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Physical Review A

Absorption and emission of radiation in the region of an avoided level crossing

M. J. O’Callaghan, Alan Gallagher, Theodore D. Holstein

Published Nov 1, 1985• 19 citations
Publisher

Abstract

The spectrum for absorption and emission of radiation by colliding atoms or a diatomic molecule is calculated for spectral regions dominated by an avoided level crossing. Example processes are absorption during an atom-atom collision with separation to either crossing atomic state, total absorption to both crossing states, and spontaneous emission during a collision with either state initially populated. Absorption and emission by bound diatomic molecules (including photodissociation) is described by the theory, and as an example it is applied to the ${\mathrm{Cs}}_{2}$ A-X band. Spectra due to single-velocity and impact-parameter collisions, as well as thermal and impact-parameter averages, are given. The shapes of the resulting spectra are parametrized by the interaction strength (or excitation transfer probability) between the crossing levels and the slopes of the ground- and excited-state potentials (assumed constant) in the region of the level crossing. The theory is applied to two observations of such regions that have been reported. We conclude that measurements of spectra in the region of level crossing is a very powerful diagnostic of the potentials and transfer probability in the level-crossing region, which is responsible for most inelastic atom-atom energy-transfer processes.

DOI
10.1103/physreva.32.2754

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The spectrum for absorption and emission of radiation by colliding atoms or a diatomic molecule is calculated for spectral regions dominated by an avoided level crossing. Example processes are absorption during an atom-atom collision with separation to either crossing atomic state, total absorption to both crossing states, and spontaneous emission during a collision with either state initially populated. Absorption and emission by bound diatomic molecules (including photodissociation) is described by the theory, and as an example it is applied to the Cs2{\mathrm{Cs}}_{2}Cs2​ A-X band. Spectra due to single-velocity and impact-parameter collisions, as well as thermal and impact-parameter averages, are given. The shapes of the resulting spectra are parametrized by the interaction strength (or excitation transfer probability) between the crossing levels and the slopes of the ground- and excited-state potentials (assumed constant) in the region of the level crossing. The theory is applied to two observations of such regions that have been reported. We conclude that measurements of spectra in the region of level crossing is a very powerful diagnostic of the potentials and transfer probability in the level-crossing region, which is responsible for most inelastic atom-atom energy-transfer processes.
A study is made of the influence of photon absorption (emission) processes on the dynamics of collisions between two atoms. Under certain conditions the radiation field can transfer colliding atoms to a bound molecular state. The main contribution to these processes is made by atoms colliding with relative velocities and impact parameters which ensure that these atoms spend a long time near each other (quasifinite motion). The appearance of quasifinite states in the absorption spectra of Rb and Cs vapors is reported and a determination is described of the matrix elements of the transitions from these states to a bound molecular state.
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.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
The processes of absorption and emission of radiation by a system of two interacting atoms is investigated. Separation between the atoms is assumed to be much larger than the atomic diameter, and interactions considered are those between the individual atoms and the radiation field and the electrostatic interaction between the atoms. Calculations include those for the time-dependent probability amplitude of the intermediate and final states as well as that of the emission line shape. The line shape of the emitted radiation consists of two peaks whose amplitude, separation, and half-width are functions of both the internuclear separation R of the atoms and the energy difference of the excited states of the two atoms. For a large energy difference, the peaks are distinct; for small energy differences, the peaks are distinct at smaller separations, but merge toward the line shape characteristic of a single, isolated atom as R increases.
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
Introduction Until now, our discussion of the interaction between radiation and matter has concentrated only on the spectral aspects of radiation. The results could determine the wavelengths for absorption and emission or the selection rules for such transitions, but could not be used to determine the actual extent of emission or absorption. These too are important considerations which are needed to fully quantify radiative energy transfer. Unfortunately, none of the classical theories can predict the extent of emission from an excited medium, or even the extent of absorption. Although the discussion in Section 4.9 (on the propagation of electromagnetic waves through lossy media) touched briefly on the concept of attenuation by absorption, it failed to show the reasons for the spectral properties of the absorption or to accurately predict its extent. We will see later that the classical results are useful only as a benchmark against which the actual absorber is compared. The objective of this chapter is therefore to present an introduction to quantum mechanical processes that control the emission and absorption by microscopic systems consisting of atoms and molecules. The results will then be used to predict the extent of emission by media when excited by an external energy source and to evaluate the absorption of incident radiation. It is now well recognized that all emission or absorption processes are the result of transitions between quantum mechanical energy levels.