Implications of a Fully Nonlocal Implementation of the Dispersive Optical Model

A fully nonlocal treatment for the dispersive optical model (DOM) is implemented for both the real and imaginary part of the self-energy inspired by ab initio theoretical calculations of this quantity. By means of the dispersion relation between the real and imaginary part of the optical potential a link between the energy domain of nuclear reactions and nuclear structure is established. The relevant scattering data for neutrons and protons on $^{40}$Ca are described with the same quality as was accomplished with previous local versions of the DOM. The solution of the Dyson equation at positive and negative energies is generated with a complete treatment of the nonlocality of the potentials. The resulting propagator has been utilized to explain and predict relevant quantities of the ground-state of the $^{40}$Ca nucleus. In particular the charge density, spectral strength and particle number can, for the first time, be accurately described. Moreover, due to the introduction of nonlocality in the imaginary part of the self-energy it is also possible to describe high-momentum protons and the contribution of the two-body interaction to the ground-state energy. The calculation of the spectral density at positive energies allows for the determination of the spectral strength of mostly occupied single-particle orbits in the continuum. Consistency of the resulting depletion numbers with the corresponding occupation numbers is studied and compared to ab initio calculations for these quantities. Starting from the $^{40}$Ca self-energy, an extension to the $^{48}$Ca nucleus is implemented focusing on the $N-Z$ dependence of the nucleon self-energy. Neutron scattering data can be described with even better quality than previous local DOM calculations. The scattering properties for protons are of similar excellent quality as for previous local results. From the solution of the Dyson equation for neutrons it is possible to calculate the neutron distribution of this nucleus allowing for the determination of the neutron skin which is relevant for the physics of neutron stars. The resulting value is larger than most calculations previously reported including an ab initio one. An argument supporting a large neutron skin is provided by analyzing proton elastic scattering data on both $^{40}$Ca and $^{48}$Ca