Self-consistent phonons in fccHe4

Abstract

The dynamic form factor, $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}, \ensuremath{\omega})$, of fcc $^{4}\mathrm{He}$ 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 $^{4}\mathrm{He}$. 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 $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}, \ensuremath{\omega})$, into a one-phonon and multiphonon contribution becomes difficult or impossible for wave-vector transfers $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}=(\frac{2\ensuremath{\pi}}{a})(\ensuremath{\zeta}, \ensuremath{\zeta}, \ensuremath{\zeta},)$ with $\ensuremath{\zeta}<1.3$ at high-energy transfer. This is due to an unusually large frequency dependence of the two-phonon scattering contribution to $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}, \ensuremath{\omega})$.