Studies of the gaussian model

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Abstract
The Gaussian model has a purely repulsive pair potential, and the properties of its fluid state can be obtained from the expansion of the pressure in powers of the activity. We obtain the eighth and ninth coefficients of this expansion, and the corresponding virial coefficients, for spaces of dimensionality of 1–4. We examine the convergence of the expansions and show that it is likely that the fluid state is stable at all densities for all dimensions. We obtain also the exact equation of state for infinite dimensionality and report some new sum rules for the cluster integrals that form the coefficients of the activity expansion.