C12(p,α*)B9reaction in the finite range microscopic distorted-wave Born-approximation formalism

Abstract

The differential cross sections for the $^{12}\mathrm{C}$($p$,${\ensuremath{\alpha}}^{*}$)$^{9}\mathrm{B}$(g.s.) and $^{12}\mathrm{C}$($p$,$\ensuremath{\alpha}$)$^{9}\mathrm{B}$(g.s.) reactions were measured at forward angles at the proton energy of 45.2 MeV. The outgoing ${\ensuremath{\alpha}}^{*}$ particle (20.1 MeV, ${0}^{+}$, $T=0$) 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 $\ensuremath{\alpha}$ and ${\ensuremath{\alpha}}^{*}$ 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 ($p$,${\ensuremath{\alpha}}^{*}$) and the corresponding ($p$,$\ensuremath{\alpha}$) angular distribution were found to be in good agreement with theoretical prediction from the microscopic model.NUCLEAR REACTIONS $^{12}\mathrm{C}$($p$,${\ensuremath{\alpha}}^{*}$)$^{9}\mathrm{B}$, $^{12}\mathrm{C}$($p$,$\ensuremath{\alpha}$)$^{9}\mathrm{B}$, $E=45.2$ MeV; measured $\ensuremath{\sigma}({E}_{p},{E}_{t},\ensuremath{\theta})$, ${E}_{\mathrm{pt}}=0.285$ MeV, $\ensuremath{\sigma}({E}_{\ensuremath{\alpha}},\ensuremath{\theta})$; finite range DWBA analysis, microscopic and cluster form factors; final state interaction; relative normalization.