Background: Radionuclides in the Mo-Tc region play an important role in modern medical diagnostics. These applications require a $\ensuremath{\gamma}$-emitting radioisotope that is injected into the patient. Various production methods of those radionuclides have been investigated in the past; among them are ($p,x$) reactions on natural or enriched molybdenum. Reliable estimations for the produced activity of the radionuclides and radioactive byproducts are required. Therefore, either precise theoretical calculations or a firm experimental database for the nuclear production reactions are needed. In addition, experimental cross-section data of proton-induced reactions on heavy nuclei are very valuable to test nuclear models that enter theoretical calculations of reaction rates relevant for nuclear astrophysics.Purpose: The present paper reports on experimental cross sections of the $^{96}\mathrm{Mo}(p,n)^{96m+g}\mathrm{Tc}$ reaction. The contribution of the ground-state population as well as for the population of the metastable state in $^{96}\mathrm{Tc}$ are determined individually. The obtained results are very valuable to test existing models that enter statistical model calculations. In addition, the present work aims at remeasuring the branching ratio of the decay of the metastable state $^{96m}\mathrm{Tc}$.Method: Highly enriched $^{96}\mathrm{Mo}$ targets were irradiated with protons at energies between ${E}_{p}=3.9\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ and ${E}_{p}=5.4\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, which are slightly above the ($p,n$) threshold (${E}_{th}=3.8\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$). By employing an offline analysis, the $\ensuremath{\gamma}$-ray decay of the reaction product was investigated and reaction cross sections were calculated by means of the activation technique.Results: Individual reaction cross sections for the production channel of the metastable state ${\ensuremath{\sigma}}_{m}$ and the ground state ${\ensuremath{\sigma}}_{gs}$ as well as the branching of the $^{96m}\mathrm{Tc}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}^{96}\mathrm{Tc}$ decay were determined.Conclusion: The measured cross sections are in good agreement with previously measured cross sections as well as with recent Hauser-Feshbach calculations. The new branching ratio for the direct decay of $^{96m}\mathrm{Tc}$ into $^{96}\mathrm{Mo}$ amounts to $4.1{\phantom{\rule{0.16em}{0ex}}}_{\ensuremath{-}0.34}^{+0.39}\phantom{\rule{0.16em}{0ex}}%$ compared to previously reported $2\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}0.5%$.
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