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

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AbstractThe 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 A00‐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.