Systematics of the semimicroscopic proton-nucleus optical potential at low energies relevant for nuclear astrophysics

Abstract

Background: Astrophysical models studying the origin of the neutron-deficient p nuclides require knowledge of the reaction rates of neutron, proton and α-proton photodisintegrations of pre-existing neutron-rich sand r-nuclei and of proton capture reaction rates. Since experimental data at astrophysically relevant interaction energies are limited, reaction rate calculations rely on the predictions of the Hauser-Feshbach (HF) theory. The HF theory requires nuclear physics input such as masses, level densities, γ-ray strength functions and proton-nucleus optical potentials (OMP) describing the average interaction between the p and the nucleus. The proton OMP plays an important role in the description of proton photodisintegrations and radiative capture reactions at low energies relevant to the p-process nucleosynthesis. Purpose: The scope of this work is to improve a global semi-microscopic optical potential for protons at low energies relevant to the p-process nucleosynthesis. This is achieved by adjusting the normalization parameters of the OMP to all available radiative proton-capture cross sections measured at energies of astrophysical interest. By establishing the systematic behaviour of these parameters, one expects to enhance the predictive power of the proton OMP when expanding to mass regions where no data exists. Method: The Hauser-Feshbach calculations were obtained using the TALYS nuclear reaction code. The normalization parameters for the real and imaginary central potentials (λV and λW ) were adjusted to fit the proton data in the energy range where the cross-section calculations are independent of other input parameters, i.e. neutron optical potential, nuclear level density and γray strength function. As a consequence, the optimization of the proton OMP was done at energies below the opening of the (p, n) reaction threshold. The goodness of the fit is based on the chi-square method as well as on visual comparisons. Results: The results show that the normalization parameter λV of the real part of the proton OMP has a strong mass dependence that can be described by a second degree polynomial function for A ≤100 (low mass range) and an exponential increase for 100 < A < 162 (intermediate mass range). Though variations of the normalization parameter of the imaginary part λW 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. Conclusions: The resulting adjustment functions were obtained by fitting all suitable proton cross-section data at low energies and can be used with reasonable confidence to generate the global semi-microscopic proton optical potential for nuclei in the medium to heavy mass region. For better statistics, more low-energy proton-capture cross section data are needed for heavier nuclei with mass A > 100.