General Nuclear Properties with Effective Interactions

This report deals with the use of some effective interactions in calculating properties of closed shell nuclei and of the nuclear surface. Closed shell nuclei have been investigated by several groups; the work of three of these groups is discussed here. Davies, Baranger et al. use a momentum-dependent Gaussian effective interaction whose parameters are adjusted to fit the binding energy and density of nuclear matter using first-order perturbation theory and also match at least the low-energy nucleon-nucleon scattering phase shifts. Pearson and Saunier use quite similar interactions except that instead of fitting low-energy scattering data, they insist that the long range part must be of the one-boson exchange form, at least in 1S0 states. Brink and Boeker study various interactions which fit nuclear matter and the alpha particle binding energy. For 16O, these groups obtain somewhat too low a binding energy. Bethe has worked out a theory of the nuclear surface, which uses a quite simple effective interaction derived from a realistic interaction. Bethe uses the Thomas-Fermi approximation and obtains an analytic form for the particle density distribution at the nuclear surface. He also calculates the nuclear surface energy and surface thickness and obtains good agreement with empirical values. The nuclear surface problem has also been studied by other authors who do not make the Thomas-Fermi approximation. In particular, if one uses a simple effective interaction of the form suggested by Skyrme, with the same criteria as Brink and Boeker, then the surface energy comes out in good agreement with empirical values. In addition, this effective interaction can be used to assess the accuracy of the Thomas-Fermi approximation. This approximation underestimates the surface energy by only 1½ MeV. (author)