  In the cluster expansion framework of Bose liquids we calculate analytical
expressions of the two-body, three-body and four-body diagrams contributing to
the g.s. energy of an infinite system of neutral alpha-particles at
zero-temperature, interacting via the strong nuclear forces exclusively. This
is analytically tractable by assuming a density dependent two-body correlation
function of Gaussian type. For the alpha-alpha potential we adopt the
phenomenological Ali-Bodmer interaction and semi-microscopic potentials
obtained from the Gogny force parametrizations. We show that under such
assumptions we achieve a rapid convergence in the cluster expansion, the
four-body contributions to the energy being smaller than the two-body and
three-body contributions by at least an order of magnitude.
