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Journal of Physics B Atomic Molecular and Optical Physics

Collisional redistribution of polarized radiation for Sr-Ar(He) systems: a numerical comparison of the semiclassical decoupling/locking model to exact results

Ronald James Bieniek, Paul S. Julienne, Frank Rebentrost

Published Dec 28, 1991• 10 citations
Publisher

Abstract

Semiclassical formulations of collisional redistribution of polarized radiation are presented at several levels of approximation, from full classical path coupled equations to the locking/decoupling model. These are numerically tested against the results of a quantum mechanical coupled-channels formalism, by the comparison of polarization curves in both spectral wings of the Sr( 1 S 0 - 1 P 1 ) transition, with Ar and He as collisional perturbers. It is found that the locking/decoupling model can often produce good agreement with exact results if the effects due to trajectories and multiple Condon points are treated properly. Significant discrepancies due to the Condon approximation used by the model are seen in the near blue wing of the spectra and attributed to antistatic effects.

DOI
10.1088/0953-4075/24/24/010

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Semiclassical formulations of collisional redistribution of polarized radiation are presented at several levels of approximation, from full classical path coupled equations to the locking/decoupling model. These are numerically tested against the results of a quantum mechanical coupled-channels formalism, by the comparison of polarization curves in both spectral wings of the Sr( 1 S 0 - 1 P 1 ) transition, with Ar and He as collisional perturbers. It is found that the locking/decoupling model can often produce good agreement with exact results if the effects due to trajectories and multiple Condon points are treated properly. Significant discrepancies due to the Condon approximation used by the model are seen in the near blue wing of the spectra and attributed to antistatic effects.
When detuned laser light is absorbed during a collision, the subsequent fluorescence will not be 100% because of rotation of the excited molecular orbitals as the collision proceeds. A semiclassical locking/decoupling model of this successfully predicted the polarization curve in the red-wing of for Sr+Ar collisions, but was much less successful for Sr+He. The averaged over all phases. Inspired by a quantal treatment effects in photofragmentation, we introduce simple phase terms for evolutionary interference between parallel and components of the molecular orbitals, from the Condon to their decoupling as atomic orbitals. The resulting interference terms have a major effect on Sr-He depolarization, bringing it into good agreement with brute-force quantal computations.
The close-coupled theory of collisions in a radiation field is used to calculate the absorption profile for the Sr $^{1}\ensuremath{\leftarrow}^{1}$S resonance line broadened by collisions with Ar. The calculations predict the polarization ratios of Sr 1P^{1}\mathrm{P}1P fluorescence following line wing excitation by either linear or circular polarized light. Ab initio calculations were used to obtain the ground and excited SrAr molecular-potential curves, which were adjusted to give improved agreement with experiment. The radiative-scattering theory gives a unified description of the absorption coefficient and polarization redistribution from the small detuning impact limit region to the far spectral wings. The cross sections for elastic and inelastic depolarizing collisions of Sr 1P1^{1}\mathrm{P}_{1}1P1​+Ar were also calculated. The calculated absorption coefficient, impact-broadening rate, linear- and circular-polarization ratios, and depolarization rate coefficients are for the most part in good agreement with experiment.
The first numerical tests, for a real system, of the quasiclassical description of redistribution of polarized radiation through atomic collisions are presented. Polarization results are reported for red-wing redistribution of Sr(1{(}^{1}(1S0{\mathrm{S}}_{0}S0​\ensuremath{\rightarrow}1{\mathrm{}}^{1}1P1{\mathrm{P}}_{1}P1​) in the presence of Ar colliders. They compare favorably to recent quantal, nonadiabatic computations. It is shown that the effects of bent trajectories are important. Modified quasiclassical formulas to account for some of these are presented and tested. The results indicate that quasiclassical analysis can be used to probe the transformation from molecular to atomic states as atoms separate in a half-collision.
We have measured the product alignment resulting from the collisional redistribution of polarized light in Sr–He inelastic spin-changing energy transfer collisions. The experimental results are in good agreement with the predictions of an analytic theoretical model, based on a standard orbital-locking and following approximation, but generalized to this inelastic collision process. The good agreement indicates a clear understanding of the energy transfer dynamics in this case, and suggests that this simple analytic approach may be generalized to a much broader range of collisional phenomena.
We have measured the far-wing collisional redistribution line shape, the redistributed fluorescence polarization, and the collisional alignment decay rates for barium perturbed by argon and xenon. The experiment was performed with a heated gas cell ($T\ensuremath{\sim}900$ K) with perturber-gas densities in the 1---30-Torr range and laser light detuned \ifmmode\pm\else\textpm\fi{} 3--- 1000 ${\mathrm{cm}}^{\ensuremath{-}1}$ from the 5535-\AA{} Ba I $6^{1}S\ensuremath{-}6^{1}P$ resonance line. Metal-vapor densities were determined by a Rayleigh scattering technique, which is outlined in detail. By correlating structure in the line shape with that of the polarization, we are able to make definitive statements about the interatomic potentials. The Ba data show strong similarities with previous experimental results for similar two-electron atoms, namely Ca, Sr, and Hg, and so our conclusions are of relevance to these systems as well.
We have measured the polarization of collisionally redistributed light as a function of detuning from line center for the Hg3P1–1S0 transition in the presence of Ar. We present a polarization profile for the red wing between 5 and 18 cm−1 and polarizations for two detunings in the blue wing. We compare this type of experiment to the complementary method of photodissociation and discuss the issue of coherence between excitation path-ways. The data are analyzed using a simple molecular reorientation model suggested by others which includes coherent excitation. The model is shown to be unable to completely account for the high polarizations measured in this experiment. We suggest reasons for the failure of this model.