  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.
