Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials.

It is proven that, for any soft potential φ(r) characterized by a finite Fourier transform e φ(k), the virial and energy thermodynamic routes are equivalent if the Fourier transform of the total correlation function divided by the density ρ, eh(k)/ρ, is an arbitrary function of ρβ e φ(k), where β is the inverse temperature. This class of approximations includes the mean spherical approximation as a particular case.