Angular distribution of the elastic scattering ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and of the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ transfer reaction have been measured at 40 MeV incident energy, respectively, in the $20°\le {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 115°$ and $20°\le {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 60°$ angular regions. The elastic scattering and transfer reactions were analyzed with Frahn's closed formalism as well as with optical model calculations. The influence of the two-step $\alpha$-transfer channel (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$→${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$→${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$) on the elastic scattering was calculated explicitly using the coupled channel extension of the closed formalism. This calculation shows that the coupling between the $\alpha$ transfer and elastic channel can account for the intermediate angle oscillations observed in the elastic scattering angular distributions.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ (g.s.) measured $\sigma \left(\theta \right)$, $E_{\mathrm{lab}}=40\mathrm{}$ MeV. Deduced optical model and closedformalism parameters. Calculated effect of $\alpha$-transfer on elastic scattering.

• Received 6 July 1982

DOI:https://doi.org/10.1103/PhysRevC.26.2487