Self-consistent description of long-range and short-range correlations in the theory of liquid $\operatorname{He}^4$. I

A wave function is proposed for the ground state of liquid $\operatorname{He}^4$ that takes into account both long-range correlations that describe the zero-point vibrations of the Bose liquid and the short-range correlations that take into account the hard Core in the potential of the interatomic interaction. The method of collective variables is used to make an exact calculation of the long-range correlations, which describe well a weakly nonideal Bose gas. The short-range correlations are taken into account implicitly. It is shown that to obtain quantitative results in the theory of liquid $\operatorname{He}^4$ the hard core in the interaction potential must be taken into account explicitly.