Modification of Dispersion Relations and Generalization of the Hartree‐Fock Method for Hard‐Core Interactions in Nuclear Matter

The influence of a hard‐core part in the interaction on dispersion relations for the generalized optical potential (mass operator) and the T ‐matrix of nuclear matter is investigated in the frame‐work of the A 00 ‐approximation. The model is based on the two‐nucleon scattering problem in vacuo, for which a hard‐core generalization of the Low equation is derived. As a consequence, T ‐matrix and mass operator are shown to split into a polynomial of the first order in the energy variable and a dispersion integral generalized by a limiting process, so that dispersion relations of the twice subtracted type result. Restriction to a self‐consistent calculation of the non‐dispersive term of the mass operator leads to a close analogue of the Hartree‐Fock equations for non‐singular interactions. This simple approximation which avoids the full‐nucleon problem is shown to yield a qualitatively correct density dependence of the ground‐state energy possibly to be improved by more realistic interactions. A formulation as an eigenvalue problem for finite nuclei is also given.