Liquid⁴He. I. Binding energy and excitation energy spectrum from two-body correlations

Abstract

As a first step in a theoretical study of the properties of liquid⁴He we have calculated the binding energy from two-body correlations in the system. Using an effective interaction or reaction matrix obtained by a modified Brueckner theory, low-temperature properties such as the binding energy, the elementary excitation energy spectrum, and the velocity of first (ordinary) sound are calculated or estimated. For simplicity we use the approximation of a reference energy spectrum with a quadratic momentum dependence for the input single-particle energy spectrum, which in principle should be fitted to self-consistent single-particle energies. The intermediate-state potential energies are, however, chosen to be equal to zero. Hence, the three-body energy contribution and also higher order energy contributions must be estimated by separate calculations. A self-consistent solution is obtained through the depletion of the zero-momentum state, which is also calculated. The calculations are done for two different two-body potentials, an Yntema-Schneider potential given by Brueckner and Gammel, and a Frost-Musulin potential given by Bruch and McGee. The theoretical results are −3.1 to −4.0°K for the binding energy, 39–44% for the depletion, and 176–217 m/sec for the sound velocity. The corresponding experimental results are −7°K, 83%, and 238.3 m/sec, respectively, i.e., the difference is generally within a factor of two. The agreement with experimental results is reasonably good (or bad), especially since three-body and higher order cluster terms are not included in this first approximation.