Molecular predissociation resonances near an energy-level crossing II: Vector field interaction

TL;DR

This paper analyzes the resonances in a two-by-two semiclassical Schrödinger system near an energy crossing, focusing on vector field interactions to determine their precise locations and widths.

Contribution

It provides optimal estimates for the location and widths of resonances in a coupled Schrödinger system with vector field interactions near potential crossings.

Findings

Resonance locations are precisely estimated.

Resonance widths are optimally bounded.

Analysis applies to systems with crossing potentials and vector interactions.

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. Assuming that the interaction is a vector-field, we obtain optimal estimates on the location and on the widths of these resonances.