Interference Effects in Neutron and X Ray Scattering

The properties of interference between the one and multiphonon contributions to the dynamic and static scattering functions, S(Q, ω) and S(Q), first considered by Ambegaokar et al., are discussed in detail for b.c.c 3He and 4He for comparison with recent neutron and proposed X ray scattering experiments. Calculations of interference for Na and of the Debye temperature appropriate to the Debye–Waller factor in b.c.c 3He are also presented. In all cases the on shell interference term which alters the one phonon scattering intensity is found to be more important than the off shell term which alters the one phonon line shape. This is characteristic of systems in which anharmonic effects produce a large phonon frequency shift but in which the phonon lifetimes remain long. The difficulty in establishing the one phonon sum rules experimentally in the presence of interference is emphasized. As noted by Horner, existing unusual variations of scattering intensity observed in solid 4He can be satisfactorily explained by taking account of interference and this difficulty without introducing an anomolous Debye–Waller factor. Comparisons with liquid 4He suggest a similar difficulty in establishing the sum rules there.