Surface region of superfluid helium as an inhomogeneous bose-condensed gas

We present arguments that the low density surface region of self-bounded superfluid He-4 systems is an inhomogeneous dilute Bose gas, with almost all of the atoms occupying the same single-particle state at T = 0. Numerical evidence for this complete Bose-Einstein condensation was first given by the many-body variational calculations of He-4 droplets by Lewart, Pandharipande, and Pieper in 1988 [Phys. Rev. B 37, 4950(1988)]. We show that the low density surface region can be treated rigorously using a generalized Gross-Pitaevskii equation for the Bose order parameter.