Pair distributions and energy-density functionals for liquidHe4drops

The pair-distribution function $g_2$ ${(\mathrm{r}}_1$,${\mathrm{r}}_2$) in drops of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is studied with the variational Monte Carlo method. It is shown that in drops having 70 or more atoms it can be approximated as a functional of the local one-particle density and the separation $r_{12}$. Energy-density functionals based on this approximation of $g_2$ give a fairly accurate description of the ground-state properties of the drops.