Surface-Mode Renormalized Density-Functional Theory of the Free Surface ofHe4

We present a density-functional theory, renormalized to account self-consistently for the effects of the zero-point motion of surface modes, for the free surface of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at zero temperature. Although detailed liquid-structure effects are included, no static density oscillations near the free surface are found in contrast to a theory of Regge. For the case of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ bounded by a single hard wall, density oscillations near the wall are obtained.