Density matrices of superfluid helium-4. II

The results of Part I of the study [1] are used to investigate the binary distribution function of the atoms and the single-particle density matrix of a many-boson system with allowance for many-particle correlations. They are used to find the thermodynamic functions of a Bose liquid at the absolute zero of temperature. Expressions for the mean value of the kinetic energy $K$, the potential energy $\Phi$, and the relative number of atoms in the Bose condensate, $N_0/N$, are found up to the terms of the second approximation with respect to the “parameter” $\sum_{\mathbf k}({\dots})/N$, which contains a double summation over the wave vector $\mathbf k$, and $N$ is the total number of atoms. All quantities are expressed in terms of the liquid static structure factor $S_q$. A numerical calculation for liquid $\mathrm{He}^4$ at $T=0^\circ$ K using the experimental values of $S_q$ gives $K/N=14.2^\circ$ K/atom, $\Phi/N=-20.6^\circ$ K/atom, total energy $E/N=-6.4^\circ$ K/atom, $N_0/N=3.7\%$.