  Reactions involving the group of nuclei commonly known as p nuclei are part
of the nucleosynthetic mechanisms at astrophysical sites. The $^{113}$In
nucleus is such a case with several open questions regarding its origin at
extreme stellar environments. In this work, the experimental study of the cross
sections of the radiative proton-capture reaction
$^{112}$Cd(p,$\gamma$)$^{113}$In is attempted for the first time at energies
lying inside the Gamow window with an isotopically enriched $^{112}$Cd target.
Two different techniques, the in-beam $\gamma$-ray spectroscopy and the
activation method, have been applied. The latter method is required to account
for the presence of a low-lying $^{113}$In isomer at 392 keV having a halflife
of $\approx 100$ min. From the cross sections, the astrophysical S factors and
the isomeric ratios have been additionally deduced. The experimental results
are compared to detailed Hauser-Feshbach theoretical calculations using TALYS,
and discussed in terms of their significance to the optical model potential
involved.
