The fermion hypernetted chain equations for the three-body distribution function are derived in this paper. These equations are relatively complicated and some care is required for their derivation. The formulas are presented explicitly and an outline for their practical implementation discussed.
The generalized momentum distribution n(p,Q), related to the half-diagonal two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2\mathrm{h}}$(r1,r2,${\mathbf{r}}_{1}^{\ensuremath{'}}$) by Fourier transformation in the variables r1-${\mathbf{r}}_{1}^{\ensuremath{'}}$ and r1-r2, plays a key role in the description of final-state interactions in the nuclear medium and other strongly interacting many-body systems. The function n(p,Q) is explored for two Jastrow-correlated models of infinite nuclear matter within a Fermi hypernetted-chain procedure. Significant departures from ideal Fermi gas behavior in certain kinematic domains provide signatures of the strong short-range correlations contained in these models. However, such deviations are less prominent than in earlier calculations based on low-order cluster truncations; correspondingly, violations of the sequential relation are greatly reduced. Simple prescriptions for improved low-cluster-order approximations to n(p,Q) are suggested by analysis of the results of the Fermi hypernetted-chain evaluation. These results are also used to assess the quality of Silver's approximation n(p,Q)\ensuremath{\approx}n(p)[S(Q)-1] for the generalized momentum distribution in terms of the ordinary momentum distribution n(p) and the static structure function S(Q), with findings that have potential implications for the interpretation of data from inclusive electron scattering by nuclei at high momentum transfers.
The Fermi-hypernetted-chain method for quantum many-body calculations is studied and investigated in some detail by calculations of the ground-state energy for neutron matter. The calculations are done for five different two-body potentials and results are compared with other theoretical results. Our Fermi-hypernetted-chain results are rather close to results obtained by lowest-order constrained variation calculations, and the results are quite dependent on the chosen potential, especially at high densities.