A strong-coupling theory of superfluid ${^4}$He

Abstract

We propose a new theoretical approach to the excitation spectrum of superfluid ${^4}He$. It is based on the assumption that, in addition to the usual Feynman density fluctuations, there exist localized modes which describe the short range behaviour in the liquid associated with microscopic cores of quantiz ed vortices. We describe in a phenomenological way the hybridization of those two kinds of excitations and we compare the resulting energy spectrum with experimental data, e.g. the structure factor and the cross section for sing le quasi-particle excitations. We also predict the existence of another type of excitation interpreted as a vortex loop. The energy of this mode agrees both wit h critical velocity experiments and high energy neutron scattering. In addition we derive a relation between the condensate fraction and the roton e nergy and we calculate the reduction of the ground-state energy due to the superfluid order.