Cross sections of $\alpha$-induced reactions slightly below doubly-magic ${}^{40}$Ca from the statistical model

Abstract

New experimental data for the ${}^{38}$Ar($\alpha$,n)${}^{41}$Ca and ${}^{38}$Ar($\alpha$,p)${}^{41}$K reactions were used to find a best-fit set of parameters for statistical model calculations. The very good agreement between the experimental data and the best-fit calculation confirms the applicability of the statistical model for nuclei in the vicinity of the doubly-magic ${}^{40}$Ca despite of their relatively low level densities. The present study investigates the sensitivities and finds that the $\alpha$-nucleus and the nucleon-nucleus potentials are the most important ingredients for the calculation of ($\alpha$,n) and ($\alpha$,p) reactions in the statistical model. Furthermore, the width fluctuation correction plays an essential role in the peculiar case of ${}^{38}$Ar. The best-fit parameters from ${}^{38}$Ar are applied to the mirror nucleus ${}^{38}$Ca and the neighboring ${}^{36}$Ar and ${}^{40}$Ar nuclei. For ${}^{38}$Ca this results in an astrophysical reaction rate of the ${}^{38}$Ca($\alpha$,p)${}^{41}$Sc reaction which has a flatter temperature dependence compared to all previous calculations. For ${}^{40}$Ar a better reproduction of ${}^{40}$Ar($\alpha$,p)${}^{43}$K data from literature is obtained. The disagreement between calculation and an early experimental data point for the ${}^{36}$Ar($\alpha$,p)${}^{39}$K reaction persists.

Comments: 14 pages, 10 figures; Phys. Rev. C, accepted for publication