Molecular predissociation resonances at an energy-level crossing

TL;DR

This paper analyzes the resonances in a two-state quantum system near an energy crossing, providing precise estimates on their positions and widths under specific conditions.

Contribution

It introduces a detailed semiclassical analysis of molecular predissociation resonances at potential crossings, with optimal estimates on resonance characteristics.

Findings

Resonance locations are precisely estimated.

Resonance widths are optimally bounded.

Results apply to systems with transversally intersecting potentials.

Abstract

We study the resonances of a two-by-two semiclassical system of one dimensional Schr\"odinger operators, near an energy where the two potentials intersect transversally, one of them being bonding, and the other one anti-bonding. Under an ellipticity condition on the interaction, we obtain optimal estimates on the location and on the widths of these resonances.