Structure of elementary excitations and temperature dependence of the momentum distribution in liquidHe4

Abstract

We study the momentum-space structure of the elementary excitations in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ by calculating the change δ$n_{\mathrm{k}\to }$(p→) in the momentum distribution of atoms on creating an excitation of momentum k→. Jastrow and Jastrow plus triplet wave functions are used for the ground state, and the excitations are created with Feynman and Feynman-Cohen excitation operators. We find that the excitations in the long-wavelength limit are harmonic vibrations with equal amount of change in kinetic and potential terms. At large k, however, they become ‘‘single-particle’’-like; and most of the energy comes from removing one particle from the ground-state momentum distribution and putting it at states with p→∼k→. The δ$n_{\mathrm{k}\to }$(p→) is used to calculate the momentum distribution n(T,p) of the liquid at low temperatures (p=0 condensate and the 1/$p^2$ and 1/p singularities of n(T,p) are discussed.