  We investigate ground-state and thermal properties of a system of
non-relativistic bosons interacting through repulsive, two-body interactions in
a self-consistent gaussian mean-field approximation wich consists in writing
the variational determined density operator as the most general gaussian
functional of the quantized field operators. Finite temperature results are
obtained in a grand canonical framework. Contact is made with the results of
Lee,Yang and Huang in terms of a particular truncations of the gaussian
approximation. The full gaussian approximation supports a free phase or a
thermodynamically unstable phase when contact forces and a standard
renormalization scheme are used. When applied to a Hamiltonian with zero range
forces interpreted as an effective theory with a high momentum cut-off, the
full gaussian approximation generates a quasi-particle spectrum having an
energy gap.
