Bose condensate in liquid $\textrm{He}^4$

Expressions for the single-particle density matrix of a Bose fluid and the amount of Bose condensate are found in terms of the liquid structure factor. A self-consistent perturbation theory with respect to the exactly solvable hard-spheres model is formulated for the logarithm of the relative number of atoms of the Bose condensate. The packing parameter for the hard spheres is found from the compensation equation for the first-order correction. This has made itpossible to take into account correctly the contribution of pair correlations between atoms of the liquid to the dynamical “erosion”of the Bose condensate. The Bogolyubov–Zubarev expression for the ground-state energy of a many-boson system is used to calculate the contribution of the three- and fourparticle correlations to the density matrix and estimate the contribution numerically. The results of the theory are used to calculate the filling of the Bose condensate in the ground state of liquid $\textrm{He}^4$ as a function of the liquid density.