The ${}^9$Be(${}^6\mathrm{Li},d)$${}^{13}$C${}^{*}$ reaction at a beam energy of 42 MeV has been investigated using a large-acceptance silicon-strip detector array and the high-resolution Q3D magnetic spectrograph. The Q3D facilitated the unambiguous determination of the reaction channel via identification of the deuteron ejectile, thereby providing the spectrum of excited states in ${}^{13}$C in the range from 10.7 to 15.0 MeV. The silicon array was used to detect and identify the ${}^{13}$C recoil-breakup products with efficiencies of up to $49\%$. The results obtained for the absolute partial branching ratios represent the first complete measurements for states in this energy region and allow the extraction of reduced widths. The quantities measured for ${\Gamma }_{n0}/{\Gamma }_{\mathrm{tot}}$ and ${\Gamma }_{n1}/{\Gamma }_{\mathrm{tot}}$ are $0.91\pm 0.11$ and $\le$0.13 (10.753 MeV), $0.51\pm 0.04$ and $0.51\pm 0.04$ (10.818 MeV), $0.68\pm 0.03$ and $0.42\pm 0.02$ (10.996 MeV), $0.49\pm 0.08$ and $0.71\pm 0.11$ (11.848 MeV), and $0.49\pm 0.08$ and $0.53\pm 0.08$ (12.130 MeV), respectively. For the two observed higher-lying energy levels, ${\Gamma }_{\alpha 0}/{\Gamma }_{\mathrm{tot}}$ and ${\Gamma }_{n1}/{\Gamma }_{\mathrm{tot}}$ have been measured as $0.54\pm 0.02$ and $0.45\pm 0.02$ (13.760 MeV) and $0.94\pm 0.03$ and $0.13\pm 0.02$ (14.582 MeV), respectively. The consequences for the proposed molecular structures in ${}^{13}$C are explored following the extraction of reduced widths.

• Received 29 June 2012

DOI:https://doi.org/10.1103/PhysRevC.86.044328