4He spectrum shift caused by 3He admixture

The shift of the 4He spectrum by the 3He admixture is evaluated with the use of the partition function for the Hamiltonian of the system, presented in the form of a path integral. The excitation spectrum Ep(λ,ρf,T) is found as a function of 3He–4He interaction λ, 3He density ρf and temperature. The latter is taken into account via the Gibbs distribution and via the 4He condensate density ρ(T), which is an element of Bogoliubov approximation in the path integral method. The cases of positive and negative shifts are found as well as the case of intersection of the distorted 4He curve with the spectrum of pure 4He in the zero shift points p0. These momentum values p=p0 for zero points of interaction λ(p0)=0 are introduced empirically with the use of experimental data. The structure of Ep is discussed in the light of experiments. The largest influence of 3He admixture is noticed in the region of roton minimum of 4He spectrum due to the influence of the pure 3He dispersion curve.