Effects of the T-matrix center-of-mass approximation in the Brueckner–Sawada theory of liquid helium II

Abstract

As a model for liquid helium II, we study the Bose–Einstein gas with a two-body interaction potential of the form ~δ(r − a), where r is the interparticle separation. Excitation spectra for various values of a are calculated using the Brueckner–Sawada approach based on the concept of the T matrix. However, unlike the work of Brueckner and Sawada and many other related works that followed, we take into account the dependence of the T matrix on the center-of-mass momentum of the interacting particles. Excitation spectra calculated with and without this dependence, using two different expressions for the two-particle propagator, indicate the validity of the Brueckner and Sawada center-of-mass approximation for physically interesting values of a. The difference between the two spectra is found to increase as a increases.