Critical temperature of Bose–Einstein condensation of a dilute Bose gas

Using the Huang–Yang–Luttinger and Lee–Yang virial expansions of a dilute Bose gas as well as our theory of phase transition, we show that in the dilute limit, the critical temperature of Bose–Einstein condensation of a Bose gas is given by [Tc−Tc(0)]/Tc(0)=γn1/3a, γ=4[ζ(3/2)]5/3/[3ζ(5/2)]=4.92506… , which is in good agreement with the experimental result of Reppy et al., γ=5.1±0.9.