  We study the structural and thermodynamic properties of a model of point
particles interacting by means of a Gaussian pair potential first introduced by
Stillinger [Stillinger F H 1976 J. Chem. Phys. 65, 3968]. By employing integral
equation theories for the fluid state and comparing with Monte Carlo simulation
results, we establish the limits of applicability of various common closures
and examine the dependence of the correlation functions of the liquid on the
density and temperature. We employ a simple, mean-field theory for the high
density domain of the liquid and demonstrate that at infinite density the
mean-field theory is exact and that the system reduces to an `infinite density
ideal gas', where all correlations vanish and where the hypernetted chain (HNC)
closure becomes exact. By employing an Einstein model for the solid phases, we
subsequently calculate quantitatively the phase diagram of the model and find
that the system possesses two solid phases, face centered cubic and body
centered cubic, and also displays reentrant melting into a liquid at high
densities. Moreover, the system remains fluid at all densities when the
temperature exceeds 1% of the strength of the interactions.
