Dynamical structure factorS(q,ω)of liquid helium II at zero temperature

Abstract

The dynamical density correlation function of liquid helium II at zero temperature is expressed in terms of a static restoring force ${\ensuremath{\Omega}}_{0}$ and a polarization operator $M$ within Mori's theory. $M$ is approximated in terms of two-mode decay integrals and ${\ensuremath{\Omega}}_{0}$ is related self-consistently to the liquid structure factor. The nonlinear integral equations for $M$ and ${\ensuremath{\Omega}}_{0}$ are solved by an interation procedure and the dynamical structure factor $S(q,\ensuremath{\omega})$ obtained is compared with the experimental results of Cowley and Woods. The elementary excitation spectrum calculated has a roton minimum $\ensuremath{\Delta}$ of 11\ifmmode^\circ\else\textdegree\fi{}K and shows Pitaevskji bending for large momenta. The existence of a resonance of $S(q,\ensuremath{\omega})$ is found to be the explanation for the measured excitation peak to exceed $2\ensuremath{\Delta}$. The variation of the single excitation strength as a function of momentum is analyzed. The multiphonon contribution to $S(q,\ensuremath{\omega})$ is discussed and the existence of a double-peak structure therein is found for intermediate wave numbers.