Three-level approximation for interacting Boson transition-temperature calculation

The normal-superfluid phase-transition temperature of a dilute Bose system whose particles interact via a two-body potential composed of a hard core followed by a weak attractive tail is studied using the three-level approximation. It is found that, for such a system, the three-level approximation does give results, for the transition temperature, approximately equal to the lambda-transition temperature of liquid 4He. The condensed state is composed of ε0 = 0, ε1 = E0/N and ε2, such that the states ε0 and ε1 lie below the cutoff momentum.