Statistical analysis of excitation functions for elastic and inelastic scattering of $\alpha$-particles on Mg and Si nuclei

The excitation functions for inelastic $\alpha$-scattering leading to the low lying excited states in $^{24}$Mg and $^{28}$Si were measured at $\Theta_{LAB}$ = 170°, 175° and 179° in the LAB energy range 22.75–28.40 MeV. Statistical analysis of these excitation functions and those previously measured for elastic scattering was performed. The direct interaction contribution $\mathit{y}_{D}$ to the reaction studied was obtained from probability distributions of cross sections and from correlation coefficients. Cross correlation coefficients between different reaction channels were calculated.