Molecular dynamics at an energy-level crossing

TL;DR

This paper analyzes molecular predissociation at an electronic energy crossing, revealing that survival probability combines exponential decay with a polynomially small remainder, and provides explicit calculations of the main remainder contribution.

Contribution

It extends previous models to the critical crossing case, explicitly characterizing the survival probability's asymptotic behavior and computing the main remainder term.

Findings

Survival probability includes exponential and polynomially small terms.

Explicit formula for the main remainder contribution.

Analysis focused on the critical crossing energy case.

Abstract

This paper is a continuation of a previous work about the study of the survival probability modelizing the molecular predissociation in the Born-Oppenheimer framework. Here we consider the critical case where the reference energy corresponds to the value of a crossing of two electronic levels, one of these two levels being confining while the second dissociates. We show that the survival probability associated to a certain initial state is a sum of the usual time-dependent exponential contribution, and a reminder term that is jointly polynomially small with respect to the time and the semiclassical parameter. We also compute explicitly the main contribution of the remainder.