Nuclear shell-model calculations and strong two-body correlations

Abstract

Two-body Hamiltonians, like the Reid interaction, are derived by fitting the two-nucleon data. It is an assumption that the many-body eigenstates of this Hamiltonian form a representation of the observed nuclear states. At best this has been demonstrated for the ground states of a few nuclei, e.g., the triton, and there the binding energy is off by 15–20%, this being attributed to uncertainties in the off-shell behavior of the interaction and to many-body forces. Since 15% of the total nuclear binding energy is much greater than the typical energy spacings observed in nuclear spectra, it is not at all clear that the calculable approximations to the many-body eigenstates of the N- N interaction can give useful information for nuclear spectroscopy. Using the method of correlated basis states coupled with an extremely large “no core” shell model basis as a set of trial variational functions, it is demonstrated that almost 100 levels in light nuclei can be identified with eigenstates of the Reid interaction. In so doing, a prescription is presented for defining effective operators in large shell-model calculations and the question of nuclear center of mass motion is reexamined.