Diatomic predissociative widths and shifts from multichannel Siegert quantization and asymptotic analysis of resonance wave functions

Abstract

Predissociative widths and shifts are studied for a diatomic molecule described by a Morse potential crossed by one or two repulsive exponential potentials. This defines two models with either two channels or three channels. The coupled channel equations are solved either with a complex rotated coordinate (in which case the boundary conditions are the same as for a bound state) or with explicit enforcement of Siegert outgoing wave only asymptotic boundary conditions. The widths and shifts derived from the complex quantized energies of the two channel model are compared to previous results for this model based on semiclassical, phase shift, or Green operator methods. In the weak coupling regime, significant improvement over previous phase shift based results is obtained. In the intermediate coupling case, Siegert quantization confirms the value given by the semiclassical approach to the coupling giving a resonance of zero width. This is in disagreement with the Green operator prediction. Additional support is given by an asymptotic analysis performed on the resonance wave function (A.A.R.W.) which gives widths in very good agreement with those derived from the complex quantized energies. The three channel model leads to the definition of a total width and of two partial widths. Asymptotic analysis of the three-channel resonance wave function gives directly partial widths which, in the weak width regime, sum accurately to the total width.