Analysis of the $^{48}$Ca neutron skin using a nonlocal dispersive-optical-model self-energy*

A nonlocal dispersive-optical-model (DOM) analysis of the $^{40}$Ca and $^{48}$Ca nuclei has been implemented. The real and imaginary potentials are constrained by fitting to elastic-scattering data, total and reaction cross sections, energy level information, particle number, and the charge densities of $^{40}$Ca and $^{48}$Ca, respectively. The nonlocality of these potentials permits a proper dispersive self-energy which accurately describes both positive and negative energy observables. $^{48}$Ca is of particular interest because it is doubly magic and has a neutron skin due to the excess of neutrons. The DOM neutron skin radius is found to be $r_{skin} = 0.245$, which is larger than most previous calculations. The neutron skin is closely related to the symmetry energy which is a crucial part of the nuclear equation of state. The combined analysis of $^{40}$Ca and $^{48}$Ca energy densities provides a description of the density dependence of the symmetry energy which is compared with the $^{48}$Ca neutron skin. Results for $^{208}$Pb will also become available in the near future.