Differential cross sections and analyzing powers of the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$($p$,$t$)${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$($p$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ reactions to the ground and the first excited states were measured at $E_p=65\mathrm{}$ MeV. They were analyzed by means of distorted-wave Born approximation calculations including both one- and two-step processes of $p-d-t$ or -${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Attention was paid to an isospin symmetry of the reaction process consisting of both isospin 0 and 1 channels, which were important in a comparable order. As intermediate states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in the sequential process, five states of either isospin 0 or 1, which were strongly excited by the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$($p$,$d$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction, were taken into account. A good fit between the data and the theoretical values was obtained, especially for the ($p$,$t$) reactions, concerning both differential cross sections and analyzing powers. The calculations including one-step and sequential processes induced, in some cases, remarkable differences from the one-step calculation for backward angles.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$($p$,$t$)${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$($p$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, $E=65\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ and analyzing powers for 4 transitions. One-step and sequential processes DWBA analysis.

• Received 9 July 1981

DOI:https://doi.org/10.1103/PhysRevC.25.97