Investigating the weak charge of $^{48}$Ca using a dispersive optical model

Abstract

A new nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{48}$Ca that reproduces the weak-form-factor measurement of CREX. In addition to elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution, the CREX-measured weak form factor has been fit to extract the neutron and proton self-energies both above and below the Fermi energy. The resulting single-particle propagators yield a weak form factor of $F_W = 0.125 \pm 0.05$ and a neutron skin of $R_\mathrm{skin} = 0.152 \pm 0.05$ fm, in good agreement with CREX. The rearrangement of the neutron distribution to accommodate such a thin neutron skin results in the high-momentum content of the neutrons exceeding that of the protons, in contrast to what is expected from high-energy two-nucleon knockout measurements by the CLAS collaboration and ab initio asymmetric matter calculations. The present analysis also emphasizes the importance of neutron experimental data in constraining weak charge observables necessary for a precise description of neutron densities. Notably, the neutron reaction cross section and further parity-violating experiments weak form factor measurements are essential to generate a unique way to determine the $^{48}$Ca neutron distribution in this framework.