A hard-sphere model of the helium film

A quantum hard-sphere system bounded by two parallel rigid walls is studied at absolute zero as a model of a helium film. A variational wave function is constructed which is of the Bijl-Dingle-Jastrow type modified by a one-body term which vanishes at the walls; Monte Carlo quadrature is used. We focus our attention particularly on the behavior of the single-particle density function and the condensed-state wave function, i.e., the order parameter. Both show significantly different behavior from that predicted by the Hartree theory. The healing length is calculated, we believe for the first time, and is rather small. The average condensate as a function of distance between two walls is also investigated. The calculation serves as a special probe for approximations to the ground-state wave function in a uniform system.This work has been supported by the U.S. Atomic Energy Commission under contract # AT(11-1)-3077 and Grant No. GH-36457 with National Science Foundation.