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Title: Asymptotic behavior of apparent generalized oscillator strengths for optically forbidden transitions in rare-gas atoms

Abstract

Apparent generalized oscillator strengths (apparent GOS's) have been measured for three types of optically forbidden transitions in rare-gas atoms as functions of the squared momentum transfer K{sup 2} at small K{sup 2} range ({<=}0.4 a.u.). The apparent GOS's were deduced from the differential cross sections for excitation, which were measured by means of the electron energy-loss spectroscopy. Electron impact energies were 100, 300, and 500 eV, and the scattering angles were from 0.8 degree sign to 10 degree sign . In the case where the first Born approximation does not hold, the apparent GOS as a function of K{sup 2} (the apparent GOS function) shows characteristic dependence on the electron collision energy according to the character of the transition. In the present observation, for the np{sup 6} {sup 1}S{sub 0}{yields}np{sup 5}(n+1)p{sup '}[1/2]{sub 0} transitions, the specific behavior has been observed in the apparent GOS functions characteristic of that for the {sup 1}S{sub 0}{yields}{sup 1}S{sub 0} type transition, in which the term symbols of the initial and the final states do not change. For the np{sup 6} {sup 1}S{sub 0}{yields}np{sup 5}(n+1)p[5/2]{sub 2,3}; [3/2]{sub 1,2} transitions, a certain new type of deviations from the first Born approximation, which is interpreted to bemore » characteristic of the {sup 1}S{sub 0}{yields}{sup 1}D{sub 2} type transition, have been observed in the apparent GOS functions with some modifications depending on respective atomic species. For the 5p{sup 6} {sup 1}S{sub 0}{yields}5p{sup 5}5d [7/2]{sub 3}; [5/2]{sub 3} transitions in Xe, it is observed that the apparent GOS curves have no impact energy dependence for impact energies from 100 eV to 500 eV, which suggests that the first Born approximation is valid for such low impact energies and the curves agree with the Bethe-GOS. It is found that the GOS's varies in proportional to K{sup 4} at small K{sup 2} region ({<=}0.1 a.u.), which suggests that the octupole moment is dominant in these transitions. We interpret that these features of the behavior are specific for the {sup 1}S{sub 0}{yields}{sup 1}F{sub 3} type transition. On the whole, it is found that the behavior of the apparent GOS function can be well understood by considering the main contribution from a certain LS-coupling state when the excited state is represented by the intermediate coupling scheme which is expressed as a linear combination of the LS-coupled states.« less

Authors:
; ; ; ;  [1];  [2]
  1. Institute for Laser Science, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585 (Japan)
  2. (Japan)
Publication Date:
OSTI Identifier:
20982325
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032705; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ARGON; BORN APPROXIMATION; DIFFERENTIAL CROSS SECTIONS; ELECTRON-ATOM COLLISIONS; ELECTRONS; ENERGY DEPENDENCE; ENERGY-LOSS SPECTROSCOPY; EV RANGE 100-1000; EXCITATION; EXCITED STATES; FORBIDDEN TRANSITIONS; KRYPTON; L-S COUPLING; MOMENTUM TRANSFER; NEON; OSCILLATOR STRENGTHS; RARE GASES; SCATTERING; XENON

Citation Formats

Suzuki, T. Y., Suzuki, H., Ohtani, S., Takayanagi, T., Okada, K., and Department of Physic, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554. Asymptotic behavior of apparent generalized oscillator strengths for optically forbidden transitions in rare-gas atoms. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.032705.
Suzuki, T. Y., Suzuki, H., Ohtani, S., Takayanagi, T., Okada, K., & Department of Physic, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554. Asymptotic behavior of apparent generalized oscillator strengths for optically forbidden transitions in rare-gas atoms. United States. doi:10.1103/PHYSREVA.75.032705.
Suzuki, T. Y., Suzuki, H., Ohtani, S., Takayanagi, T., Okada, K., and Department of Physic, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554. Thu . "Asymptotic behavior of apparent generalized oscillator strengths for optically forbidden transitions in rare-gas atoms". United States. doi:10.1103/PHYSREVA.75.032705.
@article{osti_20982325,
title = {Asymptotic behavior of apparent generalized oscillator strengths for optically forbidden transitions in rare-gas atoms},
author = {Suzuki, T. Y. and Suzuki, H. and Ohtani, S. and Takayanagi, T. and Okada, K. and Department of Physic, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554},
abstractNote = {Apparent generalized oscillator strengths (apparent GOS's) have been measured for three types of optically forbidden transitions in rare-gas atoms as functions of the squared momentum transfer K{sup 2} at small K{sup 2} range ({<=}0.4 a.u.). The apparent GOS's were deduced from the differential cross sections for excitation, which were measured by means of the electron energy-loss spectroscopy. Electron impact energies were 100, 300, and 500 eV, and the scattering angles were from 0.8 degree sign to 10 degree sign . In the case where the first Born approximation does not hold, the apparent GOS as a function of K{sup 2} (the apparent GOS function) shows characteristic dependence on the electron collision energy according to the character of the transition. In the present observation, for the np{sup 6} {sup 1}S{sub 0}{yields}np{sup 5}(n+1)p{sup '}[1/2]{sub 0} transitions, the specific behavior has been observed in the apparent GOS functions characteristic of that for the {sup 1}S{sub 0}{yields}{sup 1}S{sub 0} type transition, in which the term symbols of the initial and the final states do not change. For the np{sup 6} {sup 1}S{sub 0}{yields}np{sup 5}(n+1)p[5/2]{sub 2,3}; [3/2]{sub 1,2} transitions, a certain new type of deviations from the first Born approximation, which is interpreted to be characteristic of the {sup 1}S{sub 0}{yields}{sup 1}D{sub 2} type transition, have been observed in the apparent GOS functions with some modifications depending on respective atomic species. For the 5p{sup 6} {sup 1}S{sub 0}{yields}5p{sup 5}5d [7/2]{sub 3}; [5/2]{sub 3} transitions in Xe, it is observed that the apparent GOS curves have no impact energy dependence for impact energies from 100 eV to 500 eV, which suggests that the first Born approximation is valid for such low impact energies and the curves agree with the Bethe-GOS. It is found that the GOS's varies in proportional to K{sup 4} at small K{sup 2} region ({<=}0.1 a.u.), which suggests that the octupole moment is dominant in these transitions. We interpret that these features of the behavior are specific for the {sup 1}S{sub 0}{yields}{sup 1}F{sub 3} type transition. On the whole, it is found that the behavior of the apparent GOS function can be well understood by considering the main contribution from a certain LS-coupling state when the excited state is represented by the intermediate coupling scheme which is expressed as a linear combination of the LS-coupled states.},
doi = {10.1103/PHYSREVA.75.032705},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • The generalized oscillator strengths (GOS's) of discrete excitations np{yields}nd and np{yields}(n+1)s,d, both dipole (L=1) and octupole (L=3), are studied. We demonstrate that although the relevant transitions in the same atom are closely located in energy, the dependence of their GOS's on the momentum transfer squared q{sup 2} is remarkably different; viz., the GOS's corresponding to L=3 have at least one extra maximum as a function of q{sup 2} and dominate over those of the L=1, starting from about q{sup 2}=1.5 a.u. Peculiarities are noted in the GOS of only the Ne dipole 2p{yields}3s transition in contrast to the rest ofmore » the atoms; viz., the characteristic minimum and the maximum are not obliterated by the dominance of 2p{yields}3d GOS dipole and octupole sum as in the other atoms. The depth of the minimum of the GOS for the dipole 2p{yields}3s transition is reduced considerably by the 2p{yields}3d dipole and octupole GOS sums, while the corresponding maximum is enhanced. In the GOS sum both the minimum and maximum are still identifiable, permitting experimental observation. The calculations were performed in the one particle Hartree-Fock (HF) approximation and with account of many-electron correlations via the random phase approximation with exchange (RPAE). The GOS's are studied for values of q{sup 2} up to 50 a.u. Our calculated RPAE GOS's for the Ar 3p{yields}4s dipole transition compare very well with the recently measured data of Zhu et al. [Phys. Rev. A 73, 042703 (2006)].« less
  • Generalized oscillator strengths and integrated cross sections from threshold to 1000 eV are calculated in the Glauber approximation for 2s-3s and 2s-3d excitations. The calculations are carried out using Hartree-Fock wave function of Weiss. The results are compared with the Born calculations using the same wave function and available experimental data.
  • Accurate electron-impact differential cross sections for various optically forbidden transitions in Cu I, Mg II, and Zn II are used to calculate apparent generalized oscillator strengths (GOS's) in the electron-impact energy range 15less than or equal toEless than or equal to100 eV. Most curves of the GOS versus momentum transfer squared, K/sup 2/, appear compatible with the Lassettre-limit theorem. Extrapolation to the optical oscillator strength values is meaningless for the 15-eV curves of Mg II and Zn II for which the unphysical region is significant. The GOS minima, where they exist, near K/sup 2/..-->..0 are extremely important in assessing whethermore » a given transition is interpretable in terms of the Born approximation.« less
  • The generalized oscillator strengths f(K) as a function of momentum transfer K are calculated for the (1) 2s-2p, 3s, 3p, 3d, (2) 2p-3s, 3p, 3d, (3) 3s-3p, 3d, and (4) 3p-3d transitions of the lithium atom using the Hartree-Fock wave function of Weiss. Calculations are carried out using both the length and velocity formulations of the Born-approximation integrals. For these transitions of lithium, the f(K) values were used to obtain integrated inelastic cross sections within the first Born approximation for electron impact. The results of the total cross section for 2p, 3s, and 3d from the ground state are comparedmore » with the available Born calculations and recent experimental data.« less