Spontaneous decay of resonant energy levels for molecules with moving nuclei

TL;DR

This paper analyzes the spontaneous decay of electronic energy levels in molecules with moving nuclei, establishing the validity of the Born-Oppenheimer approximation and deriving a decay rate formula.

Contribution

It provides a rigorous proof of the Born-Oppenheimer approximation's validity and a simple formula for decay rates in molecules with dynamical nuclei.

Findings

Validation of the Born-Oppenheimer approximation at leading order

Derivation of a formula for spontaneous decay rates

Analysis under the limits of small fine structure constant and heavy nuclei

Abstract

We consider the Pauli-Fierz Hamiltonian with dynamical nuclei and investigate the transitions between the resonant electronic energy levels under the assumption that there are no free photons in the beginning. Coupling the limits of small fine structure constant and of heavy nuclei allows us to prove the validity of the Born-Oppenheimer approximation at leading order and to provide a simple formula for the rate of spontaneous decay.