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

The dynamical density correlation function of liquid helium II at zero temperature is expressed in terms of a static restoring force ${\Omega }_0$ and a polarization operator $M$ within Mori's theory. $M$ is approximated in terms of two-mode decay integrals and ${\Omega }_0$ is related self-consistently to the liquid structure factor. The nonlinear integral equations for $M$ and ${\Omega }_0$ are solved by an interation procedure and the dynamical structure factor $S(q,\omega )$ obtained is compared with the experimental results of Cowley and Woods. The elementary excitation spectrum calculated has a roton minimum $\Delta$ of 11°K and shows Pitaevskji bending for large momenta. The existence of a resonance of $S(q,\omega )$ is found to be the explanation for the measured excitation peak to exceed $2\Delta$. The variation of the single excitation strength as a function of momentum is analyzed. The multiphonon contribution to $S(q,\omega )$ is discussed and the existence of a double-peak structure therein is found for intermediate wave numbers.