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A simple reduction scheme using so-called reduced energies $E_{\rm{red}}$ andreduced cross sections $\sigma_{\rm{red}}$ allows the comparison of heavy-ioninduced reaction cross sections for a broad range of masses of projectile andtarget and over a wide energy range. A global behavior has been found forstrongly bound projectiles whereas much larger reduced cross sections have beenobserved for weakly bound and halo projectiles. It has been shown that thissimple reduction scheme works also well for $\alpha$-particle induced reactionson heavy target nuclei, but very recently significant deviations have been seenfor $\alpha$+$^{33}$S and $\alpha$+$^{23}$Na. Motivated by these unexpecteddiscrepancies, the present study analyses $\alpha$-induced reaction crosssections for targets with masses $A \approx 20-50$. The study shows that theexperimental data for $\alpha$-induced reactions on nuclei with $A \approx20-50$ deviate slightly from the global behavior of reduced cross sections.However, in general the deviations evolve smoothly towards lower masses. Theonly significant outliers are the recent data for $^{33}$S and $^{23}$Na whichare 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 thedoubly-magic $^{40}$Ca nucleus lies slightly below the results for itsneighboring nuclei. Overall, the experimental data are nicely reproduced by astatistical model calculation utilizing the simple $\alpha$-nucleus potentialby McFadden and Satchler. Simultaneously with the deviation of reduced crosssections $\sigma_{\rm{red}}$ from the general behavior, the outliers $^{23}$Na,$^{33}$S, $^{36}$Ar, and $^{40}$Ar also show significant disagreement betweenexperiment and statistical model calculation.

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