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Quantum Electronics

Collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines

А. И. Пархоменко, Anatolii M. Shalagin

Published Nov 30, 2011• 0 citations
Publisher

Abstract

Using the eikonal approximation, we have calculated effective collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines. We have established the relation between the probabilities of absorption and stimulated emission and the characteristics of the radiation and elementary scattering event. The example of the power interaction potential shows that quantum mechanical calculation of the collision frequencies in the eikonal approximation and previously known spectral line wing theory give similar results for the probability of radiation absorption.

DOI
10.1070/qe2011v041n11abeh014679

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Using the eikonal approximation, we have calculated effective collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines. We have established the relation between the probabilities of absorption and stimulated emission and the characteristics of the radiation and elementary scattering event. The example of the power interaction potential shows that quantum mechanical calculation of the collision frequencies in the eikonal approximation and previously known spectral line wing theory give similar results for the probability of radiation absorption.
Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.
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
An analysis is made of the general aspects of the physics of processes occurring in a system of colliding atoms in the presence of a radiation field. The attention is concentrated on the relationship between the spectral characteristics and various photon absorption (emission) processes in a system of interacting atoms (regarded as a quasimolecule). Nonlinear optical effects in the far wings of atomic lines are considered and the effects are interpreted. A relationship between these effects and the change in the atomic collision dynamics due to the presence of a radiation field is considered.
Spectral lines of radiating atoms are broadened by perturbations due to the surrounding plasma environment. In line-broadening calculations, the statistical average of the perturbation is weighted by the density matrix, which, in thermal equilibrium, contains correlations between the radiator and plasma. These correlations, however, have been neglected by all line-broadening theories except for the kinetic theory. The relaxation theory of line broadening is a mathematically exact derivation containing only one physical approximation: neglect of density-matrix correlations. We revisit this derivation and improve it by including the correlations. The line-broadening operator derived with the updated relaxation theory differs from that derived from the kinetic theory, though both derivations are considered to be exact. The kinetic theory derivation predicts that density-matrix correlations result a strong static shift of spectral lines. Our derivation, on the other hand, predicts that the correlations are a frequency-dependent effect that affects the line wings, and there is no shift of the line due to correlations. In addition, we predict that changes in the line shape due to correlations are only noticeable at extremely high densities. To distinguish the more appropriate model, we compare the shifts calculated with the relaxation and kinetic theory with data. The comparison shows support for the relaxation theory and casts into doubt the accuracy of the derivation of the kinetic theory of line broadening.
The shape of an isolated spectral transition is analyzed in terms of an approximation to the Waldmann–Snider kinetic equation. This equation is written in the form of a drift and collision operator acting on a density matrix. With the use of the spherical approximation, the collision operator is subdivided into an elastic Boltzmann-like collision term, an inelastic loss term, and a dephasing term. The Boltzmann-like term is responsible for Dicke narrowing of spectral lines, the inelastic loss term leads to line broadening and the dephasing term may contribute both to line broadening and shifting. Simple approximations to these terms are powerful enough to account for some of the details of experimental line shapes such as asymmetrical deviations from a Lorentzian line shape. Model numerical calculations are carried out assuming classical scattering potentials of the form 1/rn in the Boltzmann-like term and single complex frequencies for the other two. It was found that as long as the density was scaled to give the same diffusion constant, the exact form of the scattering cross section had little effect on the final line shape.