Optimized free surface of liquidHe4in hypernetted-chain approximation

Abstract

Within the hypernetted-chain approximation, coupled Euler equations are derived for the radial distribution function and the surface profile of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at zero temperature and fixed chemical potential. For the solution a reliable method based on the local-density approximation is developed. It is found that the Euler equation for $\rho$ has a solution only in the region where the bulk pressure is positive and the chemical potential negative. At the saturation point (${\rho }_{\mathrm{sat}}=0.0175\mathrm{}$ ${\mathrm{\AA }}^{-3\mathrm{}}$ and $\frac{E_{\mathrm{sat}}}{N}=-5.2\mathrm{}$ K) of our model consisting of the Lennard-Jones potential with de Boer—Michels parameters, we obtain the surface energy $E_s=0.17\mathrm{}$ K/${\mathrm{\AA }}^2$ and the monotonically decreasing surface profile with diffusivity of 6 Å based on (10-90%) criteria.