Theory of the Liquid-Solid Phase Transition in Helium II

Abstract

The liquid-solid phase transition of helium at low temperatures is shown to result from the instability of the roton mode. In a simple model of the roton-roton interactions, the instability arises at a finite value of the roton energy as a result of the hybridization of a single roton with a bound roton pair. Thus our model exhibits a discontinuous jump of the soft-mode energy at the phase transition in agreement with neutron scattering experiments.