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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

The role of adiabaticity in alkali atom-fine structure mixing

Ben Eshel, David E. Weeks, Glen P. Perram

Published Feb 25, 2014• 4 citations
Publisher

Abstract

Fine-structure mixing cross-sections for the alkalis in collisions with the rare gases are reviewed. Included in the review are all the rare gases in collisions with all of the first excited state of the alkalis, the second excited state for K, Rb and Cs and the third excited state for Rb and Cs. The cross-sections are converted to probabilities for energy transfer using a quantum-defect calculated cross-section and are then presented as a function of adiabaticity. The data shows a clear decreasing trend with adiabaticity but secondary factors prevent the probabilities from decreasing as quickly as expected. Polarizability is introduced as a proxy for the secondary influences on the data as it increases with both rare gas partner and alkali excited state. The polarizability is shown to cause the probability of fine structure transition to be higher than expected. An empirical model is introduced and fit to the data. Future work will develop a model using time-independent perturbation theory in order to further develop a physical rational for the dependence of fine structure cross sections on adiabaticity and to further understand the secondary influences on the probability for fine structure transition.

DOI
10.1117/12.2045115

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Sensitized fluorescence in cesium vapor induced by collisions with excited rubidium atoms was investigated in order to determine the total cross sections for inelastic collisions between excited rubidium atoms and cesium atoms in their ground states. The partial pressure of the rubidium vapor in the Rb–Cs mixture was kept below 2 × 10−5 mm Hg in order to eliminate effects due to the trapping of the Rb resonance radiation. The collision cross sections for the various excitation transfer processes are as follows: Q12′(Rb 5 2P1/2 → Cs 6 2P3/2) = 1.5 Å2; Q11′(Rb 5 2P1/2 → Cs 6 2P1/2) = 0.5 Å2; Q22′(Rb 5 2P3/2 → Cs 6 2P3/2) = 0.9 Å2; Q21′(Rb 5 2P3/2 → Cs 6 2P1/2) = 0.3 Å2. The fact that the cross sections are considerably smaller than those for collisions between similar atoms indicates that the Rb–Cs interactions probably involve van der Waals' forces with a much shorter range than exchange forces, which play a dominant role in Rb–Rb or Cs–Cs collisions.

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Semiclassical evaluation of fine-structure mixing cross sections for Rb and Cs atoms excited to higher nD states

Leszek Sirko, K. Rosiński

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Journal of Physics B Atomic and Molecular Physics•Apr 28, 1986•14 citations
Fine-structure mixing cross-sections for the alkalis in collisions with the rare gases are reviewed. Included in the review are all the rare gases in collisions with all of the first excited state of the alkalis, the second excited state for K, Rb and Cs and the third excited state for Rb and Cs. The cross-sections are converted to probabilities for energy transfer using a quantum-defect calculated cross-section and are then presented as a function of adiabaticity. The data shows a clear decreasing trend with adiabaticity but secondary factors prevent the probabilities from decreasing as quickly as expected. Polarizability is introduced as a proxy for the secondary influences on the data as it increases with both rare gas partner and alkali excited state. The polarizability is shown to cause the probability of fine structure transition to be higher than expected. An empirical model is introduced and fit to the data. Future work will develop a model using time-independent perturbation theory in order to further develop a physical rational for the dependence of fine structure cross sections on adiabaticity and to further understand the secondary influences on the probability for fine structure transition.
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 C6{C}_{6}C6​ 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 62P{6}^{2}P62P 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−−893KT=279--893\phantom{\rule{0.222222em}{0ex}}\mathrm{K}T=279−−893K.
A theoretical model is presented for the interaction between an alkali atom in the first excited 2 P state and a ground state rare gas atom, which is effective in causing transitions among the alkali fine structure states. The main difference from previously used models is a more detailed treatment of short range effects including deviations from straight line paths in the semiclassical treatment. An application to the case of Rb interacting with He, Ne, Ar, and Kr gives results for the depolarization and inelastic cross sections which are in reasonable accord with experiment.
The cross sections for excitation transfer between the 62P fine-structure substates in rubidium, induced in collisions with noble gas atoms, have been determined in a series of sensitized fluorescence experiments. Mixtures of rubidium vapor and noble gases at pressures varying in the range 0–5 Torr were irradiated with each component of the second 2P rubidium doublet in turn and the following cross sections for 2P mixing were obtained from measurements of sensitised-to-resonance fluorescent intensity ratios. Rb–He: Q12(2P1/2 → 2P3/2) = 29.3 Å2; Q21(2P1/2 ← 2P3/2) = 19.0 Å2. Rb–Ne: Q12 = 10.3 Å2; Q21 = 6.4 Å2. Rb–Ar: Q12 = 24.0 Å2; Q21 = 14.9 Å2. Rb–Kr: Q12 = 23.2 Å2; Q21 = 14.6 Å2. Rb–Xe: Q12 = 43.9 Å2; Q21 = 27.7 Å2 In their dependence on the magnitude of the fine-structure splitting, the values are consistent with previously determined cross sections for mixing in the first and third 2P doublets of alkali atoms.
For years, inelastic, fine-structure-changing collisions between excited alkali-metal atoms and noble-gas perturbers have been a source of information on the alkali-metal--noble-gas interaction. Here, we consider the role of elastic fine-structure-mixing collisions on alkali-metal absorption cross sections. Specifically, we consider the four optical hyperfine transitions of the D1{D}_{1}D1​ absorption spectrum for 87Rb^{87}\mathrm{Rb}87Rb, and in particular the doublet corresponding to $5^{2}S_{1/2}({F}_{g}=2)\ensuremath{-}5^{2}P_{1/2}({F}_{e}=1,2)$ transitions. Although ideally the amplitudes of the doublet's absorption cross sections are identical, we find that fine-structure mixing of D2{D}_{2}D2​ oscillator strength into the D1{D}_{1}D1​ spectrum breaks the cross sections' equality and leads to doublet asymmetry. We obtain a fine-structure mixing parameter $\ensuremath{\lambda}$ of $(5.4\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{3}$, and estimate a 52P1/25^{2}P_{1/2}52P1/2​ hyperfine-splitting density shift $\ensuremath{\zeta}$ in the 87Rb^{87}\mathrm{Rb}87Rb-Xe system of $+0.71\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}/\mathrm{amagat}$. These results have implications for spectroscopic applications of the 87Rb^{87}\mathrm{Rb}87Rb isoclinic point, which we consider as part of our conclusions.
Sensitized fluorescence in cesium vapor induced by collisions with excited rubidium atoms was investigated in order to determine the total cross sections for inelastic collisions between excited rubidium atoms and cesium atoms in their ground states. The partial pressure of the rubidium vapor in the Rb–Cs mixture was kept below 2 × 10−5 mm Hg in order to eliminate effects due to the trapping of the Rb resonance radiation. The collision cross sections for the various excitation transfer processes are as follows: Q12′(Rb 5 2P1/2 → Cs 6 2P3/2) = 1.5 Å2; Q11′(Rb 5 2P1/2 → Cs 6 2P1/2) = 0.5 Å2; Q22′(Rb 5 2P3/2 → Cs 6 2P3/2) = 0.9 Å2; Q21′(Rb 5 2P3/2 → Cs 6 2P1/2) = 0.3 Å2. The fact that the cross sections are considerably smaller than those for collisions between similar atoms indicates that the Rb–Cs interactions probably involve van der Waals' forces with a much shorter range than exchange forces, which play a dominant role in Rb–Rb or Cs–Cs collisions.
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.