We consider the capture of a cold neutron (kinetic energy < 0,1 meV) by a crystal in the case that, at first, by the emission of a phonon, the neutron is absorbed by one of the lattice nuclei forming a compound nuclear resonance. Subsequently, the resonance decays by the emission of a photon. The energy of the compound nuclear resonance must be very close to the neutron threshold, i.e. within the range of phonon energies (\lesssim 100 meV), thus implying that the absorbing nuclei must be heavy actinides. We discuss the dependence of the capture process on the initial occupation pattern of phonons and, in particular, a mechanism of enhancing the absorption process.

PACS numbers: 25.40.Fq