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Journal de physique

Absorption or emission during a collision : a test case H+ 2

C. Stehlé, N. Feautrier

Published Jan 1, 1986• 3 citations
Publisher

Abstract

The close coupled theory of scattering in a radiation field may be used to describe absorption or emission processes occurring during a collision. Using a semi-classical description of the collision we study the evolution of the collisional complex. The case of atomic hydrogen perturbed by protons is particularly interesting since the exact solution of the dynamical problem is known for a large domain of internuclear distances. In the particular case of the Ly α line we determine the characteristic time of the absorption or the emission. The « impact » and « quasistatic » limits are then analysed.

DOI
10.1051/jphys:019860047060101500

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The close coupled theory of scattering in a radiation field may be used to describe absorption or emission processes occurring during a collision. Using a semi-classical description of the collision we study the evolution of the collisional complex. The case of atomic hydrogen perturbed by protons is particularly interesting since the exact solution of the dynamical problem is known for a large domain of internuclear distances. In the particular case of the Ly α line we determine the characteristic time of the absorption or the emission. The « impact » and « quasistatic » limits are then analysed.
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.
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 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.
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.
To solve the problems of the classical model of the atom of both the atom's instability and the fact that it does not emit a line at a well-defined wavelength, we introduce the necessary quantum-mechanical ideas of angular momentum and energy quantization and provide a simple description of the hydrogen atoms. We go on to consider how to build up the structure of more complicated atoms. We also consider what quantum mechanics has to say about the exchange of energy between atoms in collisions and in interaction with light. This description includes collisional excitation and deexcitation and radiative processes (spontaneous and stimulated emission, absorption).