The differential cross sections for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p$,${\alpha }^{*}$)${}_{}{}^9{}_{}{}^{}\mathrm{B}$(g.s.) and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p$,$\alpha$)${}_{}{}^9{}_{}{}^{}\mathrm{B}$(g.s.) reactions were measured at forward angles at the proton energy of 45.2 MeV. The outgoing ${\alpha }^{*}$ particle (20.1 MeV, $0^{+}$, $T=0\mathrm{}$) was detected by measuring in coincidence the proton and triton breakup products. Finite range distorted-wave Born approximation and final state interaction calculations were employed in describing the reaction with the unbound emitted particle. The form factor for the distorted-wave Born-approximation analysis was calculated in a microscopic model employing Woods-Saxon wave functions for the three individual transferred nucleons. Microscopic wave functions for the $\alpha$ and ${\alpha }^{*}$ particles, due to Hackenbroich et al., were used. Comparisons were also made with distorted-wave Born-approximation calculations using cluster transfer form factors. Relative normalizations between the ($p$,${\alpha }^{*}$) and the corresponding ($p$,$\alpha$) angular distribution were found to be in good agreement with theoretical prediction from the microscopic model.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p$,${\alpha }^{*}$)${}_{}{}^9{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p$,$\alpha$)${}_{}{}^9{}_{}{}^{}\mathrm{B}$, $E=45.2\mathrm{}$ MeV; measured $\sigma (E_p,E_t,\theta )$, $E_{\mathrm{pt}}=0.285\mathrm{}$ MeV, $\sigma (E_{\alpha },\theta )$; finite range DWBA analysis, microscopic and cluster form factors; final state interaction; relative normalization.

• Received 21 June 1979

DOI:https://doi.org/10.1103/PhysRevC.21.1687