Proton and neutron distributions calculated using an effective single-particle potential

Abstract

An effective single-particle potential has been obtained which gives a best least-squares fit to the positions of the single-particle and single-hole states of 208Pb. The predicted r.m.s. radii for the proton and neutron distributions and the angular distributions for electron scattering at 175 and 250 MeV are in very good agreement with measured values. With the same geometrical form, the level positions for 40Ca and 48Ca have also been fitted and again the predicted r.m.s. radii for the proton distribution and the electron scattering angular distribution are in good agreement with experiment. Using this same standard geometry and adjusting the strength of the central potential to give the separation energy, the predicted r.m.s. radii for the proton distributions for 16 < A < 208 are in very satisfactory agreement with measured values for nuclei close to the stability line. Some calculations using a non-local potential are also reported. For 208Pb and 48Ca, a best fit is obtained with a purely local potential. For 40Ca, the best fit requires a non-locality range of approximately 1 fm for both neutrons and protons.