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Physical Review A

Experimental determination of Na–noble-gas velocity-changing and fine-structure-changing collision kernels

Jos E. M. Haverkort, J. P. Woerdman, P. R. Berman

Published Dec 1, 1987• 26 citations
Publisher

Abstract

We report on an experimental investigation of the collision kernels governing the effects of velocity-changing collisions, fine-structure-changing collisions, and their interplay, for Na--noble-gas pairs. The velocity distributions in the two Na excited-state fine-structure levels and in the Na ground-state hyperfine levels have been measured in the presence of a pump laser which produces velocity-selective excitation. For interpretation of these experiments we use a rate-equation model developed in the context of light-induced drift: the velocity-changing collisions are accounted for by a composite Keilson-Storer kernel describing large-angle and small-angle collisions and the fine-structure-changing collisions are treated in the sudden limit. The model is valid for arbitrarily high pump laser intensities and uses only a single adjustable parameter characterizing the small-angle scattering. It is found that the theory describes the experimental velocity distributions in all four Na levels over a wide range of experimental parameters for each Na--noble-gas pair. The relevance of the collision kernels deduced in the present work is discussed in the context of light-induced drift.

DOI
10.1103/physreva.36.5251

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Journal of Physics B Atomic and Molecular Physics•Jul 14, 1987•17 citations
We report on an experimental investigation of the collision kernels governing the effects of velocity-changing collisions, fine-structure-changing collisions, and their interplay, for Na--noble-gas pairs. The velocity distributions in the two Na excited-state fine-structure levels and in the Na ground-state hyperfine levels have been measured in the presence of a pump laser which produces velocity-selective excitation. For interpretation of these experiments we use a rate-equation model developed in the context of light-induced drift: the velocity-changing collisions are accounted for by a composite Keilson-Storer kernel describing large-angle and small-angle collisions and the fine-structure-changing collisions are treated in the sudden limit. The model is valid for arbitrarily high pump laser intensities and uses only a single adjustable parameter characterizing the small-angle scattering. It is found that the theory describes the experimental velocity distributions in all four Na levels over a wide range of experimental parameters for each Na--noble-gas pair. The relevance of the collision kernels deduced in the present work is discussed in the context of light-induced drift.
We present a model for light-induced drift (LID) in the Na--noble-gas system which should enable direct comparison with experiment. In contrast to previous theories of LID based on a two-level description of the optical absorbers and on a simplified collision treatment, the present model is based on a realistic description of laser-driven Na atoms immersed in a buffer gas. Starting from the generalized Bloch equations, we introduce a rate-equation model for the velocity distributions in the four important Na levels. The velocity-changing and fine-structure-changing collisions are described using composite Keilson-Storer collision kernels in which all adjustable parameters have been eliminated by using available literature data. We apply the model in numerical calculations of LID as a function of all experimentally accessible parameters. It is found that the ground-state hyperfine splitting can have large effects on LID, whereas the excited-state fine-structure splitting has not. The paper establishes criteria for optimum LID effects; when using a single-frequency laser the maximum attainable drift velocity is predicted to be 13.8 m/s. Using a proper set of boundary conditions, we find a pressure dependence of LID qualitatively different from the predictions based on previous work. Finally, the influence of the collision model is investigated. We find that LID is independent of the shape of the collision kernel, indicating that a strong-collision model is always valid.
We report on a quantitative experimental investigation of velocity-changing collisions by means of velocity-selective optical pumping (VSOP). We have calculated the VSOP line shape for an atom with hyperfine structure with the use of two phenomenological kernels for the collision effects: the Keilson-Storer kernel, and a two-term kernel consisting of a broad Keilson-Storer part and a narrower Gaussian component. Corrections were included to account for the finite absorption in the sample and the backward reflection of the pumping beam. The experiments were carried out in sodium vapor with neon as the perturber gas. The D1{D}_{1}D1​ line of sodium was used for optical pumping, and the orientation of the ground state was detected. Free parameters of the theory were determined by fitting the predicted line shapes to experimental curves. The Keilson-Storer kernel proved unsatisfactory, but the two-term kernel reproduced well the observed line shapes over the entire collision profiles in the neon pressure range 0-57 mtorr. In an independent experiment using rapidly modulated VSOP we also measured directly the cross section of velocity-changing collisions: $\ensuremath{\sigma}=(1.13\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2. The large weight obtained for the narrow Gaussian from the fits, as well as the collision cross section which is three times as large as the cross section deduced from tabulated gas kinetic radii, may indicate the presence of collisions with relatively small velocity changes in addition to hard-sphere encounters.
We report the results of an experimental study of the effects of velocity-changing collisions on two-photon and stepwise-absorption line shapes. Excitation spectra for the $3{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}\ensuremath{\rightarrow}4{D}_{\frac{1}{2}}$ transitions of sodium atoms undergoing collisions with foreign gas perturbers are obtained. These spectra are obtained with two cw dye lasers. One laser, the pump laser, is tuned 1.6 GHz below the $3{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}$ transition frequency and excites a nonthermal longitudinal velocity distribution of excited 3P123{P}_{\frac{1}{2}}3P21​​ atoms in the vapor. Absorption of the second (probe) laser is used to monitor the steady-state excited-state distribution which is a result of collisions with rare gas atoms. The spectra are obtained for various pressures of He, Ne, and Kr gases and are fit to a theoretical model which utilizes either the phenomenological Keilson-St\"orer or the classical hardsphere collision kernel. The theoretical model includes the effects of collisionally aided excitation of the 3P123{P}_{\frac{1}{2}}3P21​​ state as well as effects due to fine-structure state-changing collisions. Although both kernels are found to predict line shapes which are in reasonable agreement with the experimental results, the hard-sphere kernel is found superior as it gives a better description of the effects of large-angle scattering for heavy perturbers. Neither kernel provides a fully adequate description over the entire line profile. The experimental data is used to extract effective hard-sphere collision cross sections for collisions between sodium 3P123{P}_{\frac{1}{2}}3P21​​ atoms and helium, neon, and krypton perturbers.
Measurements of velocity-changing collision (VCC) kernels are obtained using velocity-selective optical pumping. This is the first measurement of the shape of an elastic VCC kernel over the full thermal range of velocity changes. Since ground-state collisions are studied (5s1/2{\mathit{s}}_{1/2}s1/2​ Rb and He, Ne, Ar, Kr, or Xe), very low buffer-gas pressures can be used, and therefore pressure broadening (dephasing collisions) does not obscure the effects of VCC's. The data are deconvolved to eliminate the effects of the natural linewidth and are then extrapolated with respect to buffer-gas pressure to determine the single-collision limit. For small initial velocities, the measured kernels are consistent with a hard-sphere model for large velocity changes, but differ significantly for small velocity changes. The measured VCC kernels for large initial velocities and large velocity changes do not exhibit this agreement with the hard-sphere kernel. This implies that information about the inter- atomic potential can be obtained from a measurement of VCC kernels. We also show the inadequacy of the much-used Keilson-Storer kernel [J. Appl. Math. 10, 243 (1952)].
The authors consider a system of optically active two-state atoms immersed in a buffer gas and irradiated by a light beam. The corresponding Bloch equations are augmented by Keilson-Storer (KS) collision kernels (1952) which account for velocity-changing collisions. Expansion of the density operator elements in the eigenfunctions of KS kernels allows one to obtain exact solutions for the Laplace transforms of the density operator elements which may be expressed as rational approximants with any prescribed degree of accuracy. As an example they apply this method to discussion of the light-induced drift effect. In particular they give analytic expressions for the drift velocity, which are illustrated by numerical results. Finally, they briefly discuss possible generalisations and applications of the presented method.