Experimental study of $\alpha$-induced reactions on $^{113}$In for astrophysical $p$-process

Neutron deficient nuclei from $^{74}$Se$-^{196}$Hg are thought to be produced by $\gamma$-induced reactions ($\gamma$,n), ($\gamma$,p) and ($\gamma,\alpha$) processes. The relatively high abundance of $^{113}$In odd A $p$-nuclei has inspired to study its production processes. As reaction with $\gamma$-beam is difficult to perform in the laboratory, $\gamma$-induced reaction rate is calculated from the inverse reaction data employing reciprocity theorem. Stacked foil activation method was used to measure the $^{113}$In($\alpha,\gamma$) and $^{113}$In($\alpha$, n) reactions cross-section near the astrophysical energies. Theoretical statistical model calculations were performed with different nuclear input parameters and compared with the experimental results. An appropriate $\alpha$-optical potential has been identified from the ($\alpha,\gamma$) and ($\alpha$, n) fitting, which provides the major source of uncertainty in the statistical model calculations. The other nuclear input parameters like level density, and $\gamma$-ray strength function were also constrained for theoretical calculations. $^{113}$In($\alpha,\gamma$)$^{117}$Sb and $^{117}$Sb($\alpha,\gamma$)$^{113}$In reaction rates were calculated using best-fitted input parameters.