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Journal of Physics B Atomic Molecular and Optical Physics

An exponential two-state model for collisional excitation via a continuum

Victor Sidis, Danielle Grimbert, C Courbin

Published Aug 28, 1988• 6 citations
Publisher

Abstract

The authors consider a new case of collision-induced transitions between two discrete (quasistationary) states embedded in a continuum. The energy difference ( delta =E 1 -E 2 ) between the two states is assumed to remain constant throughout the collision whereas the difference between their individual decay widths ( Gamma 1 - Gamma 2 ) and their imaginary couplings (iV 1,2 ) via the continuum have a common exponential dependence: (E 1 -i Gamma 1 /2)-(E 2 -i Gamma 2 /2)= delta -ig exp(- eta R) iV 1,2 =iF 1,2 exp(- eta R). Transition probabilities are determined in closed analytical form for this problem.

DOI
10.1088/0953-4075/21/16/013

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The authors consider a new case of collision-induced transitions between two discrete (quasistationary) states embedded in a continuum. The energy difference ( delta =E 1 -E 2 ) between the two states is assumed to remain constant throughout the collision whereas the difference between their individual decay widths ( Gamma 1 - Gamma 2 ) and their imaginary couplings (iV 1,2 ) via the continuum have a common exponential dependence: (E 1 -i Gamma 1 /2)-(E 2 -i Gamma 2 /2)= delta -ig exp(- eta R) iV 1,2 =iF 1,2 exp(- eta R). Transition probabilities are determined in closed analytical form for this problem.
We consider two quasimolecular states, one discrete and one quasistationary, whose dynamical coupling becomes possible only by absorption or emission of laser-field photons. In the presence of the laser field the initially discrete state also becomes quasistationary, with an energy continuum shifted with respect to the continuum into which the initially quasistationary state decays. For such an interacting system, the corresponding system of coupled equations is derived and then solved within the Landau-Zener and Demkov nonadiabatic-coupling models, with various assumptions about the time variation of decay widths. Closed-form expressions for the transition probabilities of the half and full collision are obtained. The considered general physical problem is related to electron-capture processes in slow ion--excited-atom (or atom--excited-ion) collisions in a laser field or to laser-assisted excitation-transfer processes in atom--excited-atom slow collisions.
Radiationless transitions, and the interactions causing them, perturb absorption lineshapes and the time course of light emission. In this paper we use the standard model of a discrete state interacting with a continuum, but we allow the continuum density of states to assume various energy dependent forms. This energy dependence causes the absorption line shape to deviate from lorentzian in interesting ways. The emission decay curves may also become highly non-exponential, and show quantum beat effects in many situations.
Resonances manifest as the sharp peaks observed in graphs of scattering cross section versus energy. Resonances in binary collisions are closely related to twobody bound or quasi-bound states, which are the discrete quantum states whose amplitudes fall off (usually exponentially) in space as the separation r → ∞. In the case of a single channel, a bound state is formed at a specific negative energy; that is, below the channel threshold. In the multichannel case, as mentioned in the preceding chapter, a bound state occurs when all the channels are closed; that is, below the threshold of the lowest channel. Under specific circumstances, a bound state may occur at zero energy; that is, right at the lowest threshold. Quasi-bound states are also discrete quantum states that are formed temporarily at a discrete positive energy (above the lowest threshold). Both resonant and bound states (including quasibound ones) can be described by a unified approach to cold collisions. The temporary binding of a quasi-bound state at a discrete energy enhances the scattering cross section at that energy. This occurs because the quasi-bound state eventually decays into the continuum of scattering states whose central energy equals the binding energy. The resonance width is determined by the coupling between the bound and continuum states.