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Physical Review A

J-mixing process of alkali-metal atoms treated as a three-body process within an eikonal approximation

Hong Liu, Baiwen Li

Published Oct 1, 1993• 1 citation

Abstract

The J-mixing process of alkali-metal atoms in thermal collisions with noble-gas atoms has been a nemesis due to the fact that the process is a complicated three-body collision process. Since current theoretical methods treat the collision process as a two-body one by ignoring the interaction between the perturber noble-gas atom and the alkali-metal atomic core, their results do not agree with experiments, especially in lower-n states and for heavier noble-gas atoms. Within the framework of an eikonal approximation in this paper, we have presented a theoretical description of the J-mixing process of alkali-metal atoms. Our present work shows that the direct contribution to the process from the interaction between the perturber atom and the alkali-metal atomic core is negligible, but the interaction makes its effect felt within a higher-order term which depends on the perturber-core total cross section ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{tot}}^{\mathit{A}+\mathrm{\ensuremath{-}}}$B and the matrix element 〈${\mathit{r}}^{\mathrm{\ensuremath{-}}2}$${\mathrm{〉}}_{\mathit{n}\mathit{l}}$. The theoretical cross sections obtained for Cs and Rb atoms' J-mixing processes exhibit a similar dependence on the principal quantum number n as the experimental results, expecially in the lower-n states and for the heavier noble-gas atoms.

DOI: 10.1103/physreva.48.2903

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The J-mixing process of alkali-metal atoms in thermal collisions with noble-gas atoms has been a nemesis due to the fact that the process is a complicated three-body collision process. Since current theoretical methods treat the collision process as a two-body one by ignoring the interaction between the perturber noble-gas atom and the alkali-metal atomic core, their results do not agree with experiments, especially in lower-n states and for heavier noble-gas atoms. Within the framework of an eikonal approximation in this paper, we have presented a theoretical description of the J-mixing process of alkali-metal atoms. Our present work shows that the direct contribution to the process from the interaction between the perturber atom and the alkali-metal atomic core is negligible, but the interaction makes its effect felt within a higher-order term which depends on the perturber-core total cross section

{\mathrm{\ensuremath{\sigma}}}_{\mathrm{tot}}^{\mathit{A}+\mathrm{\ensuremath{-}}}

B and the matrix element 〈

{\mathit{r}}^{\mathrm{\ensuremath{-}}2}$${\mathrm{〉}}_{\mathit{n}\mathit{l}}

. The theoretical cross sections obtained for Cs and Rb atoms' J-mixing processes exhibit a similar dependence on the principal quantum number n as the experimental results, expecially in the lower-n states and for the heavier noble-gas atoms.

Cross sections for the J mixing (transfer of excitation between fine-structure sublevels) in the nD (n=10-14) states of caesium due to collisions with noble-gas atoms are measured by the integrated intensities method. It is found that the cross sections corresponding to the different noble-gas perturbers are of the same order of magnitude for lower values of the principal quantum number n but become increasingly different from each other with increasing n and for n=13 and 14 the difference approaches two orders of magnitude. Qualitatively, the n-dependence of the cross sections is similar to that obtained in the studies of the l-mixing collisions in the Rydberg states of the alkali-metal atoms. The results are compared with those predicted by the existing theoretical models. Good agreement is obtained for He and Ne perturbers with the results of calculations by Sirko et al. in which the Fermi pseudopotential and perturbation approach were employed.

We have presented a theoretical description of J-mixing (the transfer of excitation between fine structure) cross sections of a Rydberg Cs atom induced by thermal collisions with noble-gas atoms. The theory is based on the application of impulse approximation theory and a kind of model-potential wave function. The results agree well with available recent experimental values for He, Ne, and Ar atoms. But for the heavier noble-gas atoms Kr and Xe, the theoretical cross sections are larger than the experimental ones.

The collision cross sections for alkali-metal--rare-gas spin orbit mixing between the ${n}^{2}{P}_{3/2}\ensuremath{\rightarrow}{n}^{2}{P}_{1/2}$ levels trend strongly with the Massey parameter, or adiabaticity of the collisions. The strength of the interaction, as characterized by the

{C}_{6}

dispersion coefficient, is a secondary influence on the rates. An analytic expression for the probability of energy transfer in alkali-metal--rare-gas collisions is derived using time-dependent perturbation theory. The model agrees well with a broad literature survey of the observed temperature-dependent cross sections. A simple interaction potential successfully organizes the alkali-metal--rare-gas database. The rates become very large for high-lying states, as the collisions are quite sudden and the radius of the valence electron is large. In contrast, the highly adiabatic cesium

{6}^{2}P

mixing rates are six to eight orders of magnitude smaller. The mixing rate for the Rb-He diode pumped alkali laser system varies from $0.20--1.53\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\mathrm{cm}{}^{3}/\mathrm{at}.\phantom{\rule{0.16em}{0ex}}\mathrm{s}$ for

T=279--893\phantom{\rule{0.222222em}{0ex}}\mathrm{K}

.

It is shown for the first time that the theoretical model for the collisional l mixing in atomic intermediate Rydberg states proposed by de Prunele and Pascale (1979) can also be applied to J mixing in the intermediate Rydberg states with higher quantum defect delta l values and not only to collisions with noble gas atoms and N 2 but also with ground-state alkali atoms. The model is applied to the calculation of J-mixing cross sections of nD Rydberg states of Rb (n=7-10) and Cs (n=9-23) perturbed by noble gas atoms and N 2 . J mixing in Cs(nD)-Cs(6S 1 2/)(n=11-23) collisions is also considered. The agreement with the available results is rather good.

A general approximate method for computing the cross sections for certain inelastic collision processes is developed. It is based on the possibility of obtaining, with the use of the impact-parameter method, an exact expression for the transition amplitude in a special case. The dependence of the cross section on the parameters of coupling constant, velocity, and energy difference between states is discussed for a two-level model. Detailed calculations are made of cross section for collisions of the type $A(^{2}P_{\frac{3}{2}})+B\ensuremath{\rightleftharpoons}A(^{2}P_{\frac{1}{2}})+B$, where

A

is an excited atom of an alkali metal and

B

is an atom of a noble gas. An Appendix contains a review of the effective long-range interaction of atoms.