A measurement of total cross-section values of the $^{130}$Ba(p,$gamma$)$^{131}$La 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~$approx$~130, this measurement can be an important input to test the global applicability of proton+nucleus optical model potentials. 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 $leq E_p leq$ 5.0 MeV, thus, inside the astrophysically relevant energy region. 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 semi-microscopic 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 semi-microscopic Bauge proton+nucleus optical model potential using a constant renormalization factor.
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