Cross-section measurement of the $^{130}$Ba(p,$\gamma$)$^{131}$La reaction for $\gamma$-process nucleosynthesis

Background: Deviations between experimental data of charged-particle-induced reactions and calculations within the statistical model are frequently found. An extended data base is needed to address the uncertainties regarding the nuclear-physics input parameters in order to understand the nucleosynthesis of the neutron-deficient p nuclei. Purpose: A measurement of total cross-section values of the Ba-130(p,gamma)La-131 reaction at low proton energies allows a stringent test of statistical model predictions with different proton+nucleus optical model potentials. Since no experimental data are available for proton-capture reactions in this mass region around A approximate to 130, this measurement can be an important input to test the global applicability of proton+nucleus optical model potentials. Method: The total reaction cross-section values were measured by means of the activation method. After the irradiation with protons, the reaction yield was determined by use of gamma-ray spectroscopy using two clover-type high-purity germanium detectors. In total, cross-section values for eight different proton energies could be determined in the energy range between 3.6 MeV <= E-p <= 5.0 MeV, thus, inside the astrophysically relevant energy region. Results: The measured cross-section values were compared to Hauser-Feshbach calculations using the statistical model codes TALYS and SMARAGD with different proton+nucleus optical model potentials. With the semimicroscopic JLM proton+nucleus optical model potential used in the SMARAGD code, the absolute cross-section values are reproduced well, but the energy dependence is too steep at the lowest energies. The best description is given by a TALYS calculation using the semimicroscopic Bauge proton+nucleus optical model potential using a constant renormalization factor. Conclusions: The statistical model calculation using the Bauge semimicroscopic proton+nucleus optical model potential deviates by a constant factor of 2.1 from the experimental data. Using this model, an experimentally supported stellar reaction rate for proton capture on the p nucleus Ba-130 was calculated. At astrophysical temperatures, an increase in the stellar reaction rate of 68% compared to rates obtained from the widely used NONSMOKER code is found. This measurement extends the scarce experimental data base for charged-particle-induced reactions, which can be helpful to derive a more globally applicable proton+nucleus optical model potential.