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The $\gamma$ process in supernova explosions is thought to explain the originof proton-rich isotopes between Se and Hg, the so-called $p$ nuclei. Themajority of the reaction rates for $\gamma$ process reaction network studieshas to be predicted in Hauser-Feshbach statistical model calculations usingglobal optical potential parameterizations. While the nucleon+nucleus opticalpotential is fairly known, for the $\alpha$+nucleus optical potential severaldifferent parameterizations exist and large deviations are found between thepredictions calculated using different parameter sets. By the measurement ofelastic $\alpha$-scattering angular distributions at energies around theCoulomb barrier a comprehensive test for the different global $\alpha$+nucleusoptical potential parameter sets is provided. Between 20$^{\circ}$ and175$^{\circ}$ complete elastic alpha scattering angular distributions weremeasured on the $^{113}$In \textit{p} nucleus with high precision at E$_{c.m.}$= 15.59 and 18.82 MeV. The elastic scattering cross sections of the$^{113}$In($\alpha$,$\alpha$)$^{113}$In reaction were measured for the firsttime at energies close to the astrophysically relevant energy region. The highprecision experimental data were used to evaluate the predictions of the recentglobal and regional $\alpha$+nucleus optical potentials. Parameters for a local$\alpha$+nucleus optical potential were derived from the measured angulardistributions. Predictions for the reaction cross sections of$^{113}$In($\alpha,\gamma$)$^{117}$Sb and $^{113}$In($\alpha$,n)$^{116}$Sb atastrophysically relevant energies were given using the global and local opticalpotential parameterizations.

High precision $^{113}$In($\alpha,\alpha$)$^{113}$In elastic scattering at energies around the Coulomb barrier for the astrophysical $\gamma$ process