Confined fluids - variations on a mean spherical theme

The mean spherical model of a classical fluid in thermal equilibrium is taken as prototype for fluids defined by their distribution of point density. An external potential Boltzmann factor applied to a reference, so defined, then produces the effect of the field on the reference. In this paper, the reference distribution is required only to reproduce the singlet and pair densities of the unperturbed fluid under study. For this purpose, the distribution can be borrowed from any many-body system, classical or quantum. Major attention is paid to elementary quantum models sufficiently parametrized to, in principle, match the desired mean singlet and pair densities. Included are independent Fermion models, independent Boson models, and those with a suitably defined intermediate statistics, whose use however involves an assertion whose range of validity is not known. An example of this mixed strategy is presented.