Excitation functions of the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ reactions to the ground states and first-excited $2^{+}$ states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ have been measured at ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=180\mathrm{}$° over the energy range $24\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 40$ MeV, where the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reaction is known to exhibit a strong resonant behavior at forward angles. The four measured excitation functions show prominent structures, about 1 MeV wide, strongly correlated in the elastic and inelastic channels. Angular distributions in the range $110°\le {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 180°$ were measured at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=27.8, 30,8, \mathrm{and} 36.2$ MeV. At 27.8 and 36.2 MeV, where prominent peaks exist in the (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$) backward-angle excitation function, the angular distributions of the transfer to the $0^{+}$ ground state are strongly rising toward 180° and have an oscillatory shape. The partial waves $L=(20,22)\mathrm{} \mathrm{and} 26$, respectively, are predominant at these two energies. At 30.8 MeV the data indicate the interference between odd and even partial waves.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$), ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=24-40\mathrm{}$ MeV; measured $\sigma (E,\theta )$; correlation analysis; DWBA and ${P_L}^2$ analyses; deduced $J$ values.

• Received 29 October 1979

DOI:https://doi.org/10.1103/PhysRevC.21.1802