Treatment of the Hard Core in the Two-Nucleon Potential in Nuclear-Matter Calculations

Abstract

Calculating the repulsive part of diagonal $G$-matrix elements in the Brueckner theory of nuclear matter, we have studied in detail the method of Brueckner and Gammel for treating the hard core in the two-body potential when solving the Bethe-Goldstone equation. Their method is compared with a more exact method, and also with the reference-spectrum method of Bethe. For simplicity, we use the approximation of an effective mass and a reference spectrum for the energies of the intermediate states in all methods. The calculations are repeated for several values of the parameters defining the reference spectrum and for several values of the initial relative momentum of the two interacting nucleons. The hard-core treatment of Brueckner and Gammel turns out to be a very good approximation for calculations of $G$-matrix elements on the energy shell, but gets worse as one goes off the energy shell.