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Physical Review Letters

Collisional Effects on Induced Emmission and Absorption Transition Probabilities in Atomic Systems

Chung-Nan Chang, S. P. Koutsoyannis

Published Nov 16, 1970• 0 citations
Publisher

Abstract

The transition probabilities for induced emission and absorption of electromagnetic radiation by an excited atom interacting, in addition to the radiation field, with a system of "perturbers" (in single, binary, and completed encounters) are evaluated. It is found that Dirac's result $\frac{{W}_{\mathrm{ind}}}{{W}_{\mathrm{abs}}}=\frac{({\overline{n}}_{l\ensuremath{\sigma}}+1)}{{\overline{n}}_{l\ensuremath{\sigma}}}$ must be modified by a factor $\frac{{(1\ensuremath{-}\ensuremath{\alpha}n)}^{2}}{{(1+\ensuremath{\alpha}n)}^{2}}$, where $\ensuremath{\alpha}$ is related to the interaction potential of the emitter-perturber system as well as to the level structure of the "colliding" atoms, and $n$ is the perturber number density.

DOI
10.1103/physrevlett.25.1399

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The transition probabilities for induced emission and absorption of electromagnetic radiation by an excited atom interacting, in addition to the radiation field, with a system of "perturbers" (in single, binary, and completed encounters) are evaluated. It is found that Dirac's result WindWabs=(n‾l\ensuremathσ+1)n‾l\ensuremathσ\frac{{W}_{\mathrm{ind}}}{{W}_{\mathrm{abs}}}=\frac{({\overline{n}}_{l\ensuremath{\sigma}}+1)}{{\overline{n}}_{l\ensuremath{\sigma}}}Wabs​Wind​​=nl\ensuremathσ​(nl\ensuremathσ​+1)​ must be modified by a factor (1\ensuremath−\ensuremathαn)2(1+\ensuremathαn)2\frac{{(1\ensuremath{-}\ensuremath{\alpha}n)}^{2}}{{(1+\ensuremath{\alpha}n)}^{2}}(1+\ensuremathαn)2(1\ensuremath−\ensuremathαn)2​, where \ensuremathα\ensuremath{\alpha}\ensuremathα is related to the interaction potential of the emitter-perturber system as well as to the level structure of the "colliding" atoms, and nnn is the perturber number density.
Perturbation theory for the interaction of light with a binary collisional system is applied to the calculation of line profiles, spontaneous emission rates and absorption or stimulated emission coefficients. For the usual radiation fields are perturber densities, this approximation is valid at all detunings Delta omega except the very narrow resonance region. Appropriate expansions of the total binary system wavefunctions give the emission and absorption profiles or rates, for atom-electron systems as well as for atom-atom systems, from the impact regime at small Delta omega up to the Born-Oppenheimer regime at very large Delta omega in collision-induced radiative transitions, the transitions being asymptotically allowed or forbidden. Emphasis is given to the proper averages and sums over initial and final states of the binary system which give rise to non-adiabatic effects. One shows that it is of crucial importance to include all dynamical effects during one collisional event before undertaking any calculation at small Delta omega where simultaneous collisions may occur.
Perturbation theory is applied to the interaction between a binary collisional system and a weak radiation field to obtain the rate of induced absorption or the line profile of an optically allowed transition at low density. The collisional system wave functions are not affected by the radiation field and appropriate different expansions of these functions must be used for the two electron-atom or atom-atom systems under study. Unified expressions of the profile are given which converges to the impact limit at small detunings. The semi-classical approach of the collisional problem is given to underline the correspondence with the usual autocorrelation formalism. Both approaches break down for large detunings where a quantum collisional theory must be used.
The collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions are calculated for weak radiation fields. The approximations used are valid for $\ensuremath{\hbar}\ensuremath{\omega}$ near $\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, the atomic energy differences. The example case of $S\ensuremath{-}D$ transitions induced by a spherically symmetric perturber (e.g., a noble-gas atom) is treated in detail and compared to measurements. The case of "radiative collisions," in which both colliding atoms change their state, is included in the theory and is also compared to experiment.
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 study the collisionally induced excitation and photon emission of a neutral radiator atom surrounded by a gas of neutral foreign perturbers within the binary-collision approximation. We derive an equation of motion for the reduced density matrix of the radiator and obtain the spectrum of the spontaneously emitted photons including components due to collisionally induced radiation and to Rayleigh scattering, which is valid in both impact and quasistatic regimes. In our formulation single and subsequent collisional contributions are taken into account, and various coherent and incoherent corrections are examined.
The formal structure of the time dependence of the state of an atom in a perturber bath in an intense classical monochromatic radiation field is studied. The authors allow the cross sections of binary collisions to be affected by the radiation field. The result is used to derive an expression for the collision-broadened saturated fluorescence excitation spectrum and absorption rate in terms of a collisional relaxation operator. This operator can be related to the rate of collisionally aided radiative excitation.