  The $\gamma$ process in supernova explosions is thought to explain the origin
of proton-rich isotopes between Se and Hg, the so-called $p$ nuclei. The
majority of the reaction rates for $\gamma$ process reaction network studies
has to be predicted in Hauser-Feshbach statistical model calculations using
global optical potential parameterizations. While the nucleon+nucleus optical
potential is fairly known, for the $\alpha$+nucleus optical potential several
different parameterizations exist and large deviations are found between the
predictions calculated using different parameter sets. By the measurement of
elastic $\alpha$-scattering angular distributions at energies around the
Coulomb barrier a comprehensive test for the different global $\alpha$+nucleus
optical potential parameter sets is provided. Between 20$^{\circ}$ and
175$^{\circ}$ complete elastic alpha scattering angular distributions were
measured 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 first
time at energies close to the astrophysically relevant energy region. The high
precision experimental data were used to evaluate the predictions of the recent
global and regional $\alpha$+nucleus optical potentials. Parameters for a local
$\alpha$+nucleus optical potential were derived from the measured angular
distributions. Predictions for the reaction cross sections of
$^{113}$In($\alpha,\gamma$)$^{117}$Sb and $^{113}$In($\alpha$,n)$^{116}$Sb at
astrophysically relevant energies were given using the global and local optical
potential parameterizations.
