JOURNAL OF CHEMICAL PHYSICS
VOLUME 112, NUMBER 16
22 APRIL 2000
The KRb ground electronic state potential up to 10 Å C. Amiot and J. Verge`s Laboratoire Aime´ Cotton, Baˆtiment 505, Campus d’Orsay 91405, Orsay Cedex, France
共Received 21 December 1999; accepted 26 January 2000兲 High resolution spectra of the A 1 ⌺ ⫹ →X 1 ⌺ ⫹ system of the KRb molecule, obtained after excitation using a titanium-doped sapphire laser, were recorded on a Connes-type Fourier transform interferometer. Molecular constants of the first 88 vibrational levels of the X 1 ⌺ ⫹ state are determined, and the potential energy curve is derived up to an internuclear distance of 10.419 Å 共99.3% of the potential well depth兲. The energy of the dissociation limit is found as D e ⫽4217.3 (15) cm⫺1 共referred to the bottom of the potential curve well兲, in good agreement with the theoretical predictions of Jencˇ and Brandt 关J. Mol. Spectrosc. 154, 226 共1992兲兴 who gave D e ⫽4220 (20) cm⫺1 and the value D e ⫽4217.4 (8) cm⫺1 reported by Kasahara et al. 关J. Chem. Phys. 111, 8857 共1999兲兴. © 2000 American Institute of Physics. 关S0021-9606共00兲01015-1兴
I. INTRODUCTION
vibrational and the rotational quantum numbers, respectively. Doppler-free optical–optical double resonance polarization spectroscopy of the B 1 ⌸ u state was performed at high resolution by Okada et al.8 Accurate molecular constants were dwived for this B 1 ⌸ state, up to v ⫽12, and the 共RKR兲 Rydberg–Klein–Rees potential energy curve was calculated. Numerous local perturbations were discovered in these spectra and the perturbing electronic states were characterized. Radiative lifetimes and collisional cross sections of the fluorescence quenching were also determined in this work. Quite recently the first two excited 1 ⌸ states were investigated by Kasahara et al.9 using Doppler-free optical– optical double resonance polarization spectroscopy. We have also studied by Fourier spectroscopy the two systems (3) 1 ⌸→(3) 1 ⌺ 共Ref. 10兲 and (3) 1 ⌸→(2) 1 ⌸. 11 From a theoretical point of view the KRb molecule was studied through four methods:
The KRb molecule spectroscopy is of particular interest for two main reasons: 共i兲
共ii兲
the dissociation channels K(4s)⫹Rb(5s) and K(4p)⫹Rb(5p) of the first excited atomic states are in close proximity since the energies of the four asymptotes are, in increasing order of magnitude, 12 578.96 cm⫺1 共Rb: 5p 2 P 1/2), 12 816.56 cm⫺1 共Rb: 5 p 2 P 3/2), 12 985.17 cm⫺1 共K: 4p 2 P 1/2), and 13 042.89 cm⫺1 共K: 4p 2 P 3/2). Hence, the coupling between the electronic states calculated with these limits is expected to be large. This fact was confirmed by calculations of Bussery and Aubert-Fre´con,1 of Patil and Tang,2 and quite recently of Marinescu and Sadeghpour.3 These calculations gave dispersion forces coefficients much larger for KRb than for any of the nine other heteronuclear alkali diatomic molecules; By examining the excited long-range Hund’s case 共c兲 molecular states of the ten such molecules which support bound states and can be probed by ultracold photoassociative spectroscopy, Wang and Stwalley4 found that the KRb system has very favorable Franck–Condon factors for the photoassociation process. Also, the collisions of unlike alkali–metal atoms can be driven by much shorter range van der Waals forces.
共i兲
共ii兲 共iii兲
Only a few spectroscopic studies on the electronic states of KRb have been so far reported. A long time ago Walter and Baratt5 observed a molecular band at 495.9 nm while diffuse bands at 597, 586.7, and 569 nm were reported by Beuc et al.6 The first high resolution study of the ground state was reported by Ross et al.7 In their study the A 1 ⌺ ⫹ →X 1 ⌺ ⫹ system was excited using a titanium sapphire laser. Subsequent fluorescence spectra were recorded with a Bomem Fourier transform spectrometer using a resolution of 0.045 cm⫺1. Rotational and vibrational constants were reported, covering the range v ⫽0 – 44 and J⫽28– 141 for the 0021-9606/2000/112(16)/7068/7/$17.00
共iv兲
7068
the generalized reduced potential curve method 共GRPC兲 was set up by Jencˇ and Brandt12,13 and by Bludsky et al.14 who derived previsional ground state potential curves for several guesses of the dissociation energy value; approximate ground state spectroscopic constants for nonsymmetric alkali molecules were obtained by Cavalie`re et al.15 by interpolation methods; ab initio calculations of the electronic states correlated with the first four excited separate atomic limits were reported by Leininger and Jeung,16 focusing on the weakly coupled (1) 1 ⌸ and (2) 1 ⌸ twin states. Improvements of these results were later published by Leininger et al.17 and by Yiannopoulou et al.;18 long range studies and calculation of dispersion coefficients have been, as mentioned above, reported by Bussery and Aubert-Fre´con,19 by Patil and Tang,2 and by Marinescu and Sadeghpour.3 New experimental studies on the ground and excited states are clearly desirable in order to extend the first preliminary experimental determinations and to confirm and improve the predicted theoretical results. In particular, © 2000 American Institute of Physics
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J. Chem. Phys., Vol. 112, No. 16, 22 April 2000
FIG. 1. Part of the 39K85Rb A⫺X fluorescence spectrum when the exciting laser radiation is set at 790.244 nm. The observed fluorescence series J ⬘ , v ⬙ are issued from an upper level with J ⬘ ⫽51.
knowledge highly complete as possible of the ground state should include larger internuclear distances. In this article we report on the laser induced fluorescence of the transition A 1 ⌺ ⫹ →X 1 ⌺ ⫹ recorded as high resolution Fourier transform spectra. The article is organized as follows. The experimental apparatus and procedures are described in Sec. II. The spectroscopic analysis, involving purely empirical fits, and near-dissociation expansions 共Le Roy’s methods兲 are treated in Sec. III. Section IV deals with the discussion of the results before concluding in the last section.
KRb ground electronic state potential
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FIG. 2. Part of the 39K85Rb A⫺X fluorescence spectrum when the exciting laser radiation is set at 783.212 nm. Three main series are observed with upper J ⬘ equal to 33, 82, and 72.
portion of the fluorescence spectrum when the laser is set at 783.212 nm. Three different series are visible where the Franck–Condon oscillation is evident for the series with J ⬘ ⫽33. A number of 7935 values of wave numbers were used, including 271 values observed in the low v measurements by Ross et al.7 and added to the present work data set 共7664 lines兲. The relative spectral positions of the lines were measured with a typical relative accuracy better than 0.002 cm⫺1. These transition frequencies were arranged into 207 fluorescence series spanning the vibrational range v ⫽0 to 87 for the ground state. They include 149 fluorescence series 共5819 lines兲 of 39K85Rb and 58 series 共1845 lines兲 of 39K87Rb. For each vibrational level, the range of associated rotational levels is indicated in Fig. 3. Levels with very low J values
II. EXPERIMENT
The KRb molecules were produced in a stainless steel heatpipe oven by heating a 1:4 mixture of potassium and rubidium metals 共99.95% K and 99.7% Rb from Aldrich Chemical Company兲 with 11 Torr of argon as a buffer gas. The temperature was kept at 570 K where the vapor pressures of Rb, Rb2, K and K2 are, respectively, 0.59, 0.003, 0.13, and 0.0004 Torr.20 Isolated A 1 ⌺ ⫹ →X 1 ⌺ ⫹ rovibrational transitions were excited by a cw single frequency titanium-doped sapphire laser 共Coherent 899-21兲 pumped by an argon–ion laser 共Spectra Physics 2080-155, all lines power: 18 W兲. The Ti:sa laser was operated with the shorter wavelength optics, the laser range then extending from 730 to 800 nm. The maximum delivered laser power was 2.3 W. The experimental arrangement was similar to the one described in a previous work;21 backwards fluorescence from the heat pipe was collected and focused on the entrance iris of the Fourier spectrometer. Spectra were recorded between 8000 and 13 000 cm⫺1 with a resolution of 0.015 cm⫺1 corresponding to the Doppler width at 10 000 cm⫺1. Two examples of spectra are depicted in Figs. 1 and 2. The first figure shows the series with the higher v value ( v ⫽87) when the laser is set at 790.244 nm. Figure 2 depicts a short
FIG. 3. The observed ( v ,J) data set for the two isotopic species 39K85Rb and 39K87Rb. For clarity the rotational relaxation data set is not depicted. The curve with triangles indicate the limit where the energy contribution of the CDC共6兲⫽Ov parameter is greater than 5⫻10⫺3 cm⫺1. Data at the right of this curve were discarded during the NDE analysis.
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J. Chem. Phys., Vol. 112, No. 16, 22 April 2000
TABLE I.
39
K85Rb Dunham Y lm coefficients 共in cm⫺1. Y 00 is calculated. m⫽0
l 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
C. Amiot and J. Verge`s
m⫽1 ⫺1
⫺0.015 706 11⫻10 75.845 773 ⫺0.229 708 36 ⫺0.499 131 67⫻10⫺3 0.204 381 80⫻10⫺4 ⫺0.265 856 54⫻10⫺5 0.182 325 03⫻10⫺6 ⫺0.868 251 54⫻10⫺8 0.294 531 55⫻10⫺9 ⫺0.729 102 75⫻10⫺11 0.133 281 36⫻10⫺12 ⫺0.180 081 79⫻10⫺14 0.177 786 74⫻10⫺16 ⫺0.124 742 54⫻10⫺18 0.589 602 27⫻10⫺21 ⫺0.168 679 99⫻10⫺23 0.222 053 75⫻10⫺26
m⫽2 ⫺1
⫺0.387 129⫻10 ⫺0.311 635⫻10⫺9 ⫺0.235 961⫻10⫺11 0.105 414⫻10⫺11 ⫺0.152 375⫻10⫺12 0.102 533⫻10⫺13 ⫺0.391 659⫻10⫺15 0.885 800⫻10⫺17 ⫺0.117 392⫻10⫺18 0.8406 66⫻10⫺21 ⫺0.251 248⫻10⫺23
0.381 468 93⫻10 ⫺0.121 284 62⫻10⫺3 ⫺0.581 938 38⫻10⫺6 ⫺0.276 419 56⫻10⫺7 0.199 516 10⫻10⫺8 ⫺0.117 929 03⫻10⫺9 0.442 034 30⫻10⫺11 ⫺0.128 471 42⫻10⫺12 0.350 366 69⫻10⫺14 ⫺0.891 302 35⫻10⫺16 0.176 467 47⫻10⫺17 ⫺0.237 992 28⫻10⫺19 0.201 542 96⫻10⫺21 ⫺0.963 955 71⫻10⫺24 0.198 896 88⫻10⫺26
共down to J⫽6) are observed while the highest J is equal to 185, extending noticeably the previously reported7 data set. III. ANALYSIS AND RESULTS
The data representation and potential inversion have been the constant goals in the field of diatomic molecule spectroscopy: 共i兲
共ii兲
The data representation must summarize all the experimentally derived term energy values in as compact and accurate a manner as possible. All the extrapolation ability and the physical meaning of the calculated parameters must be ensured. In the following we describe the two data representations used in the present work: the Dunham-type procedure and the near-dissociation expansions 共NDE兲 procedure; for the potential inversion, i.e., the construction of a molecular potential energy curve based on the observed term values, the semiclassical Rydberg– Klein–Rees 共RKR兲 determination will be considered.
A. Dunham’s procedure: purely empirical fits
Any observed transition energy i can be expressed as the difference between the energies of the upper and lower levels
i ⫽E ⬘ 共 v ⬘ ,J ⬘ 兲 ⫺E ⬙ 共 v ⬙ ,J ⬙ 兲 ,
共1兲
where the energies for the upper state 共indicated with a prime兲 are considered as independant term energy values only characterized by the rotational quantum number J T J ⬘ ⫽E ⬘ 共 v ⬘ ,J ⬘ 兲 .
共2兲
The ground state rovibrational energies are represented by the conventional, double summation, Dunham-type expansion in terms of the vibrational v ⬙ and rotational J ⬙ quantum numbers, such as E 共 v ⬙ ,J ⬙ 兲 ⫽
Y lm 关 共 v ⬙ ⫹1/2兲兴 l 关 2 J ⬙ 共 J ⬙ ⫹1 兲兴 m . 兺 l,m
m⫽3 ⫺7
共3兲
m⫽4 ⫺13
0.421 276⫻10 0.390 483⫻10⫺14 ⫺0.800 759⫻10⫺15 0.767 980⫻10⫺16 ⫺0.386 945⫻10⫺17 0.968 831⫻10⫺19 ⫺0.797 472⫻10⫺21 ⫺0.135 757⫻10⫺22 0.340 442⫻10⫺24 ⫺0.234 985⫻10⫺26 0.392 960⫻10⫺29
⫺0.1585⫻10⫺18 ⫺0.8360⫻10⫺19 0.2044⫻10⫺19 ⫺0.2415⫻10⫺20 0.1592⫻10⫺21 ⫺0.6302⫻10⫺23 0.1534⫻10⫺24 ⫺0.2268⫻10⫺26 0.1888⫻10⫺28 ⫺0.6862⫻10⫺31
共From now on double prime will be removed from the ground state quantum numbers v ⬙ and J ⬙ .) The number is the isotopic reduced mass. This formula is often recast into the form
兺m K m共 v 兲关 2 J 共 J⫹1 兲兴 m ,
共4兲
兺l Y lm 关 共 v ⫹1/2兲兴 l ,
共5兲
E 共 v ,J 兲 ⫽ with K m共 v 兲 ⫽
where K 0 ( v )⫽G v is the vibrational energy, K 1 ( v )⫽B v is the inertial rotational constant, and K 2 ( v )⫽⫺D v , K 3 ( v ) ⫽H v , K 4 ( v )⫽L v ,... are the centrifugal distortion constants 共CDCs兲 of successive orders. The following atomic masses were used:22 39K: 38.963 7069, 85Rb: 84.911 7924; 87Rb: 86.909 1858, leading to the reduced masses referred to that of the most abundant species 39K85Rb: ( 39K87Rb ⫽0.996 379 03) and ( 41K85Rb⫽0.983 139 45). The Dunham procedure establishes the relations between the Y lm coefficients and those a n parameters used in a power series expansion of the molecular potential about its equilibrium minimum V 共 R 兲 ⫽A
冋
共 R⫺R e 兲 Re
册冋 2
1⫹
册
兺n a n共共 R⫺R e 兲 /R e 兲 n ,
共6兲
R e being the equilibrium internuclear distance. But this potential inversion is no longer convergent when R is larger than 2R e . 23 A wide range of (l,m) coefficients was tested in the data fitting with respect to the criterion of accuracy. The most satisfactory fit was obtained with one for which m max ⫽4, so that B v , D v , H v , and L v constants were retained while the set of polynomial orders l max was varied from 6 to 14. The high interparameter correlation prevented the determination of higher order constants. The 7935 observed transitions are well reproduced, with a standard deviation of the errors equal to 0.0015 cm⫺1, i.e., a dimensionless standard deviation ¯ ⫽0.86. The empirical Dunham-type expansion
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J. Chem. Phys., Vol. 112, No. 16, 22 April 2000
KRb ground electronic state potential
Y lm parameters are reported in Table I. Although well suited for interpolation calculations these parameters have no great physical meaning and limited ability to extrapolate beyond the range of the observed data. B. Near-dissociation expansion theory
The limiting near-dissociation behavior of vibrational spacings of a diatomic molecule is determined by the asymptotically-dominant attractive inverse power term in its internuclear potential energy function. The potential energy curves close to their asymptotes are very asymmetrical and the properties of the vibrational levels near the dissociation limit depend strongly on the long-range tail of the interaction energy. At sufficiently large internuclear distance, when exchange effects are negligible, the long-range potential asymptotically has the simple inverse-power form Cn , V 共 R 兲 ⫽D e ⫺ Rn
共7兲
where D e is the energy of the molecular dissociation limit 共atomic spin–orbit averaged兲 referred to the bottom of the potential well and R is the internuclear distance. Le Roy, Bernstein,24–26 and Stwalley27,28 have derived the neardissociation limiting behavior of the above mentioned Eq. 共5兲 molecular parameters K m ( v ) 共noted with an ⬁ as superscript for indicating very large internuclear distances兲. For m⫽0 共vibration兲 we have K ⬁0 共 v 兲 ⫽D e ⫺X 0 共 n 兲关v D ⫺ v兴 2n/(n⫺2) ,
共8兲
and for m⭓1, 共rotation兲 ⬁ Km 共 v 兲 ⫽X m 共 n 兲关v D ⫺ v兴 [2n/(n⫺2)]⫺2m ,
共9兲
where v D is the effective vibrational index at dissociation. The X m (n) parameters are given by X m (n) n 2 1/(n⫺2) ¯ (n) / (C ) where is the molecular re⫽X 关 m n 兴 ¯ duced mass and X m (n) are known tabulated constants.24 The near-dissociation expansions are data representations incorporating the correct K m ( v ) behavior both near dissociation and all along the potential curve. Beckel et al.29 and Le Roy and co-workers30,31 developed the following expressions for the vibrational and rotational constants.
D e and v D . In the present case of alkali ground electronic states the power n is equal to 6, the leading term corresponding to the C 6 dispersion parameter. The following terms in Eq. 共7兲 correspond to the constants C 8 ,C 10 ... In this way the power t in Eq. 共11兲 is equal to zero so we used the following development for G v G v ⫽D e ⫺X 0 共 6 兲共 v D ⫺ v 兲 3 ⫻
t⫹ j 1⫹ 兺 M j⫽1 q t⫹ j z
,
共12兲
exp
兺
l⫽1
p lm 共 v D ⫺ v 兲 l .
共13兲
In particular, L
B v ⫽X 1 共 6 兲关v D ⫺ v兴
[2n/(n⫺2)]⫺2
exp
兺
l⫽1
p l1 共 v D ⫺ v 兲 l .
共14兲
Several nonlinear NDE least-squares fits have been done using the codes of Le Roy.32–34 Since the data for levels lying very close to dissociation are lacking, it would be unreasonable to expect to determine from NDE fits meaningful values for the constant X 0 (n) and for the parameters C n . Conversely for such fits to yield reliable extrapolations and realistic D e and v D values it is important to know a reasonable estimate of C n . Such estimates are then taken from theory.3 The present analysis clearly follows the same steps as those reported by Le Roy et al.:35 共i兲 共ii兲
共10兲
共11兲
with z⫽ v ⫺ v D . The power number s is set to either s⫽1 共development noted ‘‘outer’’ Pade´ expansion兲 or s⫽2n/(n ⫺2) 共‘‘inner’’ Pade´ expansion兲. The above G v expansion is well-behaved in the neighborhood of the highest observed vibrational levels and is much more reliable for extrapolation purposes. Fitting experimental data to those expansions will yield more realistic estimates of the extrapolation parameters
.
L
where 关 L/M 兴 is a ratio of polynomials or ‘‘Pade´’’ approximant defined as L p t⫹i z t⫹i 1⫹ 兺 i⫽1
关 1⫹q 1 共 v D ⫺ v 兲 ⫹...q M 共 v D ⫺ v 兲 M 兴
⬁ K m⭓1 共 v 兲 ⫽K m
G v ⫽D⫺K 0 共 v 兲关 L/M 兴 s
关 L/M 兴 ⫽
关 1⫹ p 1 共 v D ⫺ v 兲 ⫹... p L 共 v D ⫺ v 兲 L 兴
共ii兲 The rotational and higher-order centrifugal distortion parameters are developed in a second type of NDE development, termed an exponential expansion such that
共i兲 The vibrational expression becomes ⫽D e ⫺X 0 共 n 兲共 v D ⫺ v 兲 2n/n⫺2 关 L/M 兴 s ,
7071
共iii兲
Initial estimates of G v and B v values for the observed levels were taken from the global 共both isotopic species兲 Dunham analysis 共Table I兲; the vibrational G v and rotational B v values were fitted to Eqs. 共12兲 and 共14兲, respectively, to obtain estimates of the vibrational quantum number v D and dissociation energy D e . During the fits the leading long-range coefficient C 6 was fixed at its theoretical value 19.790 735 cm⫺1 Å.6 Although other choices would be possible the consideration of compactness and accuracy led to use the 关0,9兴 outer Pade´ expansion 关Eq. 共10兲 with s⫽1]. The first fit gave v D ⫽98.354 197 and D e ⫽4217.328(33) cm⫺1 . The largest observed residual was 0.004 cm⫺1 for the v ⫽85 level. To verify the model dependence of the above mentioned two parameters, an average procedure 共as described by Le Roy et al.36兲 was performed for up to ten development parameters. The averaged v D has a value of 98.1共5兲, in good agreement with the value found at the end of the procedure. D e becomes 4215.5 cm⫺1 but its uncertainty increased up to 1.5 cm⫺1. The v D and D e quantities obtained in the above described G v NDE analysis were held fixed together with the C 6 value in the subsequent B v NDE fits to Eq. 共14兲; an RKR potential energy curve was calculated from those NDE expansions parameters;
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C. Amiot and J. Verge`s
J. Chem. Phys., Vol. 112, No. 16, 22 April 2000
TABLE II. 39K85Rb parameters in the (N P⫽0/NQ⫽9) outer Pade´ G v NDE fit after the last iteration with constrained CDCs. The dissociation limit relative to v ⫽0, J⫽0 is equal to D 0 ⫽4179.4782 cm⫺1.
106 C6 cm⫺1 Å6 vD
De X 0 (6) cm⫺1 102 q 1 103 q 2 105 q 3 106 q 4 108 q 5 1010q 6 1012q 7 1015q 8 1018q 9
Parameter value
St. dev
19.790 735 97.958 660 1854 4217.3282 0.012 917 685 86
fixed 5.6⫻10⫺3 fixed fixed
⫺4.591 132 801 859 3.043 774 752 491 ⫺9.014 846 128 715 1.874 706 533 906 ⫺2.659 308 371 592 2.536 894 475 417 ⫺1.558 525 25 1962 5.571 123 526 533 ⫺8.805 528 436 486
1.4⫻10⫺4 1.3⫻10⫺5 6.2⫻10⫺7 1.8⫻10⫺8 3.2⫻10⫺10 3.7⫻10⫺12 2.7⫻10⫺14 1.1⫻10⫺16 2.0⫻10⫺19 FIG. 4. The 39K85Rb G v quantity as a function of v . The triangles show the NDE extrapolated points up to the dissociation limit.
共iv兲 共v兲
共vi兲
centrifugal distortion constants 共CDCs兲 共up to O v ) were calculated from this RKR curve using the program LEVEL6.0;33 the raw data were refitted after substracting the energy contributions of the CDCs (D v , H v ,...). The set was however limited in v and J, as indicated in Fig. 共3兲, so that the energy contributions of the higher order constant O v were always lower than 0.005 cm⫺1; an iterative procedure of steps 共iii兲–共v兲 was used until convergence was achieved. Only two iterations were necessary for such convergence.
The final NDE expansion parameters are reported in Tables II and III. Higher order fixed centrifugal distortion constants are summarized in Table IV of Ref. 37. The final f ⫽1.04 with an fit has a dimensionless standard error of ¯ experimental uncertainty of 0.0015 cm⫺1. This means that on average the differences between observed and calculated wave numbers are within these estimated uncertainties.
Using those final parameters reported in Table II the ⌬G v curve was constructed as a function of v and it is depicted in Fig. 4. The number of missing levels near dissociation is 10⫾1. The final G v and B v NDE parameters were taken as input for the RKR1 program.33 Table V of Ref. 37 lists the output of energies and turning points. For levels from v ⫽70 up 共with an inner turning point R ⫺ ⫽3.030 Å兲 the inner turning points were smoothed according to V 共 R ⫺ 兲 ⫽⫺538.346 962⫹0.260 556 426 ⫻107 exp共 ⫺2.103301R ⫺ 兲 , where V is expressed in cm⫺1 and R ⫺ in Å. IV. DISCUSSION
Two determinations of the ground state dissociation energy value were published previously: 共i兲
TABLE III. 39K85Rb parameters in the exponential B v NDE fit after the last iteration with constrained CDCs. The scaling factor SF defines CDC共6兲 proportional to 关CDC共5兲兴2/CDC共4兲. Parameter value 104 X 1 (6) 共cm⫺1兲 vD 103 p 1 103 p 2 104 p 3 105 p 4 107 p 5 108 p 6 1010p 7 1012p 8 1014p 9 1016p 10 1019p 11 1022p 12 SF
8.9023660 97.958660 ⫺7.121 707 919 504 2.595 383 339 197 ⫺3.170 971 380 832 1.845 287 169 219 ⫺6.700 605 923 596 1.653 578 754 206 ⫺2.858 621 531 959 3.472 045 571 617 ⫺2.905 982 844 250 1.596 611 763 206 ⫺5.183 542 791 498 7.535 574 216 240 ⫺0.038 028 675 055
St. dev fixed fixed 5.3⫻10⫺4 1.1⫻10⫺4 9.6⫻10⫺6 5.2⫻10⫺7 1.9⫻10⫺8 4.6⫻10⫺10 7.9⫻10⫺12 9.6⫻10⫺14 7.9⫻10⫺16 4.3⫻10⫺18 1.4⫻10⫺20 2.0⫻10⫺23 4⫻10⫺3
共15兲
共ii兲
A theoretical prediction by Jencˇ and Brandt13 based on the GRPC theory. The derived D e value of 4220 ⫾ 20 cm⫺1 is in good agreement with the one derived in the present work. Jencˇ and Brandt also reported the RKR potential curve turning points in the case where D e ⫽4220 cm⫺1. Figures 5 and 6 depict a comparison between these results and those derived in the present work. The agreement is quite satisfactory for the longrange part of the potential curve. A very nice experimental determination was reported by Kasahara et al.9 When exciting the 1 1 ⌸ state from the X state the authors observed a line broadening when the vibrorotational level was higher than v ⫽63, J⫽23. This line broadening may be identified as originating from predissociation to K(4s 2 S 1/2) ⫹Rb(5p 2 P 1/2) atoms. This predissociation occurs through spin–orbit interaction with the 2 3 ⌺ ⫹ state. The rotational barrier of the J⫽23 level was evaluated and the dissociation limit of the 2 3 ⌺ ⫹ state bounded. Knowing the spin–orbit energy of the Rb
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J. Chem. Phys., Vol. 112, No. 16, 22 April 2000
KRb ground electronic state potential
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assigned and analyzed. While the conventional Dunham-type analysis is well-able to represent the whole data set, the higher-order distortion parameters are not reliable and their predictive ability for vibrorotational levels is poor. Selfconsistent fits based on the use of near- dissociation expansions for representing these quantities yield equally good fits but should provide much more realistic predictions for all unobserved vibrational levels. The RKR potential energy curve was constructed for internuclear distances reaching 10 Å . One must notice however that the range of ( v ,J) data is restricted, which is not the case in Direct Potential Fitting methods currently being tested.38 One might hope that photoassociative spectroscopy may be able to observe these very last ground state bound levels as was done in the case of Rb2 . 39 FIG. 5. Comparison of the potential curve calculated by Jencˇ and Brandt 共black dots兲 and that derived in this work 共triangles兲 for the long-range part of the curve.
P levels, 237.60 cm⫺1, and the Rb(5p 2 P 3/2) – Rb(5s 2 S 1/2) energy separation, 12 816.56 cm⫺1, the authors deduced the ground state dissociation energy as 4217.4 ⫾ 0.8 cm⫺1m which is in remarkable agreement with our NDE determined value, 4217 ⫾ 1.5 cm⫺1. Although reaching v ⫽87 共about 20 cm⫺1 lower than the limit兲 the uncertainty of the present determination is still high because more than ten vibrational levels are unobserved. 2
All the observed wave numbers are available upon sending a request by electronic mail to
[email protected] V. CONCLUSION
In conclusion, some 7935 lines comprising 207 vibrorotational transitions of the KRb A⫺X spectrum have been
FIG. 6. Comparison of the potential curve calculated by Jencˇ and Brandt 共black dots兲 and that derived in this work 共triangles兲 for the inner part of the curve.
ACKNOWLEDGMENTS
Special thanks are due to Professor R. J. Le Roy from the University of Waterloo 共Canada兲 for sending us his computer codes and for numerous stimulating exchanges of information. Dr. A. Ross, Dr. C. Effantin, Dr. P. Crozet, and Dr. E. Boursey from the Laboratoire de Spectrome´trie Ionique et Mole´culaire 共Lyon I兲, are acknowledged for sending us their line positions in wave numbers. Preliminary results were kindly communicated by Monique Aubert-Fre´con 共Universite´ Lyon I兲. This work was partly supported by the National Science Foundation. We wish to acknowledge helpful discussions with Professor William C. Stwalley from Storrs University, and with Olivier Dulieu 共Laboratoire Aime´ Cotton兲. 1
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