Strong multistep interference effects in ${}^{12}\mathrm{C}(d,p)$ to the $9/2_1^{+}$ state in ${}^{13}\mathrm{C}$

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.

Figure 1

CRC calculations for the ${}^{12}\mathrm{C}\left(d,p\right){}^{13}\mathrm{C}$ stripping reaction to the 9.50 MeV $9/2^{+}$ resonance of ${}^{13}\mathrm{C}$ at $E_d=30$ MeV compared with the data of Ref. [1]. The solid curve denotes the full calculation, the dashed curve a calculation including just the two-step transfer via the ${}^{12}\mathrm{C}4.44$ MeV $2^{+}$ state, the dot-dashed curve a calculation including just the direct, one-step transfer via the ${}^{12}\mathrm{C}$ $0^{+}$ ground state, and the dotted curve a calculation including just the two-step transfer via the ${}^{12}\mathrm{C}9.64$ MeV $3^{-}$ state.

Figure 2

Calculations for the ${}^{12}\mathrm{C}\left(d,p\right){}^{13}\mathrm{C}$ stripping reaction to the 9.50 MeV $9/2^{+}$ resonance of ${}^{13}\mathrm{C}$ at $E_d=30$ MeV compared with the data of Ref. [1]. The solid curve denotes the full CRC calculation and the dashed curve a CRC calculation omitting the two-step transfer via the 9.64 MeV ${}^{12}\mathrm{C}$ $3_1^{-}$ state. The dotted curve denotes the best-fit full calculation using CCBA.