Abstract
The Ornstein–Zernike equation is solved in the mean spherical approximation (MSA) for a model liquid with an internal degree of freedom. The spatial variation of the potential outside the hard core is given by a combination of Yukawa potentials. We compute the equations of state from analytic expressions derived in this work, and also the spin-dependent pair correlation function and its value averaged over the internal degrees of freedom. The model system displays an increase of the pressure over the hard-sphere system, and the pair correlation function that depends on the internal degrees of freedom shows a structure consistent with the effect of such degrees of freedom on interparticle interactions. The usual strengths and inconsistencies of the MSA are observed in this work. These calculations provide a starting point, other than computer simulations, for treatment of liquid models with many internal degrees of freedom, for the study of polar liquids and chemical reactions in solution.
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