The hypernetted chain equation for boson systems is used to eliminate the Jastrow correlation function in an expression for the energy of the system. Variation of this integral leads to an equation for F≡ g which bears strong resemblance to the equation used in lowest order methods, but which incorporates all clusters summed by HNC. This equation is used to study the properties of lowest-order methods, which are found to be wanting. A simple extension of the method to fermion systems gives large estimates for many-body corrections to lowest-order Fermi calculations and is in good agreement with full fermion HNC calculations. © 1977.
Kallio, A., & Smith, R. A. (1977). How simple can HNC be - and still be right? Physics Letters B, 68(4), 315–318. https://doi.org/10.1016/0370-2693(77)90483-X