Stationary-state scattering theory for dissociative photodetachment on nonadiabatically coupled potential surfaces as a probe of transition states

We develop a stationary-state scattering theory of dissociative photodetachment in a transition-state region for a system in which two or more potential surfaces are mutually coupled through the nonadiabatic interaction in dissociative channels. Since the present phenomenon involves electron detachment and molecular dissociation dynamics, it is a doubly half collision in a three-body problem. We perform an asymptotic analysis for the dissociative wave functions, which formally gives a closed form of the transition amplitude in which the pulse shape and polarization of a pumping laser, the kinetic energy distribution of a detached electron, and the product distribution are all correlated. The present formal theory thus provides a unified basis for the analyses in the experimental and numerical studies. We revisit the mathematical role of the so-called in-going state for general dissociation dynamics and, in particular, argue that the traditional interpretation of the ingoing wave function due to Breit and Bethe is not necessarily valid.