Systematics of semi-microscopic proton-nucleus optical potential at low energies relevant to nuclear astrophysics

Abstract: Astrophysical models studying the origin of the p-nuclei require knowledge of the reaction rates of photodisintegrations and capture reactions. Since experimental data at astrophysically relevant energies are limited, reaction rate calculations rely on Hauser-Feshbach (HF) theory predictions. The HF theory requires nuclear physics input such as masses, level densities, $\gamma$-ray strength functions and proton-nucleus optical potentials (pOMP). The scope of this work is to improve a global semi-microscopic pOMP at energies relevant to the p-process. This is achieved by adjusting the normalization parameters of the OMP to all available proton-capture cross sections measured at low energies. By establishing the systematic behaviour of these parameters, one expects to enhance the predictive power of the pOMP when expanding to mass regions where no data exists. The HF calculations were obtained using TALYS code. The normalization parameters for the real and imaginary central potentials ($\lambda_V$ and $\lambda_W$) were adjusted to fit the proton data in the energy range where the cross-section are independent of the other nuclear inputs. Results show that the $\lambda_V$ parameter has a strong mass dependence that can be described by a second-degree polynomial function for A $\leq$ 100 and an exponential increase for 100 < A < 162. Though variations of the $\lambda_W$ have a smaller effect on the calculations, a global increase by 50$\%$ improves the results for certain nuclei without affecting the rest of the cases. The resulting adjustment functions were obtained by fitting all suitable proton data and can be used with reasonable confidence to generate the global semi-microscopic pOMP for nuclei in the medium to heavy mass region. For better statistics, more low-energy (p,$\gamma$) cross section data are needed for heavier nuclei with mass A $>$ 100.