Application of the equation-of-motion method to the spectrum of superfluid helium. II

Abstract

On the basis of the formalism developed in a previous paper, several features of the two-branch excitation spectrum observed by Cowley and Woods are discussed. In the long-wave-length limit we derive a T4 dependence of the sound velocity which is in agreement with a T3 law for the specific heat. Furthermore, a simple derivation of the Pitaevskii singularity at the end point qc≅3.55 -1 of the phonon-roton spectrum is presented and it is argued that above qc the excitations are essentially decoupled from the condensate. Finally, the author gives convincing arguments that the diffuse second branch of Cowley and Woods should converge, for q→0. near twice the roton gap where, however, it should disappear in neutron scattering but show up in Raman scattering, in accordance with experiments by Greytak et al. © 1972 The American Physical Society.