Theory of the Bose-Einstein condensation in superfluid 4He

The perturbation theory for the Bose-condensate relative density ρ0/ρ in the ground state of liquid 4He is constructed in the form of virial expansion. The expansion effectively takes into account the short-range interatomic correlations. The connection of this expansion with the perturbation series, obtained previously by the author in the case of the long-range correlations, is analyzed. The expression for ln ρ0/ρ is found by means of reformulation of the perturbation theory. It correctly takes into account both types of correlation, not separating them, and contains only the spatial distribution functions of atoms of the liquid. The numerical estimate for 4He taking into account the first two terms of the series gives ρ0/ρ ∼ 8.8%