Proton Potential Anomaly and Nonlocal Potentials

Abstract

A detailed study of the variations of the difference between the proton-nuclear potential and the neutron-nuclear potential is carried out using ground-state mass data. A previous analysis of mirror nuclei has delimited the problem and suggested that the well difference can be neither constant nor strictly $Z$ dependent. It is found by using analytical techniques as well as calculations performed with the Oak Ridge Oracle that the potential anomaly varies with the symmetry parameter $\frac{\mathrm{}(N-Z)\mathrm{}}{A}$ and that the proportionality constant does not change very greatly as one proceeds from a static well to a velocity-dependent well. This is somewhat surprising in view of many studies which suggest that the nuclear symmetry energy is considerably influenced by the velocity dependence of the nuclear potential. The relative insensitivity to velocity dependence or nonlocality is attributed to surface effects not taken into account in the analyses of infinite nuclear matter.