Features of HNC/0 Solutions for Symmetric Films of Liquid ⁴ He at T = 0 K

Abstract

Much work has been devoted in recent years^1–7 to microscopic calculations of the ground state of inhomogeneous liquid ⁴ He at T = 0 K. The Hamiltonian of an interacting N-body quantum system immersed in an external one-body field is

$$ H = - \frac{{{{\hbar }^{2}}}}{{2m}}\sum\limits_{{i = 1}}^{N} {\nabla _{i}^{2}} + \sum\limits_{{i < j = 1}}^{N} {\upsilon ({{r}_{{ij}}})} + \sum\limits_{{i = 1}}^{N} {{{U}_{{ext}}}({{r}_{i}})} , $$

((1))

where v(r _ij = |r _i — r _j |) is a two-body potential and U _ext (r _i ) an external one-body potential. In the present work we shall focus our attention on some features of variational solutions obtained when the the ground state of a Bose system is described by an N-body wave function of the Feenberg types⁸

$$ {{\Psi }_{0}}({{r}_{1}}, \ldots ,{{r}_{N}}) = \exp [\frac{1}{2}\sum\limits_{{i = 1}}^{N} {{{u}_{1}}({{r}_{i}})} + \frac{1}{2}\sum\limits_{{i < j = 1}}^{N} {{{u}_{2}}({{r}_{i}},{{r}_{j}})].} $$

((2))