Locations of Neutron Single Particle States

Abstract

The meaning and importance of single particle (SP) states in nuclear shell theory is outlined, and the method of determining them from studies of deuteron stripping reactions is described. The results on locations of SP states are summarized and analyzed to obtain information on the shell theory potential. The depth of this potential is found to have a symmetry energy dependence somewhat weaker than that for optical model potentials for protons. The “self-binding energy,” a lowering of the energy of a SP state as it fills, plays an important role; its magnitude is determined and an empirical expression for it is given. Special neutron-proton interactions must be taken into account in a few cases. The spin-orbit potential seems to be of the form f(r)σ·l where f(r) = r−1dV/dr; a volume or a simple surface force are excluded. The explicit l-dependence of SP energies is much less than that commonly used, and indicates that the potential is much closer to an oscillator than to a square well in shape. The spacings between major shells require a velocity dependent potential corresponding to an effective mass of 1.3 times the nucleon mass. The shift of SP energies with A indicates that the well gets shallower with increasing A; the depth change is about 5.8 MeV from Ca to Pb. Locations of neutron giant resonances are estimated.