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.