Current state of nuclear matter calculations

The current state of nuclear matter calculations is described with special reference to the present disagreement between the variational and Brueckner-Bethe methods. The system is assumed to consist of point nucleons with a nonrelativistic Hamiltonian containing the kinetic energy and two-body potentials. The physical ideas of the variational method, especially of its hypernetted-chain version, and of the Brueckner—Bethe method are outlined. Practical ways of testing the validity of these methods are discussed and are illustrated by numerical results taken from the literature. It is found for central forces that the hypernetted-chain variational method, if properly used, gives reliable upper bounds to the ground-state energy. Lowest-order Brueckner-Bethe results lie well above these upper bounds, and it is both important and feasible to check whether higher-order corrections will bring the Brueckner-Bethe results into agreement with the variational ones. For realistic nuclear potentials, which have tensor forces, spin-orbit forces, etc., the situation is much less clear. An adequate calculation has not yet been done by either the variational or Brueckner-Bethe method. For the Reid potential, with the presently available numerical results, the variational calculation predicts a much higher saturation density than the Brueckner-Bethe calculation. Feasible calculations that will help to resolve this discrepancy are discussed.