Extracting the asymptotic normalization coefficient for the C14→B13+p overlap from the C14(B11,C12)B13 reaction

Abstract

The availability of a comparatively complete data set for the elastic and inelastic scattering of a 45-MeV beam of $^{11}\mathrm{B}$ ions from a $^{14}\mathrm{C}$ target, together with an angular distribution for the $^{14}\mathrm{C}(^{11}\mathrm{B},^{12}\mathrm{C})^{13}\mathrm{B}$ proton pickup reaction enables a determination of the $\ensuremath{\langle}^{14}\mathrm{C}\ensuremath{\mid}^{13}\mathrm{B}+p\ensuremath{\rangle}$ asymptotic normalization coefficient (ANC) using the coupled reaction channel (CRC) technique. The complete nature of the data set allows two-step contributions to the reaction mechanism to be controlled while a set of $\ensuremath{\langle}^{12}\mathrm{C}\ensuremath{\mid}^{11}\mathrm{B}+p\ensuremath{\rangle}$ overlaps obtained from a consistent analysis of ($d,^{3}\mathrm{He}$) and ($e,{e}^{\ensuremath{'}}p$) data fixes the projectile overlaps. We find that the level of completeness of the modeling of the reaction mechanism has a significant effect on the value obtained for the ANC, with a distorted wave Born approximation analysis yielding a significantly larger ANC than the full CRC calculation. The final result obtained, when compared with the theoretical value calculated within the source term approach, is in accord with trends for proton removal from similar $p$-shell nuclei.