Brueckner-Bethe and variational calculations of nuclear matter

Abstract

Results of both Brueckner-Bethe and variational calculations for the binding energy of nuclear matter as a function of density are presented for several recent nucleon-nucleon potentials. A detailed comparison is made for the Argonne $v_{14}$ potential, the most realistic potential for which both methods have been used. The two methods agree reasonably well, with predicted saturation points of -17.8 MeV at 1.6 ${\mathrm{fm}}^{\mathrm{-}1}$ for the Brueckner-Bethe method, and -16.6 MeV at 1.7 ${\mathrm{fm}}^{\mathrm{-}1}$ for the variational method. The variational energies are 1–2 MeV above the Brueckner-Bethe energies for densities from 1.2 to 1.7 ${\mathrm{fm}}^{\mathrm{-}1}$. The results of Brueckner-Bethe calculations are also given for the Paris and Bonn potentials as well as results of variational calculations for the Urbana $v_{14}$ potential. These potentials all give similar binding energy curves, and all saturate matter at a density significantly above the empirical value.