Exploring the statistical properties of the neutron-deficient $^{109}$In isotope with the Oslo method

The nuclear level density (NLD) and the $\gamma$-ray strength function (GSF) of the neutron-deficient $^{109}$In isotope were extracted for the first time with data from the $^{106}$Cd$(\alpha,p\gamma)^{109}$In reaction using a combination of the Oslo and the shape methods. Both quantities are consistent with those of neighboring Cd and Sn nuclei, but show substantial discrepancies with currently available model predictions. In contrast to earlier observations in the neighboring isotopic chains, $^{109}$In does not exhibit any significant enhancement of the dipole strength near the neutron separation energy. To interpret this feature, random-phase time-blocking approximation calculations have been performed for $^{109}$In and the neighboring $^{110,112}$Sn nuclei. The experimental data were also employed to estimate cross sections and rates of the radiative neutron- and proton-capture reactions, $^{108}$In($n,\gamma)$$^{109}$In and $^{108}$Cd($p,\gamma)$$^{109}$In, respectively, with the reaction code TALYS. Our ($p,\gamma)$ cross section is in excellent agreement with direct measurements over a wide range of proton energies, while the ($n,\gamma)$ cross section demonstrates notable deviations from predictions in the JINA REACLIB library. The new results on the statistical properties of $^{109}$In provide valuable constraints that may help address the problem of large model uncertainties compromising the accuracy of astrophysical $p$-process simulations.