Structure of elementary excitations and temperature dependence of the momentum distribution in liquid 4He.

Abstract

We study the momentum-space structure of the elementary excitations in liquid $^{4}\mathrm{He}$ by calculating the change \ensuremath{\delta}${n}_{\mathrm{k}\ensuremath{\rightarrow}}$(p\ensuremath{\rightarrow}) in the momentum distribution of atoms on creating an excitation of momentum k\ensuremath{\rightarrow}. 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\ensuremath{\rightarrow}\ensuremath{\sim}k\ensuremath{\rightarrow}. The \ensuremath{\delta}${n}_{\mathrm{k}\ensuremath{\rightarrow}}$(p\ensuremath{\rightarrow}) is used to calculate the momentum distribution n(T,p) of the liquid at low temperatures (1 K). The temperature dependence of the fraction of atoms in the p=0 condensate and the 1/${p}^{2}$ and 1/p singularities of n(T,p) are discussed.