Free-surface density profile and tension of liquidHe3

A new variational method based on varying an assumed effective surface potential is used to study the free-surface density profile and tension of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at zero temperature. Given the radial distribution function of homogeneous liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ (measured by x-ray scattering) as input, the theory yields a surface tension of 0.134 K${\mathrm{\AA }}^{-2\mathrm{}}$, which compares reasonably well with the extrapolated experimental value of 0.11 K ${\mathrm{\AA }}^{-2\mathrm{}}$. Features of the model presented here include: (i) the prediction of a "work function" of about 0.20 K for a surface ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atom, (ii) the prediction of a surface region that is about two atomic layers in thickness, and (iii) the determination of the position of the Gibbs surface, which indicates a rather asymmetrical distribution of atoms in the surface layer. In contrast to the recent calculation of Mackie and Woo, however, no highdensity region results even though we used the same radial distribution function as input.