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

Abstract

The authors consider a new case of collision-induced transitions between two discrete (quasistationary) states embedded in a continuum. The energy difference ( delta =E1-E2) 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 (iV1,2) via the continuum have a common exponential dependence: (E1-i Gamma 1/2)-(E2-i Gamma 2/2)= delta -ig exp(- eta R) iV1,2=iF1,2 exp(- eta R). Transition probabilities are determined in closed analytical form for this problem.