Background: One of the primary objectives of the field of Nuclear Astrophysics is the study of the elemental and isotopic abundances in the universe. Although significant progress has been made in understanding the mechanisms behind the production of a large number of nuclides in the isotopic chart, there are still many open questions regarding a number of neutron-deficient nuclei, the $p$ nuclei. To that end, experimentally deduced nuclear reaction cross sections can provide invaluable input to astrophysical models.Purpose: The reactions $^{107,109}\mathrm{Ag}$($p,\ensuremath{\gamma}$)$^{108,110}\mathrm{Cd}$ have been studied at energies inside the astrophysically relevant energy window in an attempt to provide experimental data required for the testing of reaction-rate predictions in terms of the statistical model of Hauser-Feshbach around the $p$ nucleus $^{108}\mathrm{Cd}$.Methods: The experiments were performed with in-beam $\ensuremath{\gamma}$-ray spectroscopy with proton beams accelerated by the Tandem Van de Graaff Accelerator at NCSR ``Demokritos'' impinging a target of natural silver. A set of high-purity germanium detectors was employed to record the emitted radiation.Results: A first set of total cross-section measurements in radiative proton-capture reactions involving $^{107,109}\mathrm{Ag}$, producing the $p$-nucleus $^{108}\mathrm{Cd}$, inside the astrophysically relevant energy window is reported. The experimental results are compared to theoretical calculations, using talys. An overall good agreement between the data and the theoretical calculations has been found.Conclusions: The results reported in this work add new information to the relatively unexplored $p$ process. The present measurements can serve as a reference point in understanding the nuclear parameters in the related astrophysical environments and for future theoretical modeling and experimental works.
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