Ground-State Energy of LiquidHe4

A compressibility-consistent integral equation for the radial distribution function $g$ similar to a previously proposed pressure-consistent integral equation is applied to a ${\left(\frac{b}{\mathcal{r}}\right)}^5$ effective potential. The results compare well with those obtained by a molecular-dynamics calculation and are superior to the results of Percus-Yevick 2 and Percus-Yevick 2 XS calculations. The $g$ obtained from this integral equation can be used to compute the sum of the bridge diagrams. These bridge-diagram sums are used in an Euler-Lagrange equation to compute the ground-state Bijl-Jastrow wave function for liquid ${\mathrm{He}}^4$. An interatomic potential of the Lennard-Jones 6-12 type is used. The ground-state energy is found to be -6. 63°K/atom (experiment: -7. 14°K). The equilibrium density is 0. 0205 atom/${\mathrm{\AA }}^3$ (experiment: 0. 02185 atom/${\mathrm{\AA }}^3$). The structure factor and radial distribution function obtained are compared with experimental results.