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Modification of Dispersion Relations and Generalization of the Hartree‐Fock Method for Hard‐Core Interactions in Nuclear Matter
Author(s) -
Winter J.
Publication year - 1978
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19780260103
Subject(s) - nuclear matter , generalization , operator (biology) , physics , eigenvalues and eigenvectors , matrix (chemical analysis) , dispersion (optics) , hartree–fock method , dispersion relation , quantum mechanics , nucleon , mathematical physics , quantum electrodynamics , mathematical analysis , mathematics , chemistry , atomic physics , biochemistry , repressor , chromatography , transcription factor , gene
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.