Renormalized density-functional theory of nonuniform superfluidHe4at zero temperature

A density-functional theory is constructed for nonuniform systems of superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at zero temperature. In calculations of the free-surface shape and tension it is found necessary to self-consistently renormalize the theory in order to account for the important effects of the zero-point motion of the long-wavelength (wave number $q\le q_m$) surface modes. Use of a cutoff $q_m=0.99\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, self-consistently determined within the theory, yields a surface tension of 0.384 ${\mathrm{e}\mathrm{r}\mathrm{g}/\mathrm{c}\mathrm{m}}^2$, which compares well with the experimental results of 0.378 ${\mathrm{e}\mathrm{r}\mathrm{g}/\mathrm{c}\mathrm{m}}^2$. Detailed liquid-structure effects are included, but no static density oscillations near the free surface result, in contrast to a theory of Regge. When the theory is applied to the case of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ bounded by a single hard wall, density oscillations near the wall are obtained. For a much simplified version of the density functional, an analytic solution for a planar free surface, vortex-line structure, and various properties of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ droplets, including the curvature dependences of the surface tension and Gibbs surface mass, are obtained.