Molecular predissociation resonances below an energy level crossing

TL;DR

This paper analyzes the precise positions and widths of molecular predissociation resonances in 1D Schrödinger systems, revealing they are exponentially small and governed by Agmon distances at potential crossings.

Contribution

It provides a detailed mathematical characterization of resonances near energy crossings in molecular systems, including their exact locations and exponential smallness of widths.

Findings

Resonance widths are exponentially small.

Resonance positions are determined by Agmon distances.

Resonances occur below the crossing energy level.

Abstract

We study the resonances of $2\times 2$ systems of one dimensional Schr\"odinger operators which are related to the mathematical theory of molecular predissociation. We determine the precise positions of the resonances with real parts below the energy where bonding and anti-bonding potentials intersect transversally. In particular, we find that imaginary parts (widths) of the resonances are exponentially small and that the indices are determined by Agmon distances for the minimum of two potentials.