Cross sections of $\alpha$-induced reactions for targets with masses $A \approx 20-50$ at low energies

Abstract

A simple reduction scheme using so-called reduced energies $E_{\rm{red}}$ and reduced cross sections $\sigma_{\rm{red}}$ allows the comparison of heavy-ion induced reaction cross sections for a broad range of masses of projectile and target and over a wide energy range. A global behavior has been found for strongly bound projectiles whereas much larger reduced cross sections have been observed for weakly bound and halo projectiles. It has been shown that this simple reduction scheme works also well for $\alpha$-particle induced reactions on heavy target nuclei, but very recently significant deviations have been seen for $\alpha$+$^{33}$S and $\alpha$+$^{23}$Na. Motivated by these unexpected discrepancies, the present study analyses $\alpha$-induced reaction cross sections for targets with masses $A \approx 20-50$. The study shows that the experimental data for $\alpha$-induced reactions on nuclei with $A \approx 20-50$ deviate slightly from the global behavior of reduced cross sections. However, in general the deviations evolve smoothly towards lower masses. The only significant outliers are the recent data for $^{33}$S and $^{23}$Na which are far above the general systematics, and some very old data may indicate that $^{36}$Ar and $^{40}$Ar are below the general trend. As expected, also the doubly-magic $^{40}$Ca nucleus lies slightly below the results for its neighboring nuclei. Overall, the experimental data are nicely reproduced by a statistical model calculation utilizing the simple $\alpha$-nucleus potential by McFadden and Satchler. Simultaneously with the deviation of reduced cross sections $\sigma_{\rm{red}}$ from the general behavior, the outliers $^{23}$Na, $^{33}$S, $^{36}$Ar, and $^{40}$Ar also show significant disagreement between experiment and statistical model calculation.