Sum rules, structure factors, and phonon dispersion in liquid He4 at long wavelengths and low temperatures

Combining simple sum-rule arguments and a calculation of departures from the Feynman excitation spectrum, we demonstrate the existence of an inflection point in the liquid structure factor Sq, and relate Sq to the phonon dispersion coeffieient and the strength and average frequency of the multiparticle excitation spectrum in liquid He4. We find in particular 0, a result recently obtained by Woods and Cowley, to be in accord with other parameters determined by x-ray and neutron-scattering measurements.