Power series expansion of phonon spectrum in liquid helium

Abstract

With the aid of accurate microscopic calculations and rigorous sum rule arguments, available data on the phonon spectrum in liquid helium are analyzed. In particular we present a Tamm-Dancoff calculation of the correction to Feynman's spectrum and show that low-order perturbation calculations are valid. Without making any undue statement about the dispersion formula in the hydrodynamic region, we conclude that at least for 0.3<q<0.7 A−1 experimental data from inelastic neutron scattering and elastic x-ray scattering are on the whole consistent.