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Physical Review A

Collision-induced absorption in atomic electronic transitions

Alan C. Gallagher, Theodore D. Holstein

Published Dec 1, 1977• 125 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.16.2413

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Physical Review A•Nov 1, 1985•19 citations
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 \ensuremathℏ\ensuremathω\ensuremath{\hbar}\ensuremath{\omega}\ensuremathℏ\ensuremathω near \ensuremathℏ\ensuremathω0\ensuremath{\hbar}{\ensuremath{\omega}}_{0}\ensuremathℏ\ensuremathω0​, the atomic energy differences. The example case of S\ensuremath−DS\ensuremath{-}DS\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.
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.
An introduction is presented to a recently established nonperturbative approach to the transitions between atomic states induced by weak electromagnetic waves. A special case of the general solution is calculated and discussed in detail. Results of the nonperturbative approach reduce under perturbation condition to those obtained by the time- dependent perturbative method,but overcome the difficulty that the perturbative results are obviously unreasonable in the near resonant region. According to the nonperturbative solution,the electric- dipole selection rules are approximately recovered for short time. For large time,however,probabilities for forbidden transitions may become comparable with those for allowed ones.
Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.
The interaction of an intense optical-maser field with excited atoms in a gas discharge leads to a considerable change in the population of those levels which are resonant at the maser frequency. This will cause a change in the population of other levels that are connected to the maser levels through collision-induced nonradiative as well as radiative transitions. Using the 1.15-\ensuremath{\mu} optical maser, these effects have been studied in detail for the 2s2s2s levels of neon where the changes are completely due to collisions. By analyzing the intensity changes in spontaneous emission originating from a gas-discharge cell placed within the maser resonator, we have observed the approach to a partial thermalization of two closely spaced levels. In this way we have been able to obtain the atomic-collision cross section for excitation transfer between the 2s22{s}_{2}2s2​ and 2s32{s}_{3}2s3​ levels. In pure neon this has been found to be ${\ensuremath{\sigma}}_{23}=(2.3\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2. For a helium-neon mixture the measured cross section is ${\ensuremath{\sigma}}_{23}=(1.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2. The experimental method used to determine these cross sections eliminates the uncertainties caused by the effects of electron-atom collisions and radiative cascade. These techniques also yield the ratio of the Einstein coefficients for the transitions $2{s}_{2}\ensuremath{\rightarrow}2{p}_{10}$ and $2{s}_{3}\ensuremath{\rightarrow}2{p}_{10}$. The measured ratio is $\frac{{A}_{2}}{{A}_{3}}=3.0\ifmmode\pm\else\textpm\fi{}0.4$.
The first analysis is made of stimulated Raman scattering and two-photon absorption (emission) processes resulting in a change in the states of two colliding particles. These processes are caused the by interaction between dipole moments induced as a result of polarization of the particles by the radiation. Equations are derived to describe multiphoton transitions during a collision between two particles in a radiation field. Using the approximation of rectilinear trajectories, expressions are derived and analyzed for the cross section of collisional two-photon transitions in weak and strong fields. It is shown that in fields of ≈103 cgs esu, the cross section of these transitions may reach 10–4 cm2
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.