The population of the 9.50 MeV $9/2_1^{+}$ resonance in ${}^{13}\mathrm{C}$ by single-neutron transfer reactions is expected to be dominated by the two-step route through the ${}^{12}\mathrm{C}$ $2_1^{+}$ (4.44 MeV) state, with another possible contribution via the strongly excited $3_1^{-}$ (9.64 MeV) resonance in ${}^{12}\mathrm{C}$. However, we find that a good description of the angular distribution for population of this state via the ${}^{12}\mathrm{C}\left(d,p\right){}^{13}\mathrm{C}$ reaction is only possible when both direct $0_1^{+}\otimes g_{9/2}$ and two-step (via the 4.44 MeV ${}^{12}\mathrm{C}$ $2_1^{+}$ state) $2_1^{+}\otimes d_{5/2}$ paths are included in a coupled reaction channel calculation. While the calculated angular distribution is almost insensitive to the presence of the two-step path via the 9.64 MeV ${}^{12}\mathrm{C}$ $3_1^{-}$ resonance, despite a much greater contribution to the wave function from the $3_1^{-}\otimes f_{7/2}$ configuration, its inclusion is required to fit the details of the experimental angular distribution. The very large interference between the various components of the calculations, even when these are small, arises through the “kinematic” effect associated with the different transfer routes.

• Received 6 October 2015

DOI:https://doi.org/10.1103/PhysRevC.92.054618