Investigating the link between proton reaction cross sections and the quenching of proton spectroscopic factors in $^{48}$Ca

Abstract

The nucleon self-energies of $^{40}$Ca and $^{48}$Ca are determined using a nonlocal dispersive optical model (DOM). By enforcing the dispersion relation connecting the real and imaginary part of the self-energy, scattering and structure data are used to constrain these self-energies. The ability to calculate both bound and scattering states simultaneously puts these self-energies in a unique position to consistently describe exclusive knockout reactions such as $(e,e'p)$. The present analysis reveals the importance of high-energy proton reaction cross-section data in constraining spectroscopic factors required for the description of the $(e,e'p)$ cross sections. In particular, it is imperative that high-energy proton reaction cross-section data are measured for $^{48}$Ca in the near future so that the quenching of the spectroscopic factors in the $^{48}$Ca$(e,e'p)^{47}$K reaction can be unambiguously constrained using the DOM. Measurements of proton reaction cross sections in inverse kinematics employing rare isotope beams with large neutron excess will provide corresponding constraints on proton spectroscopic factors for exotic nuclei. Moreover, DOM generated spectral functions indicate that the quenching of spectroscopic factors compared to $^{40}$Ca is not only due to long-range correlation, but also partly due to the increase in high-momentum protons in $^{48}$Ca on account of the strong neutron-proton interaction. Single-particle momentum distributions of protons and neutrons in $^{48}$Ca calculated from these spectral functions confirm that neutron excess causes a higher fraction of high-momentum protons than neutrons.