Difference between zero- and first-sound propagation in solid Kr

We point out that the zero-sound-first-sound difference in solid rare gases is a very sensitive probe of the phonon self-energy. Recent advances in our knowledge of the interatomic potentials of these solids have enabled us to remove much of the ambiguity from this source and hence focus directly on the influence of different model self-energies. We have investigated the approximations of Koehler and Goldman, Horton, and Klein using a self-consistent harmonic basis with no explicit inclusion of hard-core effects. We find that the previously unexplained experimental result for solid Kr near melting, that $C_{44}$ as measured by neutron scattering is 12% greater than obtained from Brillouim scattering, lies between the predictions of these two approximations.