Perturbation of finite-lattice spectral levels by nearby nuclear resonances

TL;DR

This paper analyzes how nearby nuclear resonances affect the spectral levels of finite crystalline structures, revealing conditions for the existence of exponentially decaying molecular states and deriving their decay rates.

Contribution

It provides a theoretical proof linking nuclear resonance properties to the decay rates of molecular states in finite crystalline structures.

Findings

Existence of molecular states decaying exponentially in time.

Decay rate formula involving nuclear resonance parameters.

Conditions for spectral level perturbation by nuclear resonances.

Abstract

We consider finite linear or cyclic crystalline structures with molecular cells having narrow pre-threshold nuclear resonance. We prove that if the real part of such a nuclear resonance lies within the energy band (the convex hull of the energy levels) of the crystalline structure arising of a separated molecular level, then there exist molecular crystalline states that decay exponentially in time and the decay rate $\Gamma_R^{(m)}$ of these states in the main order is described by the formula $\Gamma_R^{(m)}\cong 4\frac{\mathop{\rm Re} a}{\Gamma_R^{(n)}}$ where $a$ is the value of the residue of the molecular channel transfer function at the nuclear resonance point and $\Gamma_R^{(n)}$ is the nuclear resonance width.