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Physical Review A

Effects of velocity-changing collisions on two-photon and stepwise-absorption spectroscopic line shapes

P. F. Liao, John E. Bjorkholm, P. R. Berman

Published Jun 1, 1980• 74 citations
Publisher

Abstract

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 $3{P}_{\frac{1}{2}}$ 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 $3{P}_{\frac{1}{2}}$ 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 $3{P}_{\frac{1}{2}}$ atoms and helium, neon, and krypton perturbers.

DOI
10.1103/physreva.21.1927

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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 3S12\ensuremath→3P12\ensuremath→4D123{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}\ensuremath{\rightarrow}4{D}_{\frac{1}{2}}3S21​​\ensuremath→3P21​​\ensuremath→4D21​​ 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 3S12\ensuremath→3P123{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}3S21​​\ensuremath→3P21​​ 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.
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.
Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming C6{C}_{6}C6​ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small \ensuremath{\Delta}vz{v}_{z}vz​ collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}vz{v}_{z}vz​ collisions is used. It is also demonstrated how the inelastic (3P3/2{P}_{3/2}P3/2​-3P1/2{P}_{1/2}P1/2​) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
The authors report studies of collision-induced features of the $3{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}\ensuremath{\rightarrow}4{D}_{\frac{3}{2}}$ two-photon absorption in atomic-sodium vapor undergoing collisions with several rare-gas perturbers. The results yield the collisional redistribution function which describes the nonresonant excitation of the 3P123{P}_{\frac{1}{2}}3P21​​ intermediate state. Good agreement with theory is obtained only if effects of $3{P}_{\frac{1}{2}}\ensuremath{\leftrightarrow}3{P}_{\frac{3}{2}}$ state-changing collisions are included in the calculations. Results are used to obtain a value for a pressure-broadening coefficient in the Na-Kr system.
Optical pumping of the ground states of sodium can radically alter the shape of the laser-induced fluorescence excitation spectrum, complicating measurements of temperature, pressure, etc., which are based on these spectra. Modeling of the fluorescence using rate equations for the eight hyperfine states of the sodium D manifolds can be used to quantify the contribution to the ground state pumping of transitions among the hyperfine excited states induced by collisions with buffer gas atoms. This model is used here to determine, from the shape of experimental spectra, cross sections for $\ensuremath{\Delta}F$ transitions of the P3/2{P}_{3/2}P3/2​ state induced by collisions with helium and argon atoms, for a range of values assumed for the ${P}_{1/2}, \ensuremath{\Delta}F$ cross sections. The hyperfine cross sections measured using this method, which to our knowledge is novel, are compared with cross sections for transitions involving polarized magnetic substates mF{m}_{F}mF​ measured previously using polarization sensitive absorption. Also, fine-structure transition $(\ensuremath{\Delta}J)$ cross sections were measured in the pumped vapor, giving agreement with previous measurements made in the absence of pumping.
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.