Cross section measurements of the $^{58}$Ni($alpha$,$gamma$)$^{62}$Zn reaction were performed in the energy range $E_{alpha}=5.5-9.5$ MeV at the Nuclear Science Laboratory of the University of Notre Dame, using the NSCL Summing NaI(Tl) detector and the $gamma$-summing technique. The measurements are compared to predictions in the statistical Hauser-Feshbach model of nuclear reactions using the SMARAGD code. It is found that the energy dependence of the cross section is reproduced well but the absolute value is overestimated by the prediction. This can be remedied by rescaling the $alpha$ width by a factor of 0.45. Stellar reactivities were calculated with the rescaled $alpha$ width and their impact on nucleosynthesis in type Ia supernovae has been studied. It is found that the resulting abundances change by up to 5% when using the new reactivities.
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