Abstract
A product of two-body (${f}_{\mathrm{ij}}$) and three-body (${f}_{\mathrm{ijk}}$) correlation functions is used as a variational wave function for liquid $^{4}\mathrm{He}$. The ${f}_{\mathrm{ijk}}$ take into account the backflows produced by two particles recoiling from each other. The distribution functions, the energy, and its uncertainty are all calculated using the Lennard-Jones-deBoer-Michel potential, and diagrammatic hypernetted-chain summation methods. The calculated equilibrium energy of -6.72 (\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode^\circ\else\textdegree\fi{}K, is significantly lower than the -5.9\ifmmode^\circ\else\textdegree\fi{}K obtained with only a product of ${f}_{\mathrm{ij}}$, and agrees with the -6.84\ifmmode^\circ\else\textdegree\fi{}K estimated from a Monte Carlo integration of the many-body Schr\odinger equation. The proposed wave function is simple enough to be useful in Fermi liquids.
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