On the Born-Oppenheimer approximation of diatomic molecular resonances

TL;DR

This paper presents a new approach to simplifying the Hamiltonian of diatomic molecules, enabling better analysis and localization of molecular resonances using semiclassical and elliptic region techniques.

Contribution

It introduces a novel reduction method for diatomic molecular Hamiltonians that preserves the collision set and combines semiclassical pseudodifferential operators with localized operators.

Findings

Effective Hamiltonian combines semiclassical pseudodifferential and localized operators.

The approach allows precise localization of molecular resonances.

Applications demonstrate improved understanding of molecular resonance behavior.

Abstract

We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the semiclassical parameter being the inverse of the square-root of the nuclear mass), and a semibounded operator localised in the elliptic region corresponding to the nuclear collision set. We also study its behaviour on exponential weights, and give several applications where molecular resonances appear and can be well located.