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Journal of Physics B Atomic and Molecular Physics

Correlation effects in collisional depolarisation and redistribution of radiation

Gerard Nienhuis

Published Jan 14, 1983• 25 citations
Publisher

Abstract

The author derives an expression for the spectrum of the radiation scattered by an atom that suffers binary collisions in the weak-field limit. The frequency of the incident radiation is in near-resonance with a multiplet transition. The authors accounts for strong atom-perturber correlations that are induced when the incident or the detected frequency is in the far wing of an absorption line. For an isolated transition between two degenerate atomic levels the model picture of quasistatic absorption followed by adiabatic reorientation of the excited state predicts a redistributed fluorescence line with a polarisation that is determined by geometrical factors.

DOI
10.1088/0022-3700/16/1/003

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Journal of Physics B Atomic and Molecular Physics•Aug 14, 1986•1 citation
The author derives an expression for the spectrum of the radiation scattered by an atom that suffers binary collisions in the weak-field limit. The frequency of the incident radiation is in near-resonance with a multiplet transition. The authors accounts for strong atom-perturber correlations that are induced when the incident or the detected frequency is in the far wing of an absorption line. For an isolated transition between two degenerate atomic levels the model picture of quasistatic absorption followed by adiabatic reorientation of the excited state predicts a redistributed fluorescence line with a polarisation that is determined by geometrical factors.
The scattering of radiation in the presence of collisions can be described quantum-mechanically in terms of essentially two processes. The first may be thought of as an absorption to the excited state followed subsequently (after propagating in the excited state) by emission. This gives rise to radiation redistributed about the transition frequency. The effects of m-degeneracy are particularly interesting for this first process. As an example a case is considered in which the incident frequency is in the quasi-static line wing, while the scattered frequency is close to the line center. It is found that under these circumstances the dominant contribution from this process in the scattered spectrum is obtained for an absorption of the incident frequency taking place during a strong (close) collision and reemission of the scattered frequency when the atom is essentially unperturbed
The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.
We apply the analysis of paper I to degenerate atomic systems and calculate the effect of correlations between an atom (the absorber) and perturbers in the binary-collision approximation. The result of our calculation is a generalized absorption profile that specifies the final state of the atom an absorption event. This profile is then related to the total intensities of Rayleigh scattering and fluorescence (redistributed radiation) from the atom. The profile is expressed in terms of collision operators that depend on the index of the multipole of the atom that is created. Some of the operators represent correlations between radiative and collisional events and cannot, except in certain limits, be expressed in terms of the usual line-broadening operators. This, of course, implies that one needs extra dynamical information, on top of that obtainable from ordinary absorption experiments, to be able to describe redistribution. Conversely, redistribution offers a probe of collisional dynamics, not given by absorption experiments, via the polarization of fluorescent light. We give practical expressions for the calculation of these operators and discuss their implications.
We present a calculation of the scattering of monochromatic radiation by a degenerate atom in the binary-collision approximation. We limit ourselves to field strengths such that $\ensuremath{\Omega}{\ensuremath{\tau}}_{c}\ensuremath{\ll}1$, where $\ensuremath{\Omega}$ is the Rabi frequency for the atomic transition, and ${\ensuremath{\tau}}_{c}$ is the duration of a strong collision. Our calculation is not limited to the impact regime, $\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\ll}{\ensuremath{\tau}}_{c}^{\ensuremath{-}1}$, or to the region where thermal correlations may be neglected, i.e., $\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\ll}\frac{\mathrm{kT}}{\ensuremath{\hbar}}$. (Here $\ensuremath{\Delta}\ensuremath{\omega}$ is the difference between either the incoming or outgoing photon's frequency and the atom's natural frequency.) To do this we derive an equation of motion for the correlation function, valid outside the quantum-regression regime, whose solution for practical cases is straightforward. We present solutions for the weak-field (linear-response) regime in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles created.
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.
Perturbation theory for the interaction of light with a binary system is applied to collisional redistribution of radiation in the weak-field limit. Within the very large domain of validity of the binary model applied to collisions between non-hydrogenic atoms and atomic perturbers at low densities, redistribution can be viewed as collisional-induced absorption followed by spontaneous decay during a second collision. The formalism can be applied from the quasimolecular domain at large detunings Delta omega 1 or Delta omega 2 up to the impact regime, but emphasis is placed here on the non-impact region, at small Delta omega 1 or Delta omega 2, where non-adiabatic effects are important in collision-induced radiative absorption or emission rates as well as in the redistribution. The impact limit of the redistribution function is easily rederived in this way.