Background: Given the importance of including nonlocality in the effective interactions in reaction models, a recent phenomenological study focusing on neutron-target nonlocal optical potentials suggests the need for the inclusion of explicit energy dependence [Lovell et al., Phys. Rev. C 96, 051601 (2017)].

Purpose: In this work, we inspect whether the same is true for proton nonlocal optical potentials.

Method: Similarly to the earlier work, we perform a ${\chi }^2$ analysis of proton elastic scattering data on ${}^{40}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$ at energies of $E\approx 10–45$ MeV, assuming the Tian, Pang, and Ma nonlocal form for the optical potential. We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parametrization.

Results: No matter which starting point is used, or whether we include backward angles in the fitting procedure, our results show the emergence of a strong energy dependence in the potential. We also show that while our parametrization represents only a modest improvement over the original energy-independent potential for those cases included in the fit, our new energy-dependent potential extrapolates much better for nuclei not included in the fit and for energies above those included.

Conclusions: As for the neutron case, we conclude that nonlocality alone cannot provide a complete description of proton elastic scattering data and that a significant energy dependence is required.

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• Direct reactions
• Nuclear forces
• Nuclear reactions