Abstract
A dispersive-optical-model analysis of $p+$$^{40,42,44,48}\mathrm{Ca}$ and $n+$$^{40}\mathrm{Ca}$ interactions has been carried out. The real and imaginary potentials have been constrained by fitting elastic-scattering data, total and reaction cross sections, and level properties of valence hole states deduced from $(e,{e}^{'}p)$ data. The resulting surface imaginary potential increases with asymmetry for protons, implying that in heavier Ca isotopes, protons experience stronger long-range correlations. Presently, there is not enough data for neutrons to determine their asymmetry dependence. Global optical-model fits usually assume that the neutron asymmetry dependence is equal in magnitude, but opposite in sign, to that for protons. Such a dependence was found to give unphysical results for heavy Ca isotopes. The dispersive optical model is shown to be a useful tool for data-driven extrapolations to the drip lines. Neutron and proton data at larger asymmetries are needed to achieve more reliable extrapolations. The present analysis predicts $^{60}\mathrm{Ca}$ and $^{70}\mathrm{Ca}$ to be bound, while the intermediate isotopes are not.
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