Abstract
The shift Δ 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 a constant volume. The cases of positive and negative shifts are found as the result of competition between interactions g and λ.
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