Relativistic Stark resonances in a simple exactly soluble model for a diatomic molecule

TL;DR

This paper presents an exact solution for a 1-D relativistic diatomic molecule model in an electric field, analyzing resonance behaviors and spectral properties using advanced mathematical methods.

Contribution

It introduces a novel exactly solvable relativistic model for diatomic molecules and applies the Weyl-Titchmarsh-Kodaira method to analyze spectral resonances.

Findings

Resonances move in the complex energy plane with changing parameters

Ground state resonance behavior depends on interatomic distance and potential strength

Resonance behavior aligns with non-relativistic results at low field and small distances

Abstract

A simple 1-D relativistic model for a diatomic molecule with a double point interaction potential is solved exactly in a constant electric field. The Weyl-Titchmarsh-Kodaira method is used to evaluate the spectral density function, allowing the correct normalization of continuum states. The boundary conditions at the potential wells are evaluated using Colombeau's generalized function theory along with charge conjugation invariance and general properties of self-adjoint extensions for point-like interactions. The resulting spectral density function exhibits resonances for quasibound states which move in the complex energy plane as the model parameters are varied. It is observed that for a monotonically increasing interatomic distance, the ground state resonance can either go deeper into the negative continuum or can give rise to a sequence of avoided crossings, depending on the strength of the potential wells. For sufficiently low electric field strength or small interatomic distance, the behavior of resonances is qualitatively similar to non-relativistic results.