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The mean spherical approximation (MSA) can be solved semi-analytically forthe Gaussian core model (GCM) and yields - rather surprisingly - exactly thesame expressions for the energy and the virial equations. Taking advantage ofthis semi-analytical framework, we apply the concept of the self-consistentOrnstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function Kis introduced in the MSA closure relation which is determined to enforcethermodynamic consistency between the compressibility route and either thevirial or energy route. Utilizing standard thermodynamic relations this leadsto two different differential equations for the function K that have to besolved numerically. Generalizing our concept we propose anintegro-differential-equation based formulation of the SCOZA which, althoughrequiring a fully numerical solution, has the advantage that it is no longerrestricted to the availability of an analytic solution for a particular system.Rather it can be used for an arbitrary potential and even in combination withother closure relations, such as a modification of the hypernetted chainapproximation.Comment: 11 pages, 11 figures, submitted to J. Chem. Phy

Thermodynamically self-consistent liquid state theories for systems with bounded potentials