The (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$) reaction has been studied at a laboratory energy of 25.5 MeV for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ targets and at energies of 25.5, 27.0, and 29.0 MeV for a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ target. Angular distributions have been measured from ${\theta }_{\mathrm{lab}}=15\mathrm{}° \mathrm{to} 160°$ for transitions to low-lying states in the residual nuclei. The resulting angular distributions have been analyzed (1) using an exact-finite-range distorted-wave Born-approximation formalism including multistep processes and (2) using a Hauser-Feshbach compound-nuclear model. In general, the shapes of the forward angle (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$) data are well described by the finite-range distorted-wave Born-approximation and finite-range coupled-channels Born-approximation calculations. The magnitude of the measured transition to the 1.63-MeV ($2^{+}$) state in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ is approximately 100 times larger than predicted by an ${\mathrm{SU}}_3$ theory for a simple one-step transition, and this transition is shown to be an example in which a finite-range coupled-channels Born-approximation analysis is required. Arguments concerning the direct nature of the reaction process populating these states are discussed, and spectroscopic information is extracted.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$), $E_{\left({}_{}{}^3{}_{}{}^{}\mathrm{He}\right)}=25.5, 27.0, 29.0$ MeV, measured $\sigma (E,\theta )$ Hauser-Feshbach and finite-range CCBA analysis, spectroscopic factors.

• Received 1 March 1976

DOI:https://doi.org/10.1103/PhysRevC.14.475