40510.39
5
6411.587
5655.023
21381.05
3
39059.53
5
5733.5
5658.527
22842.85
3
40510.39
5
6411.587
5752.386
20144.81
1
37523.59
3
6809.77
5752.535
20144.81
1
37523.59
3
6809.77
5755.022
21623.02
5
38994.38
3
6972.323
5769.045
24918
7
42247.07
9
6161.879
5780.017
20646.7
7
37942.92
9
5780.017
5861.368
21623.02
5
38679.18
7
6280.505
5877.37
13351.55
9
30361.26
11
6556.863
5881.424
23512.45
5
40510.39
5
5889.165
26575.22
7
43550.8
5
6194.71, 6313.388
5925.831
25376.47
9
42247.07
9
6161.879
5954.445
21153.4
9
37942.92
9
5780.017
5965.53
22236.01
1
38994.38
3
6972.323
5993.185
44461.65
5
27780.65
7
6122.864
6090.016
15114.28
11
31530.05
9
6194.438
6131.218
24546.2
5
40851.65
5
6274.285
6189.655
22842.85
3
38994.38
3
6972.323
6193.105
21381.05
3
37523.59
3
6809.77
5
6262.27, 6411.587
6313.388, 7003.609
6262.27, 6411.587, 6831.587
120
Fluorescence wavelengths/ Å
Even levels Energy/ cm-1 J
Odd levels Energy/ cm-1 J
Excitation wavelength/ Å
6287.361
21623.02
5
37523.59
3
6809.77
6443.904
22428.65
11
37942.92
9
5780.017
6457.361
23512.45
5
38994.38
3
2563.706
6505.499
20646.7
7
36014.07
5
6946.87
6539.466
22236.01
1
37523.59
3
6809.77
6585.089
22761.28
7
37942.92
9
5780.017
6754.203
23141.41
11
37942.92
9
5780.017
6771.721
10950.26
3
24739.06
3
4398.442
6791.15
42501.64
5
27780.65
7
6281.388
121
8.3
Hyperfine structure studies of Praseodymium
The electronic shell of Ta I has been investigated almost completely. Almost all strong lines in FT spectra of Ta I have been classified, only weak lines in UV, far infrared regions and some strong lines in far infra red region are still unclassified. Due to unavailability of a good tunable laser in the UV region strong lines of Ta II are also remained unclassified. The fine and hyperfine structure of the praseodymium atom was investigated in great detail by A. Ginibre [104], [105]. There are also contributions from Böklen et al. [106], Reddy et al. [107], and Childs et al. [108]. The fine and hyperfine structure of the singly ionized Praseodymium (Pr II) was investigated by White, King, and Ginibre [109, 110, 111]. Still is a lot left to be done to have complete knowledge of the atomic structure of Pr I and Pr II. Many weak lines in Pr I and strong lines in Pr II are still unclassified and have been never excited by laser radiation. So we decided to work with Praseodymium. The group in Hamburg already had started laser spectroscopic investigations of hyperfine structure of Praseodymium. In this work, besides classification of known lines either by laser induced fluorescence or laser excitation, a number of new lines were also found. The laser spectroscopic investigation of the hyperfine structure of Pr in this work was performed mainly accomplished with Rhodamine 6G laser which had its maximum in the yellow region. A Stilben 3 dye laser was also used for the study of some lines of Pr. During our investigation of hyperfine structure of praseodymium, using the method of laser induced fluorescence spectroscopy, we found a large number of praseodymium lines. Some of the lines belong to transitions between atomic levels and some belong to transitions between ionic levels. In some cases we discovered new upper or lower levels. There are some lines for which we realize that both levels are not known. The purpose of this work was to continue the search for new levels and to complete the understanding of the atomic structure of Pr I and Pr II, and also to explain unclassified lines applying laser spectroscopy. 8.3.1
Blend situation and discovery of the level 2911111/2
The occurrence of blends is more common in the praseodymium spectrum than in the Ta spectrum. Often it happens, that we see LIF from two or more distinct levels at a particular excitation wavelength. This gives an idea how close the levels and (or) the spectral lines lie and how large the number of levels in praseodymium really is. Even tantalum (with a core of two to five 5d-electrons in most of the electronic configurations) has a large number of levels but the praseodymium
122
Figure 58: Blend situation. Six different hyperfine strcutures were recorded scanning the laser wavelength between 5779.55 and 5779.8 Å. (with a core of two to three 4f-electrons) has much more levels. Commonly used spectral tables contain no lines of Pr I and Pr II between 5779Å and 5782Å. The energy levels and spectral lines of Praseodymium lie very close to each other, so it was tried to find new lines in this gap. We started the excitation at 5779Å and increasing the excitation wavelength in steps of approximately 0.2 Å. At each step fluorescence signals were searched by scanning the monochromator. With the excitation wavelength 5779.67Å more than 24 fluorescence signals were found. If the fluorescence signals belong to the same level or not was determined by investigating the hyperfine structure of the excited transitions by scanning the laser frequency and recording the LIF signal separately at each frequency. We observed six different structures with center of gravity wavelengths between 5779.59 Å and 5779.74 Å. Three of them could be classified as transitions between known levels. One structure led to the discovery of a new even level, 29111.85 cm−1 with J=6.5. But last two transitions could not be identified. The six different hyperfine patterns are shown in the fig. 58. The hyperfine structure recorded at the fluorescence line 6158.13Å showed the structure of the transition 11814o15/2 cm−1 to 2911113/2 cm−1 which could be identified due to the known hf constants of these levels. But the hyperfine structure recorded at the fluorescence line 5919.1Å showed a blend structure, which is only possible, when a blend of the excited line occurs both different excited levels decay
123
Figure 59: Discovery of the even level 2911113/2 and blend situation observed at the fluorescence line 5919.1Å accidently with nearly the same wavelength. The arrow in the fig. 59 indicates this case. That both decay lines are recorded simultaneously is caused by the relatively large width of the entrance slit of the monochromator. To eliminate the effect of second transition, the width of entrance slit of monochromator should be kept small. On the other hand, appearing of a foreign structure indicates an excitation blend occurs, and this is a chance to find a new level. In our case, the additional structure in λF = 5919 Å was already recorded at λF = 6158.13 Å. 8.3.2
Blending lines 5675.321 and 5675.279 and discovery of the new level 30560.917/2
We noticed that there are some unclassified lines of Praseodymium in the commonly used list of Praseodymium lines, which lie in the region of a laser working in the spectral range of Rhodamine 6G. We have already worked with this laser light and have discovered more than 100 new levels of Pr I, which are being published soon. The line 5675.324Å was an unclassified line of Pr I. A. Ginibre [54]observed this line and measured its splitting. Our classification program [101, LW] gave some suggestions for this line. To make sure which suggestion is the right transition scheme of this line, we excited the line by setting the laser wavelength to 5675.32Å, and searched for fluorescence lines by scanning a monochromator. Fortunately we observed 124
30560
27165 5882.32
5785 5675.279
5693
13565 13280
5361
5675.33
13002 12945 6471 5415
11913
6298
11764
11746 5443
5318
11322
9579 8835 8733
Figure 60: Blend situation of the exciting lines 5675.33 Å and 5675.279 Å. Additional fluorescence lines were observed when level 30560.917/2 cm−1 was excited by another laser wavelength, 5882.32 Å. seven LIF signals. Then the hyperfine structure of each of these lines was recorded by scanning the laser frequency. It was found that these seven fluorescence lines belong to two groups. One group includes four LIF signals and the other group three LIF signals. Both groups showed different hyperfine structures. This means that we had excited simultaneously two levels. The splitting of these lines are 80 mK and 720 mK, respectively. In her thesis, Ginibre found two lines at 5675.324Å and 5675.38Å having splitting of 40 mK and 0, respectively. It is clear that one of the transition we have excited is the line with 40 mK splitting which Ginibre observed in her work. This line is a decay from the level 2719511/2 to 9579o9/2 . The upper level was introduced by Kuwamoto [112] and the group of Prof. Guthöhrlein had excited once this level in Hamburg. The hyperfine structure of this second transition could not be explained by the existing levels of Pr I. Thus a new level was surely involved. The evaluation gave the following results: Center of gravity wavelength = 5675.279Å Ao = 451(2) MHz, Jo = 8.5, Au = 837(3) MHz and Ju = 9.5 This line had its highest peak at 5675.38 Å, which is the position observed by Ginibre. The line 5765.38 Å of Ginibre turned out to be
125
(b)
(a)
Figure 61: (a) Best fit of the line 5882.321Å (b) Best fit of the line 5675.27Å. a single hyperfine component of an extended structure which in its main part blends the line 5675.279 Å. We searched in the list of known Pr levels for one having Au = 837 MHz and Ju = 9.5. This is fulfilled by the level 12945.51cm−1 . The new level 30560.917/2 cm−1 is then obtained after adding center of gravity wave number of the transition to the wave number of the lower level. The introduction of this level explained all four fluorescence lines. One of the fluorescence lines, 5882.3 Å, was used as second laser excitation to confirm the new level. The recorded hyperfine structure showed a splitting of -548 mK. This is in excellent agreement with the measured splitting of this line of —550 mK given by Ginibre. This fact confirms our new level. Both laser excitation lines and two of the fluorescence lines were unclassified lines, which are now classified via the discovery of new level 30560.917/2 cm−1 . Table 7.13: Decay lines from 30560.917/2 and comparison of our and Ginibre’s work Wavelength/Å Measured Ginibre’s Remarks ∆W/mK ∆W/mK 5318.617 -661 -660 Unclassified line 5361.086 -711 -700 Unclassified line 5675.279 -74 0 Unclassified line as5675.38 5693.554 261 New line 5785.278 367 New line 5885.321 -549 -550 Unclassified line 6330.83 399 New line
126
Figure 62: Blending lines 5675.321 Å and 5675.279 Å 8.3.3
The new level 3204119/2
The line 5847.018 Å is another line which Ginibre observed in her work as unclassified line of Pr I with ∆W = -570 mK. Our classification program showed one suggestion for this line with ∆W = —675 mK. To clear up the situation the laser was set to 5847.0Å and the monochromator was scanned to search for LIF signals. We observed four LIF signals; the line at 5235 Å was strongest one. The monochromator then was fixed at 5235 Å and the laser frequency was scanned to record the hyperfine structure of the excited transition. The recorded structure had a splitting of -567 mK. This rejected the only suggestion we had and led to the discovery of a new level. Fortunately, one of the fluorescence lines, 5798 Å could be used for another excitation of the new level. Our monochro˚ We asmator measures wavelengths with an uncertainty of ±2 A. sumed that if we let the monochromator fixed at the wavelength of the strongest fluorescence line and tune the laser from 5800-5796Å, we would surely get another excitation of the new level. Finally we succeeded, and observed a signal at 5798.131Å. The new level 32041.82719/2 was discovered from the evaluation of the two recorded structures. This level explains all fluorescence lines and laser excitations.
127
(a)
(b)
Figure 63: (a) Best fit of the line 5847.018Å and (b) best fit of the line 5798.201Å Table 7.14: Decay lines from 3204119/2 and comparison of our and Ginibre’s work Wavelength/Å Measured Ginibre’s Remarks ∆W/mK ∆W/mK 5235.153 -747 -740 Unclassified line 5305.498 -803 New line 5647.633 280 New line 5798.200 423 New line 5847.023 -573 —570 Unclassified line
8.3.4
The levels 3100517/2 and 31005o13/2
Two levels [31005.717/2 and 31005.717o13/2 ] discovered in this work have almost the same energy but different angular momentum and parity. During our systematic investigation of the hyperfine structure of Pr, we found two unclassified lines 5761.703 Å(new line) and 5750.72 Å, and the analysis of the recorded structures at both wavelengths gave two new levels with almost the same energy. This looked strange at first glance and I thought I might have made some mistake, but when I looked at the angular momentum and parity of each level, it looked interesting and possible that both two levels might exist. Then I prepared a plan to confirm these levels at least with one second laser excitation. We tried to excite each level by setting the laser to wavelengths suggested by our classification program. Fortunately 128
Figure 64: Discovery of the level 3204119/2 cm−1 . I was able to confirm both levels on the same day. 8.3.5
The level 324029/2
The line 5768.329 Å was known but unclassified line given in the work of Ginibre. In order to classify this line, we set the laser in the neighbourhood of this wavelength and searched for fluorescence lines. Five fluorescence lines were found. One of the fluorescence line 5879 Å was in the working range of dye laser. The monochromator was set to the strongest fluorescence 4745 Å and the laser was tuned in the neighbourhood of the 5879 Å. After few laser scans the desired signal was found. The center of gravity wavelength was found to be 5878.408 Å. The hyperfine structure was recorded at the fluorescence wavelength 4745 Å, for both laser excitations. The analysis of both recorded structures gave the same value of magnetic dipole hyperfine constant. This further confirmed that both laser excitations belong to the decay from the same level. Usually two laser excitations are sufficient for the discovery and confirmation of the new level. Both laser wavelengths and fluorescence wavelengths appear in the combination list of the new level. But in this case we could not found such a level. However the level 32402.889/2 was showing fluorescence lines as possible decays, but not the laser excitation wavelength 5878.408 Å. It was decided to treat new level 32402.889/2 as being existing with the assumption that the decay from 32402.889/2 at the laser 129
Figure 65: The best fit of the line 5878.40Å excitation 5878.408Å involves an unknown lower level. All possible transitions from this level in the range of our tunable cw dye laser ( Rhodamine 6G, 5650Å- 5950Å) were tried to find at least a second laser excitation of the new level. Fortunately we were successful at 5656.456 Å, and the level 32402.889/2 was confirmed. The decay from 32402.889/2 with the laser excitation wavelength 5878.408 Å leads to the discovery of a new lower level 15396.17o9/2 . Unfortunately we were unable to confirm this level yet.
8.3.6
The level 3233615/2
The line 5747.8Å was another unclassified line. Some suggestion were shown by our classification program. To find the right classification, the laser was set to 5748.8 Å and monochromator was scanned to find fluorescence lines. 5691 Å, 5884 Å and 5902 Å were observed as fluorescence lines. The hyperfine structure was recorded at the strongest fluorescence line, 5691 Å. The hyperfine structure was not matching with the hyperfine structure of suggestions shown by our classification program. This indicated that at least one new level is involved in the observed transitions. Then the monochromator was let at this fluorescence line and the laser was scanned in the neighbourhood of 5884 Å since our monochromator measures the ˚ After few fluorescence line wavelength with an uncertainty of ±2A. laser scans the fluorescence signal was found and then the hyperfine 130
Figure 66: The best fit of the line 5768.329Å, which led to the discovery of the level 324029/2
Figure 67: The best fit of the line 5656.456Å, which confirmed the level 324029/2
131
structure was recorded. An additional fluorescence, 5772 Å, was also found. Similarly the hyperfine structure was recorded by scanning laser in the neighbourhood of 5772 Å and 5902 Å. We had four different excitations of the new level but we were unable to identify the level until we performed excitation at 5690.815 Å. The reason for this is that some lower levels corresponding to these transitions were not known. In order to resolve the situation the fluorescence line was used as laser excitation and the hyperfine structure was recorded. The excitation at 5690.815 Å made it possible to find a new level, 3233615/2 , and the lower levels missing in the list. The lower levels were identified to be 15347o13/2 and 15398o15/2 . Both lower levels are now confirmed, and the group in Hamburg has also found at least one transition to these lower levels. 8.3.7
The level 25909o17/2
In some cases it happened that only one fluorescence line was observed and some times fortunately just this fluorescence line could also be used for excitation of the level. In this way we had two hyperfine structures by interchanging fluorescence lines and laser excitation wavelengths. We found few levels in this way. The level 25909o17/2 is one of them. When exciting the Pr atoms at a wavelength 5831.449 Å one strong fluorescence line 5698 Å was found. After recording the hyperfine structure by scanning the laser wavelength, the fluorescence and excitation wavelengths were interchanged. The monochromator was let fixed at 5831 Å and the laser was scanned in the neighbourhood of 5698 Å until the signal was found. Then by scanning laser the hyperfine structure was recorded. The analysis of recorded structure led to the discovery of the new level 25909o17/2 . The best fits are shown in the figs. 68, 69 All new lines of Pr I observed during this work are presented in two tables according to their mode of observation. All lines which correspond to transitions excited by the laser are listed in table 7.17 as new lines observed through laser excitation. All lines which are observed as laser induced fluorescence decays are given in table 7.18 as new lines of Pr I found by LIF. In the same way all formerly known but not yet classified lines which are classified in this work are presented in two separate tables. The lines which are classified by laser excitation are given in table 7.19 and the lines which are classified by laser induced fluorescence are given in table 7.20.
132
Figure 68: The best fit of the line 5697.96Å
Figure 69: The best fit of the line 5831.449Å
133
Table 7.15: New odd levels of Pr I. Energy/ cm-1 15347.433 15398.916 15426.41 24781.13 25172.3 25900.347 25909.17 26332.066 26718.699 26888.462 27816.306 27844.901 28698.03 28754.38 28800.01 28859.804 28920.81 28978.446 29075.83 29429.862 29579.88 29622.954 29663.117 29775.016 29836.92 29899.984 29942.883 29950.75 29985.524 29989.113 30346.23 30411.982 30644.64 30787.09 30788.071 31005.717 31039.957 31270.87 31447.878 31528.61 31668.54 31817.865 31895.22 33052.849 33687.801 35453.371
J
A/ MHz 13/2 15/2 13/2 13/2 7/2 11/2 17/2 15/2 9/2 11/2 5/2 17/2 11/2 15/2 5/2 7/2 5/2 7/2 5/2 11/2 7/2 17/2 13/2 13/2 13/2 17/2 15/2 19/2 11/2 15/2 17/2 13/2 13/2 13/2 15/2 13/2 15/2 17/2 9/2 9/2 15/2 15/2 15/2 13/2 9/2 17/2
λExcitation / Å
673(3) 889.5(2) 737.1(2) 861(4) 708(10) 846(2) 854(2) 506(5) 826(3) 638(3) 1174(5) 603(3) 764(5) 639(2) 1057(6) 538(5) 1011(2) 1047(2) 829(2) 693(2) 720(3) 503(5) 651(5) 615(3) 535(5) 528(3) 583(5) 418(3) 773.4v 528.4(3) 518(5) 658(6) 628(5) 507(4) 528(4) 588(4) 552(5) 512(4) 665(1) 744(5) 544(5) 443(4) 668(3) 555(3) 744(2) 598(2)
a5884.383 a5871.613 a5648.435 a5917.921 a5902.335 a5791.72 a5657.223 a5455.519 a5911.865 a5828.961 a5940.217 a5831.661 a5826.156 a5793.305 a5856.149 a5686.675 a5697.964 a5831.449 a5691.076 a5926.888 a5875.902 a5729.075 a5673.887 a5807.807 a5885.114 a5673.272 a5752.75 a5774.431 a5829.824 a5800.471 a5781.578 a5788.449 a5704.282 a5769.526 a5807.768 a5749.67 a5665.232 a5693.472 a5736.026 a5768.03 a5743.208 a5810.134 a5871.622 a5749.434 a5911.973 a5792.823 a5702.772 a5920.326 a5754.663 a5736.138 a5698.037 a5681.908 a5704.728 a5661.919 a5679.5 a5684.63 a5664.335 a5847.885 a5810.243 a5650.601 a5807.588 a5783.448 a5799.095 a7848.88 a5794.673 a5817.54 a5913.005 a5699.118 a5868.643 a5825.442 a5789.571 a5810.442 a5750.015 a5666.84 a5762.403 a5834.894 a5761.703 a5834.904 a5760.099 a5750.355 a5689.899 a5863.629 a5798.143 a5887.799 a5791.621 a5744.87 a5789.756 a5793.468 a5729.974 a5919.864 a5716.087 a5762.82 a5910.736 a5923.096 a5938.696 a5785.336 a5860.705 a5691.051 a5764.232 a5859.809 a5820.643
134
Table 7.16: New Even levels of Pr I. Energy/ cm-1 27993.78 28889.23 29071.02 29111.85 29128.82 29363.37 29377.64 29523.39 29523.96 29698.57 29766.74 29980.03 30232.08 30275.02 30356.67 30461.52 30466.62 30560.9 30590.69 30963.41 31005.72 31010.2 31299.66 31677.75 31771.68 31900.66 32041.83 32070.5 32336.86 32373.84 32402.88 32445.22
J
A/ MHz 5/2 11/2 11/2 13/2 11/2 11/2 11/2 13/2 9/2 9/2 9/2 9/2 9/2 21/2 9/2 7/2 19/2 17/2 5/2 5/2 7/2 11/2 5/2 9/2 11/2 11/2 19/2 7/2 15/2 11/2 9/2 13/2
λexcitation / Å
752(5) 635(2) 635(5) 577(2) 544(5) 746(5) 683(2) 628(5) 647(4) 629(5) 699(4) 672(3) 737(2) 375(5) 788(4) 692(5) 403(6) 451(5) 622(4) 661(5) 692(5) 705(2) 800(3) 433(3) 718(5) 525(5) 385(6) 668(2) 475(5) 660(5) 544(3) 655(5)
a5765.524 a5932.318 a5826.377 a5693.336 a5690.975 a5765.27 a5933.434 a5919.097 a5779.682 a5746.121 a5751.345 a5674.748 a5669.7 a5774.266 a5665.099 a5751.944 a5772.375 a5796.835 a5772.01 a5664.592 a5714.574 a7888.873 a5919.361 a5899.581 a5826.248 a5859.809 a5760.6 a5774.438 a5854.441 a5768.91 a5882.059 a5733.227 a5667.221 a5843.783 a5817.017 a5705.818 a5789.48 a5675.279 a5882.321 a5760.734 a5767.202 a5881.144 a5764.747 a5750.72 a5866.556 a5877.998 a5877.998 a5767.067 a5781.95 a5728.578 a5831.551 a5799.78 a5865.949 a5821.887 a5748.69 a5798.196 a5847.018 a5881.102 a5700.948 a5847.842 a5747.842 a5772.491 a5690.815 a5760.199 a5724.697 a5768.333 a5879.408 a5656.456 a5656.92 a5847.093
135
Table 7.17: New lines of Praseodymium I ( laser excited lines). λ/Å 5656.456 5665.099 5665.232 5667.222 5673.320 5673.887 5679.500 5679.600 5679.660 5679.810 5683.463 5684.634 5684.870 5686.675 5686.913 5693.336 5693.472 5698.130 5702.772 5704.728 5715.200 5728.578 5729.967 5736.026 5736.138 5736.380 5736.700 5741.069 5741.900 5743.208 5744.870 5750.355 5750.573 5750.669 5750.770 5759.690 5759.838 5763.428 5768.002 5769.526 5781.650 5783.485 5790.320 5791.621 5792.823 5793.305 5797.410 5797.683
even 9/2 11/2 7/2 7/2 11/2 11/2 11/2 15/2 7/2 9/2 5/2 15/2 11/2 9/2 13/2 11/2 3/2 11/2 7/2 15/2 9/2 9/2 15/2 9/2 11/2 7/2 13/2 7/2 9/2 7/2 7/2 13/2 9/2 7/2 17/2 11/2 9/2 9/2 5/2 7/2 13/2 21/2 15/2 9/2 7/2 9/2 13/2 9/2
J values odd 11/2 9/2 5/2 9/2 13/2 11/2 13/2 13/2 7/2 11/2 5/2 13/2 13/2 11/2 15/2 9/2 5/2 13/2 7/2 13/2 9/2 11/2 15/2 7/2 13/2 9/2 13/2 9/2 9/2 5/2 9/2 15/2 7/2 7/2 17/2 11/2 9/2 9/2 7/2 5/2 11/2 19/2 13/2 9/2 7/2 11/2 13/2 7/2
136
Level energies/ cm-1 even odd 32402.88 14728.9 29377.64 11730.6 11274.18 28920.81 30461.52 12821.08 10904.07 28525.57 9268.75 26888.46 12234.62 29836.92 8363.91 25965.9 8013.14 25614.98 12746.23 30347.57 28731.57 11141.58 12250.56 29836.92 9268.75 26854.43 8320.29 25900.35 10470.3 28049.72 28889.23 11329.71 11361.74 28920.81 10904.07 28448.81 12049.36 29579.88 12250.56 29775.02 32402.88 14910.53 31677.75 14226.25 14221.3 31668.54 11549.61 28978.45 12234.62 29663.12 11869.28 29297.11 10423.68 27850.47 9918.17 27331.71 30232.08 12821.08 11668.79 29075.83 14045.87 31447.88 13654.55 31039.96 8320.29 25705.13 11274.18 28658.67 14302.87 31687.07 6313.25 23670.45 10920.38 28277.21 12746.23 30092.24 11646.26 28978.45 11472.35 28800.01 7630.17 24921.47 12665.07 29950.75 13146.6 30411.98 14186.36 31447.88 12321.92 29579.88 8643.83 25900.35 9464.46 26708.78 5822.754 26066.25
λ/Å 5797.960 5799.780 5806.940 5807.768 5807.807 5810.134 5810.243 5819.800 5825.442 5826.155 5826.377 5828.948 5828.990 5830.850 5831.551 5831.661 5834.904 5843.780 5847.885 5853.041 5863.629 5865.949 5866.556 5871.613 5871.622 5877.052 5878.408 5884.383 5886.623 5910.736 5911.973 5919.864 5923.096 5923.375 5938.696
even 11/2 11/2 9/2 5/2 11/2 7/2 17/2 17/2 11/2 7/2 11/2 9/2 11/2 9/2 9/2 9/2 11/2 7/2 15/2 7/2 15/2 11/2 7/2 11/2 7/2 5/2 9/2 15/2 13/2 11/2 9/2 15/2 9/2 5/2 11/2
J values odd 13/2 9/2 11/2 7/2 11/2 5/2 15/2 19/2 13/2 7/2 9/2 7/2 9/2 11/2 9/2 7/2 13/2 9/2 17/2 7/2 17/2 11/2 5/2 13/2 5/2 3/2 9/2 13/2 13/2 11/2 11/2 15/2 11/2 7/2 11/2
137
Level energies/ cm-1 even odd 11282.87 28525.57 31771.68 14534.42 14897.77 32113.71 11646.26 28859.8 9675.04 26888.46 11869.28 29075.83 12736.67 29942.88 14302.87 31480.85 13250.69 30411.98 8013.14 25172.3 28889.17 11730.6 30772.44 13621.41 9483.54 26634.4 31874.35 14728.9 31677.75 14534.42 8029.28 25172.3 13872.29 31005.72 30461.52 13353.89 12804.49 29899.98 11472.35 28552.75 14221.3 31270.87 31771.68 14728.9 31005.7 13964.63 32373.84 15347.43 12049.36 29075.83 14836.02 31846.63 32402.88 15396.17 32336.86 15347.43 16069.9 33052.85 14981.54 31895.22 12519.72 29429.86 14780.94 31668.54 15016.89 31895.22 8737.448 25614.98 15061.17 31895.22
Table 7.18: New lines of Praseodymium I (Lines classified via LIF). λ/Å 3802.529 3824.588 3982.699 4072.799 4117.017 4150.889 4225.52 4236.127 4250.68 4336.353 4338.18 4349.641 4364.26 4376.103 4379.694 4415.003 4417.639 4437.925 4438.8 4442.15 4450.08 4450.129 4455.341 4471.95 4495.111 4540.626 4551.979 4553.92 4564.33 4675.1 4690.531 4693.696 4717.31 4719.51 4742.14 4744.043 4751.248 4756.388 4758.435 4768.451 4783.910 4792.985 4799.307 4834.405 4840.735 4854.82 4858.884 4867.282 4868.28 4875.431 4890.625 4901.945 4911.347
even 9/2 11/2 13/2 9/2 11/2 9/2 11/2 13/2 11/2 13/2 11/2 11/2 15/2 11/2 13/2 11/2 11/2 5/2 9/2 15/2 11/2 11/2 11/2 13/2 15/2 7/2 11/2 9/2 11/2 11/2 9/2 15/2 9/2 9/2 1/2 9/2 7/2 11/2 15/2 7/2 15/2 9/2 9/2 15/2 9/2 15/2 11/2 7/2 13/2 9/2 13/2 11/2 9/2
J values odd 11/2 13/2 13/2 7/2 9/2 11/2 13/2 15/2 13/2 13/2 13/2 13/2 17/2 11/2 11/2 13/2 11/2 7/2 9/2 17/2 9/2 13/2 11/2 11/2 13/2 7/2 9/2 7/2 9/2 9/2 7/2 13/2 9/2 7/2 3/2 9/2 7/2 9/2 13/2 7/2 13/2 9/2 7/2 15/2 9/2 13/2 11/2 7/2 13/2 9/2 15/2 13/2 11/2
138
Level energies/ cm-1 even odd 5822.89 32113.71 4866.53 31005.72 7951.35 33052.85 4432.24 28978.45 4866.53 29149.11 8029.28 32113.71 4866.53 28525.6 7951.35 31551.17 6892.95 30411.98 7951.35 31005.72 6313.25 29357.87 4866.53 27850.47 8363.91 31270.9 9268.75 32113.71 6603.63 29429.86 6714.22 29357.9 9483.54 32113.71 6451.72 28978.45 30772.4 8250.17 8765.57 31270.87 4866.53 27331.71 6892.95 29357.9 9675.04 32113.71 7630.17 29985.52 8765.57 31005.72 6535.53 28552.75 4866.53 26828.84 32402.88 10499.9 6892.95 28795.82 6892.95 28277.21 5822.89 27136.47 8363.91 29663.12 30772.44 9579.832 4432.24 25614.98 10765 31846.6 32402.88 11329.71 7617.44 28658.67 6313.25 27331.71 8765.57 29775.02 8013.14 28978.45 8765.57 29663.12 4432.24 25290.22 8029.28 28859.8 8363.91 29043.2 30232.08 9579.832 8765.57 29357.9 6313.25 26888.46 8013.14 28552.75 10470.3 31005.7 8643.83 29149.11 6603.63 27045.19 9268.75 29663.12 31677.75 11322.42
λ/Å 4928.421 4929.442 4941.173 4949.442 4954.122 4968.944 4999.723 5012.058 5012.314 5019.26 5028.688 5029.449 5045.063 5049.656 5051.12 5060.65 5069.835 5083.612 5086.854 5110.84 5133.603 5135.382 5141.825 5192.438 5193.721 5196.209 5196.542 5220.492 5235.833 5239.225 5239.807 5240.186 5241.513 5260.827 5270.807 5273.979 5277.908 5288.671 5292.236 5293.003 5304.099 5304.127 5314.565 5317.355 5325.856 5329.284 5332.279 5345.563 5351.464 5364.245 5365.039 5368.712 5369.215 5397.292 5400.627
even 13/2 9/2 9/2 13/2 11/2 19/2 11/2 11/2 15/2 15/2 11/2 13/2 11/2 11/2 9/2 9/2 13/2 11/2 11/2 17/2 11/2 9/2 13/2 5/2 9/2 13/2 9/2 3/2 13/2 11/2 7/2 11/2 9/2 9/2 13/2 7/2 7/2 13/2 13/2 13/2 15/2 7/2 11/2 9/2 11/2 11/2 19/2 13/2 15/2 7/2 9/2 7/2 13/2 13/2 17/2
J values odd 11/2 7/2 7/2 13/2 13/2 17/2 11/2 11/2 13/2 13/2 9/2 11/2 13/2 9/2 7/2 7/2 11/2 9/2 13/2 15/2 9/2 9/2 13/2 7/2 7/2 13/2 11/2 5/2 15/2 11/2 7/2 11/2 11/2 7/2 11/2 9/2 7/2 13/2 15/2 13/2 15/2 7/2 11/2 11/2 13/2 13/2 17/2 15/2 15/2 7/2 7/2 9/2 15/2 11/2 15/2
139
Level energies/ cm-1 even odd 6603.63 26888.46 30730.55 10449.94 8320.29 28552.75 9464.46 29663.12 9483.54 29663.12 11151.49 31270.87 6892.95 26888.46 9483.54 29429.86 10466.73 30411.98 9745.42 29663.12 8268.75 29149.11 10470.3 30347.57 6892.95 26708.78 29377.644 9579.832 5822.89 25614.98 9105.017 28859.8 10266.51 29985.52 9483.54 29149.11 6313.25 25965.9 11714.38 31275.18 9675.04 29149.11 5822.89 25290.22 11562.79 31005.72 6451.72 25705.13 29698.57 10449.94 10423.68 29663.12 4432.24 23670.45 9650.06 28800.01 7951.35 27045.19 10904.07 29985.52 6535.53 25614.98 13035.73 32113.71 10356.71 29429.86 29453.07 10449.94 13146.6 32113.71 31005.71 12049.95 9918.17 28859.8 7951.35 26854.43 7951.35 26841.65 12118.11 31005.72 8363.91 27212.01 9704.75 28552.75 4866.53 23670.45 11184.41 29985.52 12234.62 31005.72 10904.07 29663.12 11151.49 29899.98 7630.17 26332.07 8363.91 27045.19 6535.53 25172.3 4432.24 23066.25 8013.14 26634.4 10423.68 29043.2 11462.86 29985.52 10531.98 29043.2
λ/Å 5419.594 5422.689 5428.396 5442.053 5471.244 5475.211 5479.535 5480.506 5482.024 5483.372 5497.329 5498.378 5499.821 5511.458 5530.214 5541.292 5554.772 5556.943 5563.288 5584.664 5606.393 5614.743 5621.647 5625.723 5631.954 5640.558 5650.707 5650.809 5663.88 5690.815 5728.377 5737.618 5741.603 5750.355 5750.62 5753.05 5753.07 5856.154 5857.699 5859.593 5898.471 5961.296 6283.526
even 15/2 9/2 15/2 13/2 9/2 13/2 9/2 11/2 17/2 11/2 17/2 9/2 11/2 9/2 5/2 11/2 7/2 9/2 11/2 13/2 15/2 11/2 9/2 13/2 11/2 9/2 7/2 7/2 11/2 15/2 17/2 13/2 9/2 13/2 9/2 13/2 13/2 17/2 13/2 9/2 9/2 15/2 7/2
J values odd 15/2 11/2 17/2 13/2 11/2 13/2 11/2 11/2 19/2 13/2 17/2 9/2 13/2 11/2 7/2 11/2 7/2 9/2 13/2 15/2 17/2 9/2 11/2 15/2 11/2 9/2 7/2 9/2 11/2 15/2 19/2 11/2 11/2 15/2 9/2 15/2 15/2 15/2 11/2 7/2 11/2 15/2 7/2
140
Level energies/ cm-1 even odd 8765.57 27212.01 11549.61 29985.52 11483.45 29899.98 12041.67 30411.98 11713.22 29985.52 10266.51 28525.57 8643.83 26888.46 13872.29 32113.71 11714.38 29950.75 12180.13 30411.98 11714.38 29899.98 30232.08 12049.95 12234.62 30411.98 13974.73 32113.71 28731.57 10654.11 11944.2 29985.52 7617.44 25614.98 8643.83 26634.4 13035.73 31005.72 12041.67 29942.88 13439.04 31270.87 8829.09 26634.4 9105.017 26888.46 13897.98 31668.54 12234.62 29985.52 9105.017 26828.84 8013.14 25705.13 8013.14 25704.81 8829.09 26479.97 32336.86 14769.55 14028.75 31480.85 9464.46 26888.46 30772.44 13360.53 13654.55 31039.96 8320.29 25704.81 13897.98 31275.18 9464.46 26841.65 9770.33 26841.65 6603.63 23670.45 8643.83 25705.13 31677.75 14728.9 14780.94 31551.17 9704.75 25614.98
Table 7.19: Classification of known and unclassified lines of Praseodymium I by laser excitation. λ/Å 5681.908 5685.550 5686.439 5686.600 5690.975 5691.051 5691.055 5691.076 5698.037 5704.282 5714.574 5733.227 5735.055 5747.842 5749.434 5750.728 5751.944 5753.217 5753.386 5755.43 5764.232 5768.329 5768.800 5772.491 5774.439 5785.336 5785.468 5785.910 5795.140 5798.143 5798.920 5799.095 5807.588 5847.620 5856.149 5859.680 5868.643 5882.059 5884.150 5886.623 5887.799 5899.028 5899.66 5906.270 5913.005
even 11/2 11/2 13/2 13/2 11/2 11/2 13/2 15/2 13/2 7/2 9/2 9/2 7/2 15/2 13/2 7/2 11/2 9/2 11/2 13/2 7/2 9/2 15/2 15/2 9/2 13/2 7/2 7/2 9/2 17/2 13/2 9/2 17/2 15/2 11/2 9/2 11/2 9/2 13/2 13/2 9/2 15/2 13/2 7/2 15/2
J values
Level energies/ cm-1 even odd 12180.13 29775.04 10904.07 28487.66 9464.46 27045.19 11462.86 29043.2 28889.23 11322.42 16121.23 33687.8 10470.3 28036.94 8765.57 26332.07 12118.11 29663.12 11274.18 28800.01 29698.57 12204.3 30356.67 12919.18 9704.75 27136.47 32336.86 14943.85 12041.67 29429.86 31005.7 13621.41 29377.64 11997.08 30730.55 13353.89 13035.73 30411.98 28032.99 10668.96 16344.21 33687.8 32402.88 15071.65 14221.3 31551.17 32336.86 15018.14 30232.08 12919.18 15772.56 33052.85 11869.28 29149.11 11274.18 28552.72 8029.28 25280.4 14028.75 31270.87 12118.11 29357.9 12746.23 29985.52 12736.67 29950.75 9745.42 26841.65 8829.09 25900.35 8643.82 25704.81 13376.99 30411.98 30356.67 13360.53 13654.55 30644.64 16069.9 33052.85 14468.31 31447.88 30283.14 13335.86 10266.51 27212.01 11869.28 28795.82 13439.04 30346.23
odd 13/2 13/2 15/2 15/2 11/2 9/2 13/2 15/2 13/2 5/2 11/2 7/2 7/2 17/2 11/2 7/2 11/2 9/2 13/2 15/2 9/2 9/2 15/2 13/2 7/2 13/2 9/2 7/2 11/2 17/2 13/2 11/2 19/2 15/2 11/2 9/2 13/2 11/2 13/2 13/2 9/2 13/2 15/2 9/2 17/2
141
Table 7.20: Classification of known and unclassified lines of Praseodymium I by detection of LIF. λ/Å 3248.724 3468.666 3698.719 3874.796 3918.909 4091.112 4096.853 4137.501 4144.680 4285.815 4338.238 4339.614 4344.961 4349.657 4377.847 4435.253 4465.968 4537.133 4577.000 4585.935 4601.125 4643.002 4649.744 4656.768 4665.947 4699.649 4700.622 4706.258 4739.842 4772.500 4820.512 4836.008 4839.350 4860.176 4868.275 4876.216 4919.625 4949.734 4967.866 4987.609 5001.586 5028.300 5080.923 5110.841 5134.009 5150.314 5161.719 5177.399 5207.863 5219.102 5255.779
even 9/2 11/2 11/2 11/2 13/2 13/2 13/2 13/2 9/2 9/2 7/2 9/2 9/2 11/2 11/2 7/2 7/2 13/2 11/2 13/2 13/2 7/2 17/2 9/2 7/2 11/2 9/2 7/2 13/2 13/2 17/2 11/2 9/2 13/2 13/2 11/2 11/2 15/2 15/2 9/2 11/2 9/2 7/2 17/2 13/2 17/2 17/2 11/2 15/2 7/2 11/2
J values odd 9/2 9/2 11/2 11/2 11/2 15/2 13/2 11/2 7/2 9/2 7/2 7/2 11/2 9/2 9/2 5/2 5/2 11/2 13/2 11/2 13/2 9/2 17/2 11/2 9/2 11/2 9/2 7/2 15/2 13/2 17/2 11/2 7/2 15/2 13/2 11/2 9/2 15/2 13/2 9/2 13/2 9/2 9/2 15/2 15/2 15/2 17/2 9/2 13/2 7/2 13/2
142
Level energies/ cm-1 even odd 30772.44 0 4866.53 33687.8 4866.53 31895.22 6313.25 32113.71 6603.63 32113.71 6603.63 31039.96 6603.63 31005.72 7951.35 32113.71 4432.24 28552.75 5822.89 29149.11 6535.53 29579.88 5822.754 28859.8 9105.017 32113.71 6313.25 29297.11 6313.25 29149.11 6535.53 29075.83 6535.53 28920.81 7951.35 29985.52 4866.53 26708.78 7630.17 29429.86 7630.17 29357.9 7617.44 29149.11 9770.33 31270.87 4432.24 25900.35 31005.71 9579.832 10841.48 32113.71 8029.28 29297.11 7617.44 28859.8 7951.35 29043.2 9464.46 30411.98 10531.98 31270.87 9765.04 30347.57 8320.29 28978.45 10470.3 31039.96 10470.3 31005.72 9483.54 29985.52 6313.25 26634.4 9745.42 29942.88 8363.91 28487.66 9105.017 29149.11 9675.04 29663.12 5822.89 25704.81 31005.71 11329.71 11714.38 31275.18 10470.3 29942.88 10531.98 29942.88 10531.98 29899.98 28889.17 9579.832 10466.73 29663.12 9704.75 28859.8 8829.09 27850.47
λ/Å 5281.561 5381.658 5388.161 5439.161 5444.555 5484.391 5522.750 5554.090 5664.331 5689.099 5699.118 5860.705 5899.978 5913.005 6014.185 6057.518 6143.398 6248.248
even 15/2 15/2 11/2 13/2 11/2 17/2 13/2 11/2 15/2 13/2 15/2 15/2 13/2 15/2 5/2 15/2 19/2 7/2
J values odd 13/2 15/2 13/2 15/2 13/2 15/2 13/2 9/2 17/2 15/2 17/2 13/2 13/2 17/2 5/2 15/2 17/2 9/2
143
Level energies/ cm-1 even odd 11483.45 30411.98 10466.73 29043.2 11282.87 29836.92 11562.79 29942.88 9675.04 28036.94 11714.38 29942.88 10423.68 28525.57 8829.09 26828.84 12250.56 29899.98 13467.46 31039.96 12804.49 30346.23 15994.81 33052.85 13467.46 30411.98 13439.04 30346.23 28731.57 12108.89 13439.04 29942.88 13626.85 29899.98 9704.75 25704.81
References [1] McMillan. E., Grace. N. S., Phys. Rev. 44, 949 (1933) [2] Gisolf and Zeeman, Nature 132, 566 (1933) [3] Schmidt. T., Z. Phys. 121, 63 (1943) [4] Klinkenberg . P. F.A., Van Den Berg G. J., and Van Den Bosch J. C., Physica, 16, 861 (1952) [5] Van Den Berg G. J., Klinkenberg . P. F.A., and Van Den Bosch J. C., Physica, 18, 221 (1952) [6] Kamei. T., Phys. Rev., 99, 789 (1955) [7] Moore, C. E.,Atomic Energy Levels, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. (U. S.) 35, Vol. I, Vol. II, Vol. III (1971). (Reprint of NBS Circ. 467, originally issued in 1949, 1952, and 1958). [8] Murakawa. K., J. Phys. Soc. Japan, 17, 891 (1962) [9] Büttgenbach. S., Meisel. G., Z. Phys. 244, 149 (1971) [10] Bürger. K. H., Büttgenbach. S., Dicke. R., Gebauer. H., Kuhnen. R., and Träber. F., Z. Phys. 298, 159 (1980) [11] Salih. S., Duquette. D. W., Lawler. J. E., Phys. Rev. A. 27, 1193 (1982) [12] Duquette. D. W., Doughty. D. K., Lawler., Phys. Lett. A. 99, 307 (1983) [13] Persson. J., Berzinsh. U., Nilsson. T., Gustafsson. M., Z. Phys. D 23, 67 (1991) [14] Wännsto(e)m. A., Gough. D. S., and Hannaford. P., Z. Phys. D., 22, 723 (1992) [15] Berzinsh. U., Gustafsson. M., and Persson. J., Z. Phys. D 27, 155 (1993) [16] Nisar., A. Z. Phys. D 41, 159 (1997) [17] Fivet, W. et al. Euro. Phys. J. D. 37, 29 (2006) [18] Guthöhrlein, G. H., Mocnik, H., Windholz, L. Z. Phys. D 35, 177 (1995) [19] Guthöhrlein, G. H., Windholz, L. Z. Phys. D 27, 343 (1993) [20] Guthöhrlein, G. H., Helmrich, G., Windholz, L. Phys. Rev. A 49, 120 (1994) [21] Hammerl. H., Guthöhrlein, G. H., Elantkovska. M., Funtov. V., Gewhenberger. G., Windholz, L. Z. Phys. D. 33, 97 (1995)
144
[22] Mocnik, H., Arcimowicz, B., Salmhofer, W., Windholz, L. Guthöhrlein, G. H., Z. Phys. D 36, 129 (1996) [23] Huss, A., Windholz, L. Europhysics Conference Abstract 20D, 142 Abstract A4-68 (1996) [24] Jaritz, N., Messnarz, D., Engleman Jr, R., Jäger, H., Guthöhrlein, G. H., Windholz, L., Europhysics Conference Abstracts 27B, S.193 (2003) [25] Windholz, L. Guthöhrlein, G. H., Physica scripta T 105, 55 (2003) [26] Messnarz, D., Jaritz, N., Arcimowicz, B. Zilio, V.O., Engleman Jr., R., Pickering, J.C., Jäger, H., Guthöhrlein, G. H., Windholz, L. Physica Scripta 68, 170 (2003) [27] Arcimowicz. B., J. Eur. Phys. D 13, 187 (2001) [28] Jaritz, N., Guthöhrlein, G. H., Windholz, L., Messnarz, D., Engleman Jr., R., Physica Scripta 71, 611 (2005) [29] Jaritz, N., Windholz, L., Messnarz, D., Jäger, H., , Engleman Jr., R., Pickering, J.C., Jäger, H., Physica Scripta 69, 441 (2004) [30] Windholz, L., Jaritz, N., Zaheer, U. Farroq, M., Guthöhrlein, G. H., Arcimowicz, B. Engleman Jr., R., Pickering, J.C., Jäger, H., Egas Conference 37, 291, S2:3, 50(2005) [31] Brown, B, M. and Tomboulian, D. H. , Phys. Rev. 88, 1158 (1952) [32] Wyrat, J, F., Optica pura y aplicada 10, 177 (1977) [33] Wyrat, J, F., and Blaise, J., Physica Scripta 42, 209 (1990) [34] Dembczynski. J. Arcimowicz. B. Guthöhrlein, G. H., Windholz, L., Z. Phys. D 39, 143 (1997) [35] Messnarz. D. “Laser spektroskopische und parametrische analyse der Fein und Hyperfine struktur des Tanal Atoms und Tantal Ions” Dissertation, Wissenschaft Und Technik Verlag Berlin, ISBN 3-89685-390-6 (2001) [36] Zilio, V.O. and Pickereing , J. C., Mon. Not. Astron. Soc. 334(1), 48, (2002) [37] Eriksson et al., Physica Scripta 65, 480 (2002) [38] Messnarz, D. and Guthohrlein, G. H., Physica Scripta 67, 59 (2003) [39] Jaritz N., “Experimentelle Und Theoretische Untersuchung der Hyperfieinstruktur Von Tantal” Dissertation, Institute of Experimental Physics, Technical University Graz.
145
[40] Cowan. R. D. “The theory of Atomic structure and Spectra” University of California Press, Berkley 1981. PC version modified by Ralchenko Y. V. and Kramida A. E. Institute of Spectrosopy at Troitsk, Moscow. [41] Kröger S., Kröger M., Computer physics communications 90, 381, (1995) [42] White. H. E. Phys. Rev. 34, 1397-1403 (1929) [43] Rosen. N., Harrison. G. R., and McNally, Jr. J. R., Phys. Rev 60, 722 (1941) [44] Lew. H. Phys. Rev. 89, 530 (1953) [45] Brix. P., Phys. Rev. 89, 1245 (1953) [46] Baker. J. M. and Bleaney. B, Proc. Phys. Soc. London, Sect. A 68, 936 (1955) [47] Murakawa, K.,J. Phys. Soc. Japan 15, 2306 (1960) [48] Judd. B. R. Lindgren. I., Phys. Rev. 122, 1802 (1961) [49] Wybourne. B. G.„ J. Chem. Phys. 37, 1807 (1962) [50] Amado. Y. C., Phys. Rev. 126, 1004-1008 (1962) [51] Spector, N., J. Opt. Soc. Am. 54, 1359 (1964) [52] Reader. J., and Sugar. J., Phys. Rev. 137, 784 (1965) [53] Macfarlane. R. M., Burum. D. P., and Shelby. R. M., Phys. Rev. Lett 49, 636 (1982) [54] Ginibre, A. Physica Scripta 39, 6 (1989) [55] Iimura. H. Nakahara. Y., Ichikawa. S. , Kotani. K., Wakasugi. M., and Horiguchi. T., J. Phys. Soc. Jpn. 59, 4208 (1990) [56] Kim M. K.and Kachru. R., Phys. Rev. B 44, 9826 (1991) [57] Iimura. H., Nakahara. Y., Ichikawa. S., Kubota. M., and Horiguchi. T., Phys. Rev. C 50, 661 (1994) [58] Maosheng. L., et al, Phys. Rev. A 62, 052504 (2000) [59] Ramsey, N. F., “Nuclear moments” Wiley, New York (1953) [60] Edmond, A. R., “Angular momenta and Quantum Mechanics” Princeton Univ. Press, Princeton, New Jersey (1960) [61] Judd., B. R., “Operator techniques in Atomic Spectroscopy” McGrawHill, New York (1963)
146
[62] Sobel’man, I. I., “An introduction to the theory of atomic spectra” Pergamon, Oxford (1972) [63] Jackson, D. A., Kuhn, H., Proc. Roy. Soc. A 167, 205 (1938) [64] Ezekiel, S., Weiss, R., Phys. Rev. Lett. 20, 91 (1968) [65] Duong, H. T. et al. C. R. Acad. Sci. B 276, 909 (1973) [66] Brinkmann, U. Hartig, W., Telle, H., Walther, H., App. Phys. 5, 109, (1974) [67] Frisch, R., Z. Physik, 86, 42 (1933) [68] Ashkin, A., Phys. Rev. Lett. 25, 1321 (1971) [69] Jacquinot, P. et al., Opt. Comm. 8, 163 (1973) [70] Rabi. I. I. et al., Phys. Rev., 53, 318 (1938) [71] Rabi. I. I., Phys. Rev., 87, 379 (1952) [72] Marrus, R. McColn, D., Phys. Rev. Lett. 15, 813 (1965) [73] Bennett, W. R., Jr. Phys. Rev. 126, 580 (1962) [74] Lamb, W. E.. Jr. Phys. Rev. A 134, 1429 (1964) [75] Leven, M. D. Schawlow, A. L. Phys. Rev. A. 6, 10 (1972) [76] Hänsch, T. W. et al., Phys. Rev. Lett. 27, 707 (1971) [77] Borde. C., C. R. Acad. Sci. B 271, 371 (1970) [78] Schimoda, K., “High resolution laser spectroscopy”, Springer, New York (1976) [79] Penning, F. M., Physica 8, 137, (1928) [80] Kenty, C., Phys. Rev. 80, 95 (1950) [81] Meissner, K. W., Miller W. F. Phys. Rev. 92, 896 (1953) [82] Green, R. B., R. A. Keller, G. C. Luther, P. K. Schenck, and J. C. Travis, 1976, Appl. Phys. Lett. 29, 727 [83] Barbiere, B., Beverini, N., Rev. Mod. Phys. 62, 603 (1990) [84] King, D. Schenck, P. K., Smith, K. C., and Travis, J. C. Appl. Opt. 16, 2617 (1977) [85] Grandin, J. F., Husson, X. J. Phys. B 14, 433 (1981) [86] Caesar, T., and Huelly, J. L., J. Phys. C 44, 216 (1983) 147
[87] Skolnick, M. L., IEEE J. Quantum Electron. 6, 139 (1970) [88] Thomason, W. H., Elbers, D. C., Rev. Sci. Instrum. 46, 409, (1975) [89] Demtröder, W., "Laser Spectroscopy", Springer (1982) [90] Thorne, A. P., "spectrophysics", Chapman & Hall, London (1974) [91] White, H. E., "Introduction to atomic spectra", McGraw Hill (1934) [92] Kuhn, H. G., "Atomic Sepctra", Academic Press new York (1962) [93] Sobel’mann, I. I., Vanshtein, L. A., Yukov, E. A., "Excitation of atoms and broadenings of spectral lines" springer (1981) [94] Schüler, H., Z. Phys. 35, 323 (1926) [95] Schüler, H., Z. Phys. 59, 149 (1930) [96] Paschen, F., Ann. Phys. 18, 867 (1933) [97] Feldmann, D. Opt. Comm. 29, 67 (1979) [98] Miyazaki, K. et al. Phys. Rev. A 28, 2229 (1983) [99] Behrens, H. O. Guthohrlein. G. H., J. Phys. C7-44, 149 (1983) [100] Behrens, H. O., Guthohrlein. G. H., Kasper, A., J. Phys. C7-44, 239 (1983) [101] L. Windholz, G.H. Guth"hrlein, Physica Scripta T105, 55-60 (2003) [102] R. Peck, K. Reeder, J. Opt. Soc. Am. 62, 958 (1972) [103] Quiering, T., Universitat der Bundeswehr, Hamburg,: diploma thesis (1984) [104] Ginibre A. : Physica Scripta, 23, 206 (1981) [105] Ginibre A.: Thèse, Université de Paris Sud, Centre d’ Orsay (1988) [106] Böklen, K.D., Bossert T., Foerster W.: Z. Physik A 274, 195 (1975) [107] Reddy M.N., Rao G.N.: Physica C 150, 457 (1988) [108] Childs. W.J. and L. S. Goodman L. S.: Phys. Rev. A 24, 1342 (1981) [109] White H.E.: Phys. Rev. 34, 1397 (1929) [110] King A. S .: Astrophys. J. 68, 194 (1928) [111] Ginibre: Physica Scripta 39, 710 (1989) [112] T. Kuwamoto, et. Al. J. phys.soc. Japan 65, 3180 (1996)
148
