The motion of impurities and the spectrum of excitations in liquid helium-four

Abstract

In this paper we calculate the effective mass of a helium-three impurity in helium-four and the spectrum of elementary excitations in pure helium-four. Both these calculations are carried out within the framework of the Feynman-Cohen variational method. We have solved exactly the variational equation for the backflow field for the impurity and we find that is of dipole form at large distances but deviates from this form at short distances. The best value of the effective mass is about 1.75 m 3. We have used this exact solution to calculate the energy spectrum of the elementary excitations. The value of the roton minimum is 11.0° K.Both these results are somewhat sensitive to the detailed form of the liquid structure factor—which has to be taken from experiment. The physical properties of the impurity and excitation wavefunctions are examined and we tentatively suggest that the roton minimum represents a transition point at which single-particle excitation becomes possible.