Coupled-channel calculations are performed for the ${}^{12}\mathrm{C}$($d,p$)${}^{13}\mathrm{C}$ and ${}^{13}\mathrm{C}$($p,d$)${}^{12}\mathrm{C}$ reactions between 7 and 60 MeV to study the effect of inelastic couplings in transfer reactions. The effect of treating transfer beyond Born approximation is also addressed. The coupling to the ${}^{12}\mathrm{C}$ $2^{+}$ state is found to change the peak cross section by up to 15%. Effects beyond Born approximation lead to a significant renormalization of the cross sections, between 5% and 10% for deuteron energies above 10 MeV and larger than 10% for lower energies. We also performed calculations including the remnant term in the transfer operator, which has a small impact on the ${}^{12}\mathrm{C}$($d,p$)${}^{13}\mathrm{C}$(g.s.) and ${}^{13}\mathrm{C}$($p,d$)${}^{12}\mathrm{C}$(g.s.) reactions (where g.s. indicates ground state). Above 30-MeV deuteron energy, the effect of the remnant term is larger than 10% for the ${}^{12}\mathrm{C}$($d,p$)${}^{13}\mathrm{C}$($1/2^{+}$, 3.09 MeV) reaction and is found to increase with decreasing neutron separation energy for the 3.09-MeV state of ${}^{13}\mathrm{C}$. This is of importance for transfer reactions with weakly bound nuclei.

• Received 15 April 2005

DOI:https://doi.org/10.1103/PhysRevC.72.014610