\(1/N\)-expansion for the critical temperature of the Bose gas

Abstract

We revised the large-\(N\) expansion for a three-dimensional Bose system with short-range repulsion in normal phase. Particularly, for the model potential that is characterised only by the \(s\)-wave scattering length \(a\) the full numerical calculations of the critical temperature in the \(1/N\)-approximation as a function of the gas parameter \(an^{1/3}\) are performed. Additionally to the well-known result in the dilute limit we estimated analytically the leading-order strong-coupling behavior of the Bose-Einstein condensation transition temperature. It is shown that the critical temperature shift of the non-ideal Bose gas grows at small \(an^{1/3}\), reaches some maximal value and then falls down becoming negative.