Self-consistent phonons in fcc ^{4}He

The dynamic form factor, S(Q, ce), of fcc 'He at high density is calculated, including the one-phonon, the two-phonon, and interference contributions, for comparison with the recent neutron-scattering measurements of Eckert et al. and of Thomlinson et al. The purpose is to test how well the standard self-consistent phonon (SCP) theory, which takes no account of short-range correlations in the atomic vibration, can describe a moderately anharmonic crystal such as fcc He. The SCP theory is found to provide a good overall description of the neutron scattering data including both the one-phonon and multiphonon character. It is also found that the usual separation of S(g,re), into a one-phonon and multiphonon contribution becomes difficult or impossible for wave-vector transfers Q = (2n/a)(j, $,$,) with f & 1.3 at high-energy transfer. This is due to an unusually large frequency dependence of the two-phonon scattering contribution to S(0 ~)