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The Journal of Chemical Physics

Laser-assisted excitation transfer as a single-atom multiphoton process

Peter W. Milonni

Published Apr 15, 1977• 14 citations
Publisher

Abstract

An approach to the calculation of cross sections for laser-assisted excitation transfer processes is outlined for the dipole–dipole case. The internal atomic variables are treated in the Heisenberg picture, while the simplest form of semiclassical collision theory is used for the atomic trajectories. A simple physical picture in the spirit of the Weizsäcker–Williams method emerges: The laser-assisted excitation transfer may be treated approximately as a single-atom multiphoton process in an applied field.

DOI
10.1063/1.434409

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An approach to the calculation of cross sections for laser-assisted excitation transfer processes is outlined for the dipole–dipole case. The internal atomic variables are treated in the Heisenberg picture, while the simplest form of semiclassical collision theory is used for the atomic trajectories. A simple physical picture in the spirit of the Weizsäcker–Williams method emerges: The laser-assisted excitation transfer may be treated approximately as a single-atom multiphoton process in an applied field.
Formulas are derived for the differential and integral cross sections associated with laser-induced excitation transfer. The theory is patterned closely after our recent treatment of laser-induced chemi-ionization. It is found that cross sections specific to single-photon absorption are proportional to the square of the cosine of the angle between the laser polarization and the initial relative velocity of the two colliding atoms. The distortion by a laser of the cross section for an elastic scattering event also is treated. Finally, a cross-section formula is derived for a collision-induced two-photon absorption, mediated by a single intermediate electronic state.
The semiclassical theory is developed for a simultaneous collisional and radiative process,, and applied to the laser-induced ionisation in a collision of two excited alkali atoms (in their lowest n2P states) in a laser field. Perturbation theory is used to evaluate the probability for this process in the case of straight-line paths at large impact parameter. The collision perturbation is taken to be the dipole-dipole interaction between the two atoms, which together with the dipole interaction with the radiation leads to the occurrence of s and d intermediate atomic states and p and f final states for the ejected electron.
The excitation transfers through collision between hydrogen atoms and between other simple identical atoms are considered theoretically by an impact parameter method. A rotating atom approximation and a fixed atom approximation (concerned with the direction of electronic polarization) are applied to the problem. The cross-section for the transfer of the excitation (2 p 2 P ) of a hydrogen atom with thermal velocity (kinetic energy of 0.025 ev) to the other hydrogen atom in the ground state is estimated to be 3065 Å 2 with the rotating atom approximation and 680 Å 2 with the fixed atom approximation. In the case of helium atoms, the cross-section for the transfer of the excitation (2 p 1 P ) is also estimated to be 606.7 Å 2 with thermal velocity.
A theory has been formulated to characterize charge-transfer collisions in the presence of an external laser field. The molecular-state-expansion method is used to describe the scattering process within the impact-parameter formalism. Electron translation factors are included in the molecular-state expansion so that the scattering wave function satisfies the correct boundary conditions. The theory is applied to the process K+{\mathrm{K}}^{+}K++Na\ensuremath{\rightarrow}K+Na+{\mathrm{Na}}^{+}Na+. In addition, we have made a detailed analysis of laser-assisted charge transfer for low-energy collisions. In this case, a Landau-Zener formula can be derived which shows that the cross section increases with decreasing incident energy. In general the laser coupling is dominant in the low-energy region, while the dynamical coupling becomes important as the collision energy increases.
The transfer of energy from the translational to the internal degrees of freedom or vice versa is analyzed for radiatively assisted inelastic collisions among atoms in a gas. For a specific atomic-level configuration, it is shown that the absorption of a laser photon may induce a transition between two levels that are displaced by the collisional interaction (a dipole-dipole potential in this treatment) if a fraction of the kinetic energy of the atomic relative motion is simultaneously absorbed. The process thus results in a cooling of the atomic kinetic temperature. In other level configurations, energy goes in the opposite direction, with a heating of the kinetic temperature. This mechanism is described by means of the Wigner-function formalism, which allows a passing to the quasiclassical limit for the atomic motion in a simple way.