Abstract
By a Monte Carlo variational calculation, it is shown that the description of the ground-state properties of a hard-sphere Bose system is improved if the Jastrow wave function contains a correlation structure at distances intermediate between the first and the second shell of neighbors. We relate these correlations to the zero-point motion of rotons. We predict that the oscillations of the structure factor $S(k)$ and of the radial distribution function $g(r)$ increase at finite temperatures. Such intermediate-distance correlations improve the description of the solid phase by a Jastrow wave function, but the description is still not satisfactory compared to localized wave functions. Backflow associated with rotons induces explicit three-particle correlations in the wave function, and a new form for such correlations is proposed for variational calculation for $^{4}\mathrm{He}$.
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