Two-Body Forces and Nuclear Saturation. III. Details of the Structure of the Nucleus

TLDR

The characteristics of particle motion in the nuclear medium have been examined in detail. The authors formulate a self‑consistent potential model in which a uniform, constant potential with reduced nucleon mass reproduces the strong momentum dependence of the nuclear potential, evaluate the volume energy using two‑body central and tensor forces that match low‑energy scattering up to 90 MeV, and show that the collective nucleon potential influences single‑particle excitation energies and surface/symmetry energies in agreement with empirical data. The self‑consistency constraints strongly stabilize nuclear saturation, yielding volume energies, densities, and excitation spectra that agree closely with observed values and demonstrating marked stability against tensor‑force–induced distortions.

Abstract

The characteristics of particle motion in the nuclear medium have been examined in detail. The origin of the strong dependence of the potential energy on the nucleon momentum is discussed and an equivalent formulation is exhibited in which a uniform and constant potential is assumed but the nucleon moves with markedly reduced mass. The determination of the potential is shown to lead to a self-consistency problem which is to some extent similar to that appearing in the Hartree method of self-consistent fields. Solution of this problem shows that the self-consistency requirements impose severe restrictions on the solution and have a strong stabilizing influence in the saturation problem. The volume energy of the nucleus has been evaluated by using two-body potentials closely equivalent to a combination of central and tensor forces which agree with the low-energy parameters and predict scattering correctly up to 90 Mev. The result agress closely with the observed values of energy and density.The collective character of the nucleon potential is described and shown to manifest itself markedly in the excitation energy of single-particle levels where a considerable fraction of the energy is taken up in small adiabatic shifts of the states of the remaining nucleons.The origin of the surface and symmetry energy is discussed; an evaluation of these effects gives a result in good agreement with empirically derived values. The stability of the nucleus against distorition arising from the polarizing effects of the tensor force is also examined and it is found that the nucleus shows marked stability against such distortion.