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Physical Review A

Nonadiabatic theory of atomic line broadening: Redistribution calculations for Sr (1 P← 1 S)+Ar

Paul S. Julienne, Frederick H. Mies

Published Nov 1, 1986• 64 citations
Publisher

Abstract

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 $^{1}\mathrm{P}$ 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 $^{1}\mathrm{P}_{1}$+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.

DOI
10.1103/physreva.34.3792

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The close-coupled theory of collisions in a radiation field is used to calculate the absorption profile for the Sr 1\ensuremath←1^{1}\ensuremath{\leftarrow}^{1}1\ensuremath←1S 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 close-coupled theory of atomic collisions in the presence of a radiation field may be used to calculate the distribution of final atomic states which results from absorption of polarized light during a collision. The theory applies equally well to optical collisions (line broadening) and to radiative collisions (laser-induced collisional energy transfer). For an optical collision the detuning $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\infty}}$ is restricted to be larger than either the Rabi frequency or the widths due to natural, Doppler, or pressure broadening. The radiation field is assumed to be weak enough that the transition probabilities are linear in field intensity. The molecular picture is emphasized in which the wave function is expanded in a basis of field-free molecular states and the Hamiltonian is blocked in accordance with molecular quantum numbers. The quantities needed to predict experimental observables are reduced radiative scattering SSS-matrix elements ${s}_{\ensuremath{\omega}}$ in the asymptotic Hund's case-(e) representation. The theory of product orientation and alignment is equivalent to that which has been developed for molecular photodissociation. It requires coherent sums of ${s}_{\ensuremath{\omega}}$ matrix elements from different transition branches, that is, for PPP-, QQQ-, and RRR-type transitions corresponding to changes of -1, 0, and +1 in total molecular angular momentum. On the other hand, the total absorption coefficient and the branching ratio to different final fine-structure states irrespective of orientation or alignment depend on incoherent sums of the same matrix elements.
Profiles of the singly ionized strontium resonance line at 421.6 nm (4p 2{\mathrm{}}^{2}2P1/2{\mathrm{P}}_{1/2}P1/2​--4s 2{\mathrm{}}^{2}2S1/2{\mathrm{S}}_{1/2}S1/2​) which are collisionally broadened by argon have been measured from the line core to near-wing region (within the distance of \ensuremath{\Delta}\ensuremath{\nu}\ensuremath{\lesssim}50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ from the line center). The observed broadening rate of the core is (1.87\ifmmode\pm\else\textpm\fi{}0.25)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}20}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$/${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at 690 K. A clearly asymmetric profile has been observed in the wing region. These results are discussed by considering semiclassical impact and quasistatic theories combined with theoretical interaction potentials for the Sr+{\mathrm{Sr}}^{+}Sr+-Ar pair which were previously reported by the present authors.
Redistribution and depolarisation of light scattered by atoms undergoing collisions outside the impact region of the line profile has been studied experimentally and theoretically. In a cell experiment intensity and linear degree of polarisation of the fluorescence components 32S1/2 to or from 32P1/2,3/2 of Na atoms induced by collisions with Ar buffer gas atoms were measured as functions of the laser frequency omega L. The decrease of polarisation of the D2 component observed when omega L is shifted away from the D2 toward D1 resonance disagrees with calculations on the basis of the factorisation approximation of the theory of redistribution. Using Baylis (1975) potentials for the Na/Ar system, the effect is interpreted in terms of adiabatic coupling of the 32P3/2 electronic angular momentum to the collision axis during 'strong' collisions, giving rise to a greater than average depolarisation.
The depolarisation of the redistributed Na D1and D2line fluorescence caused by Na-Ar collisions after far-wing excitation was investigated. In the limit of zero Ar density the J=1/2orientation and J=3/2alignment reflect the distribution among Zeeman sublevels of Na 32PJproduced after absorption of a photon into one or several excited Na-Ar molecular states at small internuclear separation, followed by a mixing between these states during dissociation. Measurements of these quantities as functions of the detuning up to Delta omegaJ=50 cm-1in the red wings are compared with quantum-mechanical coupled-channel (CC) calculations using realistic molecular potentials and thermal averaging, and with predictions from the factorisation approximation (FA) of the theory of redistribution. Fair agreement with CC calculations and FA predictions was obtained within the impact region, proving the validity of the factorisation assumption there. Outside this region the overall depolarisation is primarily due to reorientation of the Na 3P electronic angular momentum and is reproduced qualitatively by the CC calculations but not by the FA theory. Additional depolarisation connected with the fine-structure coupling was observed.
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 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.