Analytic predissociation linewidths from scattering theory

Abstract

Analytical predissociation linewidths are derived from the scattering solutions to the two-state curve crossing problem. Four cases are considered: ‘inner’ and ‘outer’ crossings in the ‘weak’ or ‘strong’ coupling limits. It is shown that linewidths in each case take the form Γ = Γ_o cos² η, where Γ₀ is related to the Landau-Zener transition probability and η is a phase integral between one of the classical turning points of the known bound state curve, and the turning point of the continuum potential. Γ₀ is a decreasing function of energy in the weak interaction limit, whereas for strong interaction, it is an increasing function of energy. The outer crossing, strong coupling case is shown to provide an interpretation of the characteristic appearance of the visible spectra of ICl and IBr.