4He spectrum shift caused by 3He admixture II

Abstract

The shift ∆E of a maxon-roton 4 He excitation spectrum E via the 3 He admixture is considered theoretically. The Bogoliubov formula for E(ρ, g) as a function of Bose-condensate density ρ and of 4 He/ 4 He 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 ρ on g, 4 He/ 3 He interaction λ as well as on the pressure P , induced by the 3 He 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.