Perturbation of finite-lattice spectral levels by nearby 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 $Γ_R^{(m)}$ of these states in the main order is described by the formula $Γ_R^{(m)}\cong 4\frac{\mathop{\rm Re} a}{Γ_R^{(n)}}$ where $a$ is the value of the residue of the molecular channel transfer function at the nuclear resonance point and $Γ_R^{(n)}$ is the nuclear resonance width.