Capture of Neutrons by Atoms in a Crystal

The precise determination of the properties of nuclear resonance levels from the capture of slow neutrons is made difficult by the fact that most of the substances used for absorbers and detectors are in the solid state, so that the calculations of Bethe and Placzek for the influence of the Doppler effect are inapplicable, since these were based on the assumption of a perfect gas. In this paper, their calculations are generalized to include the effect of the lattice binding. Under the assumption that the crystal may be treated as a Debye continuum, it is shown that for sufficiently weak lattice binding, the absorption curve has the same form as it would in a gas, not at the temperature $T$ of the crystal, however, but at a temperature which corresponds to the average energy per vibrational degree of freedom of the lattice (including zero-point energy). In cases of somewhat stronger lattice binding, the line form is found to be more complicated, and may even have a fine structure. Plots are given of the absorption line in several typical cases. An approximate formula for the cross section for self-indication is also derived.