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PHYSICAL REVIEW A

VOLUME 54, NUMBER 4

OCTOBER 1996

Absolute generalized oscillator strengths of 4s, 4s 8, 4p14p 8 excitations of argon determined by the angle-resolved electron-energy-loss spectrometer Q. Ji, S. L. Wu, R. F. Feng, X. J. Zhang, L. F. Zhu, Z. P. Zhong, and K. Z. Xu Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui, 230027, People’s Republic of China

Y. Zheng Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver, British Columbia Canada V6T 1Z1 ~Received 12 February 1996! The absolute differential cross sections and generalized oscillator strengths of resolved 3 p 6 1 S 0 →3p 5 ( 2 P 1/2)4s, 3p 5 ( 2 P 3/2)4s 8 transitions in argon were determined by angle-resolved electronenergy-loss spectrometer at an incident electron energy of 1500 eV and scattering angles from 2° to 11.5°. Corrections of the experimental results for the angular factor and pressure effect have been made. These results are compared with other experimental and theoretical results. The absolute differential cross sections and generalized oscillator strengths of unresolved nondipole excitations 3 p 6 →3 p 5 4p14p 8 are reported. The profile of the generalized oscillator strength curve is similar to that of neon atoms. @S1050-2947~96!09809-5# PACS number~s!: 32.70.Cs, 34.80.Dp

I. INTRODUCTION

Argon atoms play a major role in the performance of the high-pressure Ar-Kr-F2 laser system @1# and in direct nuclear-pumped lasing media using He-Ar mixtures @2,3#, because of its presence in high concentration. So the precise cross sections and oscillator strengths for resonance lines in argon are needed. Based on these data, measurements of relative cross sections for inner-shell and subshell excitations and ionizations can also be absolutely made. For transitions from ground state (3s 2 3p 6 1 S 0 ) to 3p 5 ( 2 P 1/2)4s and 3 p 5 ( 2 P 3/2)4s 8 states in argon, which correspond to 11.624and 11.828-eV resonance lines, respectively, considerable results have been reported. But most of them were about the energy level structure and optical oscillator strengths ~OOS’s! obtained by the optical method, such as by measuring the self-absorption @4# of radiation as a function of gas pressure, observing vacuum-ultraviolet radiation due to deexcitations @5,6#, etc. As is well known, one of the main difficulties in experiments employing the optical method comes from indirect cascade population processes. But this does not matter when using the electron collision method. So electron collision processes of argon are of great interest for both practical and theoretical work. The investigation of differential cross sections ~DCS’s! and generalized oscillator strengths ~GOS’s! by electron impact is very important in many fields such as astrophysics, discharge processes, plasma physics, and laser physics. According to the Bethe theory @7#, the DCS for a fast electron impact can be factorized into a factor involving the kinematics of the electron before and after the collision, and the transition probability of the resulting excitation of the target, the so-called GOS, by the following Bethe-Born formula @8,9#: f ~ E,K ! 5

E k0 2 ds . K 2 ka dV

~1!

Here f (E,K) and d s /dV stand for GOS and DCS, respec1050-2947/96/54~4!/2786~6!/$10.00

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tively. E and K are the excitation energy and momentum transfer while k 0 and k a are the incident and scattered electron momenta, respectively. All quantities in Eq. ~1! are in atomic units. The multichannel quantum defect theory can calculate a unique energy-dependent quantum defect as well as the corresponding absolute oscillator strength densities for each particular initial- and final-state combination including the bound and continuous states @10#. It provides a powerful tool in predicting the electronic excitation spectrum and the DCS. Therefore, a large amount of the data of the excitation cross sections by electron impact, especially for high excitation states, can be obtained by interpolation from a few of the measured GOS densities. For an experimental study, the angle-resolved electronenergy-loss spectrometer ~AREELS! is a good instrument for research of DCS and GOS. With the development of EELS, a number of DCS and GOS measurements have been reported. However, most of them are relative results or at low incident energy. As shown in Table I, Tam and Brion @11# reported relative DCS measurements of the 3 p→4s excitation in argon in 1973. The incident electron energies were 30 and 50 eV and the angular range was 0°–90°. Lewis, Weigold, and Teubner @12# measured relative cross sections for the unresolved 3 p→4s14s 8 transition at an angle region 0°–140° with the incident electron energies between 30 and 120 eV. Chutjian and Cartwright @13# reported absolute differential cross sections for electron-impact excitation of 23 individual composite electronic states of argon lying within 14.30 eV of the ground state in 1981. Incident electron energies were 16, 20, 30, 50, and 100 eV, and the range of scattering angles was 5°–138°. Li et al. @14#, working at 500-eV incident energy with an improved energy resolution ~,0.1 eV!, measured the GOS’s for the 4s and 4s 8 transitions. But the K 2 region was limited from 0.035 to 1.0. Just after this report, Bielschowsky et al. @15# determined the absolute values for the GOS’s of the 3p 6 ( 1 S 0 )→3p 5 4s14s 8 transitions in argon by 1-keV electrons and calculated them using the first Born and Glauber approximations, checking 2786

© 1996 The American Physical Society

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ABSOLUTE GENERALIZED OSCILLATOR STRENGTHS . . .

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TABLE I. Summary of experimental studies of GOS and DCS for the 3 p 6 →3 p 5 4s, 4s 8, 4p and 4p 8 in argon.

Reference

Transitions

Tam and Brion @11# Lewis, Weigold, and Teubner @12# Chutjian and Cartwright @13#

3p→4s 3p→4s14s 8 3p→4s, 4p, 4p8 3p→4s, 4s 8 3 p→4s 3p→4s 3p→4s, 4s 8 3p→4 p14 p 8

Li et al. @14# Bielschowsky et al. @15# Wong, Lee, and Bonham @16# Present work

the results given by Wong, Lee, and Bonham @16#, who reported the K 2 values for the extrema of GOS curves of argon using 25-keV incident electrons for the first time. Unfortunately, the energy resolution of 0.6 eV was not good enough to resolve 4s,4s 8. All the previous experimental studies were somehow limited, because either they were performed at low energy, the K 2 region was not wide enough to cover the first maximum and minimum, or energy resolution was not high enough to resolve the 3p→4s excitation from 3p→4s 8 excitation. So it is necessary to continue studying at high energy, highenergy resolution, and covering a wide K 2 region. Furthermore, the previous DCS and GOS measurements for the 3 p 6 →3p 5 4p14p 8 non-dipole-allowed excitations in argon were also relative and at low incident energy. For theoretical research, there is a shortage of calculations of the excitations in argon, because it is a heavier atom, so that the LS coupling is not applicable. Bonham @17# predicted the existence of the minimum and maximum in the GOS for the 3p 6 ( 1 S 0 )→3p 5 4s14s 8 using the first Born approximation ~FBA!. This work was extended by Shimamura @18#. Bielschowsky et al. @15# reported results by the first Born and Glauber approximations, correctly predicting the positions of the observed maximum and minimum in the GOS curve as a function of K 2. Peterson and Allen @19# got a set of semiempirical cross sections for plasma-modeling purposes combining the Born approximate and experimental generalized oscillator strengths. Ab initio results include those obtained with the distorted-wave theory @20#, the Born approximation with both single and multiconfiguration Hartree-Fock wave functions @21#, and the many-body formulation @22,23#. In this paper, the differential cross sections and generalized oscillator strengths of 3 p 6 ( 1 S 0 )→3p 5 ( 2 P 1/2)4s, 3 p 5 ( 2 P 3/2)4s 8 transitions were carefully measured by angleresolved electron-energy-loss spectrometer at an incident electron energy of 1500 eV and within a region of K 2 values from 0.13 to 4.41. The energy resolution was 80 meV full width at half maximum ~FWHM! which was good enough to resolve these two excitations. On the other hand, the absolute GOS’s for the transitions of 3 p 6 1 S 0 →3p 5 4p14 p 8 at an incident energy of 1500 eV are first reported, but the ten structures are not resolved.

Incident energy ~eV! 30, 50 30–120 16, 20, 30, 50, 100 500 1000 25 000 1500

K 2 region ~a.u.!

Results

0.12–6.48 0.12–29.6 0.28–24.1

Relative DCS Relative DCS Absolute DCS

0.035–1.0 0.02–5.0 0.8–4.0 0.13–4.41

Absolute GOS Absolute GOS Relative GOS Absolute GOS

II. APPARATUS AND EXPERIMENTAL PROCEDURE

The electron impact apparatus and the experimental procedure to obtain the data used in the present work have been described in detail before @24–26#. The apparatus consists basically of an electron gun, a hemispherical electrostatic monochromator made of aluminium, a rotatable energy analyzer with the same type, an interaction chamber, a number of cylindrical electrostatic optics lenses, and a channel electron multiplier for detecting the analyzed electrons. All of these components are enclosed in four separate vacuum chambers made of stainless steel. Pulse-counting and multiscalar techniques were used to obtain energy-loss spectra. It is known that the angular accuracy has great influence on observed signal intensities, particularly in the case of forward scattering. A calibration of zero angle for scattering angles has been done based on the symmetry of the scattering intensity corresponding to the 4s 8 excitation from the ground state in argon. In present work the true scattering zero angle is 0.15° less than the geometric zero angle of the instrument. The angular resolution of the apparatus has been determined approximately according to the angular distribution of the direct electron beam from the monochromator with an impact energy of 1500 eV and is shown in Fig. 1. From Fig. 1 the angular resolution is about 0.75° ~FWHM!,

FIG. 1. Angular resolution of the spectrometer.

Q. JI et al.

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which is good enough for the present measurement. To determine DCS’s and GOS’s of the 3 p 6 1 S 0 →3p 5 ( 2 P 1/2)4s, 3p 6 1 S 0 →3p 5 ( 2 P 3/2)4s 8 , and unresolved 3p 6 →3p 5 4p14 p 8 excitations of argon, a number of electron-energy-loss spectra were measured at a series of scattering angles ~corresponding to different momentum transfer values! sequentially in repetitive scans by the above spectrometer. These scattering angles were 2°, 3°, 4°, 5°, 5.5°, 6°, 6.5°, 7°, 7.5°, 8°, 9°, 10°, and 11.5°. There was some small change in the intensity of the incident electron beam during the measuring period. In order to minimize this systematic error, each time an elastic and inelastic EELS was measured at an angle, the EELS at an angle of 2° was measured alternately. Measured counts of the peaks of both elastic and inelastic scattering were normalized to that of the 4s 8 excitation at 2°. On the other hand, during the experiment, two principal types of double scattering processes must be reduced to the least level especially at large angle u. First, an electron inelastically scattered at an angle a is elastically scattered at an angle u-a. Second, an elastically scattered electron at an angle b is inelastically scattered at an angle u-b. In order to eliminate the error of intensity caused by double scattering, we measured the pressure relation of the intensity ratios for the transitions of the 3p 6 →m to the elastic scattering at all scattering angles, where m represents 3 p 5 4s, 3 p 5 4s 8, or unresolved 3p 5 4p14 p 8 . Because the cross sections for double scattering processes depend on the square of the pressure p ~or density! of the measured gas, but the cross sections for single scattering processes depend on pressure, and also because the cross sections of elastic scattering are much more than that of the inelastic scattering at larger angles, there is an approximate relation between the measured intensity ratios and p as in the following: I p /I el 5c p1 ~ I p /I el ! p50 ,

~2!

where c is a coefficient and I p , I el represent the scattering electron intensities corresponding to the transition m including the single and double scattering and the elastic scattering, respectively. (I p /I el ) p50 is a ratio extrapolated to zero gas pressure. The electron-energy-loss spectra of the series of scattering angles were measured at five different values of pressure. The values of (I p /I el ) p50 and c were obtained by using the least-squares program to fit the data points I p /I el . As for different angles, there is a different ratio of (I p /I el ) p50 to I p /I el for different pressures. Multiplying the ratio by the inelastic scattering intensity after the correction of instability of beam current, we obtained a true relative inelastic scattering intensity without pressure effect. Furthermore, in the collision cell case, the scattered electrons go out not from a ‘‘point’’ but from a ‘‘line.’’ The scattering length seen by the energy analyzer at a scattering angle u is proportional to 1/sinu at larger scattering angles @27#. But at smaller scattering angles it does not increase further because of the fixed length of the collision cell. In the previous experiment on helium @25#, the angular factor had been obtained to correct for the ‘‘line source’’ for our apparatus. When the angle u is larger than 4°, the angle factor A~u! is equal to sinu, and the angles are 2°, 3°, and 4°, the angle factors are 0.389, 0.498, and 0.612, respectively.

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FIG. 2. Typical energy-loss spectra of argon taken at the impact energy of 1500 eV and scattering angles of 0° and 2° ~upper: 0°; lower: 2°!. The intensity of the spectrum at the angle of 2° is put on a scale by normalizing the intensity of 3 p 6 →3 p 5 4s 8 excitation at the angle of 2° to the corresponding one at the angle of 0°. III. RESULTS AND DISCUSSION

In Fig. 2 are typical energy-loss spectra taken at the impact energy of 1500 eV and at scattering angles of 0° and 2°. It is shown that the most intense peak at 11.828 eV corresponds to the excitation to the 3 p 5 4s 8 state from the ground state, an adjacent peak at 11.624 eV corresponds to the excitation to the 3p 5 4s state from the ground state, and the unresolved peaks from 12.90 to 13.80 eV correspond to the excitations from the ground state to 3p 5 4 p and 3p 5 4p 8. The energy-loss peaks have been identified by comparing them with the spectroscopic data of the transition energies from the table compiled by Moore @28#. These spectra illustrate the rapid change in the relative peak intensities of 3 p 6 →3 p 5 4 p14p 8 excitations as the scattering angle is increased from u50° to 2°. Subtracting backgrounds, correcting for the instability of beam current and the effects of double scattering processes, and multiplying the corresponding angular factors A~u! which were obtained from the experiment on helium @25#, we obtained the relative DCS’s for these two transitions. The relative GOS’s obtained from Eq. ~1! were then put on an absolute scale by normalizing the limit value as K 2→0 to the OOS. The measured relative GOS’s of the 4s and 4s 8 excitations were extrapolated to K 2→0 by the following formula: f ~ K,E ! 5

1 ~ 11x ! 6

m

(

n50

fn

S D x 11x

n

,

~3!

where x5(K/ a ) 2 , a5(2I) 1/21[2(I2W)] 1/2. I is the first ionization energy and f 0 is the OOS of 4s or 4s 8 excitation, respectively. For sufficiently high incident electron energy, where the first Born approximation is valid, the apparent GOS should be equal to the Born-calculated GOS. The GOS

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FIG. 3. Absolute GOS’s of the 4s,4s 8 and 4p14 p 8 excitations ~present work; Ref. @14#!.

FIG. 5. The sum of absolute GOS’s of the 4s,4s 8 excitations ~present work; Refs. @15–18#!.

values of the 3 p 6 →3p 5 4s,4s 8 transition at K 250 should be the OOS values that have been measured using our EELS spectrometer at an angle of 0° and are 0.0676 and 0.259, respectively @24#. The absolute GOS’s for these two transitions were then obtained and are shown in Fig. 3. For nondipole transition, the relative GOS was normalized based on the data of the absolute GOS of 4s 8 at the angle of 4° using the ratio of the intensity of 4s 8 to 4p14 p 8 at the same angle. The results are also shown in Fig. 3. Figure 4 shows the absolute DCS for these dipole and nondipole transitions. The overall percent error of the DCS’s and GOS’s obtained in the present work came from the statistics of counts, ds , the angular determination and the angular factor, da @25#, the measured ~OOS! value with systematic error, do @24#, and the pressure correction, dp . In our measurement the maximum of each error is ds 52%, da 54%, do 56%, and dp 52%. The total error is 8% at the 1s level. The absolute GOS’s of resolved 4s and 4s 8 excitations

are shown in Fig. 3, along with the experimental results of Li et al. @14#. From Fig. 3, it is found that the GOS curves of both 4s and 4s 8 have a minimum and a maximum. Compared with the results of Li et al. @14# at electron incident energies of 400 and 500 eV, our experimental results show good agreement within the error range below K 250.7, but are generally larger than them at the K 2 region 0.7–1.0. As for the sum of absolute GOS’s of 4s and 4s 8 excitations, our experimental results shown in Fig. 5, along with the experimental results of Bielschowsky et al. @15# and Wong, Lee, and Bonham @16#, the theoretical results of Shimamura @18#, Bonham @17#, and Bielschowsky et al. @15# using the FBA method and the Glauber-Yukawa frozen-core ~YFC! calculation. From Fig. 5, it is found that the curve of the sum of absolute GOS’s of 4s and 4s 8 excitation also have a minimum and a maximum. The GOS values of our result seem to be in reasonable agreement with the experimental results of Bielschowsky et al. @15# and Wong, Lee, and Bonham @16# only below K 2,1. When K 2.1, our results are smaller than other experimental results and higher than the theoretical results using the FBA method @17,18#, but much closer to theoretical results using the Glauber YFC method. The position of the minimum and maximum of the GOS curve of experimental and theoretical results are shown in Table II. It is found that the minimum position of our result is at a larger K 2 value than the experimental results of Bielschowsky et al. @15# and Wong, Lee, and Bonham and the theoretical results using the FBA method @15,17,18#, but it is approximately equal to the result using the Glauber YFC method @15#. The maximum position of our result is in between the results of Bielschowsky et al. @15# and Wong, Lee, and Bonham @16# and is at a smaller K 2 value than theoretical results. It had been pointed out by Bielschowsky et al. @15# that the first minimum of the GOS is more correctly described by the Glauber calculations compared to the FBA results, showing that the former offers a better description of the collision process. It was also pointed out by Wong, Lee, and Bonham @16# that multiple scattering may produce a slight shift in the position of the maximum and minimum.

FIG. 4. Absolute DCS’s of the 4s,4s 8 and 4p14p 8 excitations ~present work!.

Q. JI et al.

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TABLE II. The positions of minimum and maximum of GOS values for 3 p 6 →3 p 5 4s,4s 8 transitions of argon. Experimental

Theoretical FBA

K 2 ~a.u.! Minimum Maximum

Present work

Ref. @15#

Ref. @16#

Ref. @15#

Ref. @18#

Ref. @17#

Glauber YFC Ref. @15#

'1.6 '2.6

'1.3 '2.1

1.25 2.96

'1.2 '3.0

'1.5 '3.1

'1.5 '3.1

'1.6 '3.1

This possibility may result in the slight discrepancy of the maximum and minimum positions among experimental results. Especially in the experiment of Bielschowsky et al. @15#, although it is considered that the large-angle data had been obtained at an average pressure of 331025 Torr and are considered to be free of multiple scattering, there is the possibility that the pressure effect may bring out a slight shift of maximum and minimum positions. As for the unresolved 3p 6 →3p 5 4p14 p 8 excitations, the previous works were limited in quantity. So there were no suitable theoretical or experimental results with which to be compared. But the profile of the curve was similar to the curve of the 2 p 6 →2p 5 3p excitations of neon @29#. From Fig. 3, it is found that there are two maxima and a minimum within the K 2 region 0.13–4.41. The position of first maximum is at K 2'0.6; the second one is at K 2'3.3 and is broader than the first one. The position of the minimum is at K 2'2.0. The profile of the GOS curve is similar to the corresponding one in neon. Since the outer-shell structures of both argon and neon atoms are similar, we have good reason to come to this conclusion.

@1# Ch. Brau, in Excimer Laser, edited by Ch. K. Rhodes, Topics in Applied Physics, Vol. 30 ~Springer, Berlin, 1979!, p. 87. @2# R. J. De Young, N. W. Jalufka, and F. Hohl, AIAA J. 16, 99 ~1978!. @3# K. W. Jalufka, R. J. De Young, F. Hohl, and M. D. Williams, Appl. Phys. Lett. 29, 188 ~1976!. @4# J. P. de Jongh and J. van Eck, Physica ~Utrecht! 51, 104 ~1971!. @5# J. W. McConkey and F. G. Donaldson, Can. J. Phys. 51, 914 ~1973!. @6# J. E. Mentall and H. D. Morgan, Phys. Rev. A 14, 954 ~1976!. @7# H. Bethe, Ann. Phys. ~Leipzig! 5, 325 ~1930!; Z. Phys. 76, 293 ~1930!. @8# M. Inokuti, Rev. Mod. Phys. 43, 297 ~1971!. @9# R. A. Bonham, in Electron Spectroscopy Theory, Techniques and Applications, edited by C. R. Brundle and A. D. Baker ~Academic, New York, 1979! Vol. 3, p. 127. @10# K.-H. Sze, C. E. Brion, X.-M. Tong, and J.-M. Li, Chem. Phys. 115, 433 ~1987!. @11# W.-C. Tam and C. E. Brion, J. Electron Spectrosc. Relat. Phenom. 2, 111 ~1973!. @12# B. R. Lewis, E. Weigold, and P. J. O. Teubner, J. Phys. B 8, 212 ~1975!.

IV. CONCLUSION

Absolute values for the generalized oscillator strengths and differential cross sections for the resolved 3p 6 →3 p 5 4s,4s 8 transitions in argon atoms have been determined experimentally. The results have been obtained from relative GOS’s normalized to known absolute values of OOS. The GOS curve shows a non-negligible intensity minimum and a maximum. There are slight discrepancies of both positions between experimental and theoretical results. The absolute generalized oscillator strengths and differential cross sections for the unresolved 3 p 6 →3 p 5 (4p14p 8 ) transitions are reported. There are two maxima and a minimum. The profile of the GOS curve is similar to the corresponding one of neon. ACKNOWLEDGMENTS

Financial support for this work was provided by the National Natural Science Foundation of China and National Education Committee of China. We wish to express our sincere thanks to Professor J. M. Li for useful discussions.

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@25# K. Z. Xu, R. F. Feng, S. L. Wu, Q. Ji, X. J. Zhang, Z. P. Zhong, and Y. Zheng, Phys. Rev. A 53, 3081 ~1996!. @26# R. F. Feng, B. X. Yang, S. L. Xing, F. Zhang, Z. P. Zhong, X. Z. Guo, and K. Z. Xu, Sci. China ~to be published!. @27# C. E. Kuyatt, in Methods of Experimental Physics, edited by L. Marton ~Academic, New York, 1968!, Vol. 7, Pt. A,

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