Long-range Jastrow correlations

We develop a promising many-body method to evaluate the equation of state for dense neutron matter and liquid helium. The ground state of the Fermi fluid is described by a conventional Jastrow ansatz. We admit the presence of short- and long-range correlations. Under this assumption we study the generating function which has been introduced by Wu and Feenberg. We employ a graphic formulation and develop the diagrammatic expansion of the generating function and the radial distribution function. If long-range correlations are assumed, the diagrams have singular parts. We give a proof that the total contribution of such diagrams to the generating function which contain two, three, and four correlation lines is of finite value. The same property is shown for a selected class of singular diagrams containing α correlation lines (α>4). To verify the cancellation phenomenon we introduce a two-body function which serves graphically as an insertion into selected singular diagrams. For the remaining classes of diagrams we need three-, four-, ⋯, n-body insertions. The result is cast into the form of a theorem. The cancellation rests on the exclusion principle and does not depend on the special shape of the correlation function. Finally, a generalized hypernetted-chain summation of diagrams which represent the radial distribution function is executed. The procedure includes exchange contributions and can be employed if short-and/or long-range correlations are present.