He-4 spectrum shift caused by He-3 admixture

Abstract

The shift of a maxon-roton He-4 excitation spectrum E via the He-3 admixture is considered theoretically. The Bogoliubov formula for E(ρ, g) as a function of Bose-condensate density ρand of He-4/He-4 interaction g is used as an element of partition function formalism of the whole system, presented in the form of a path (functional) integral. The dependence of ρon g, He-4/He-3 interaction λas well as on the pressure P, induced by He-3 admixture, is taken into account. The new model of g, suitable for analytical calculations, is used for a description of a change of P within the constant volume. The cases of positive and negative shifts are found as the result of competition between interactions g and λ.