Self-consistent phonons in fccHe4

Abstract

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