Anomalous population of two4+states inC12(Li6,d)O16

In the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, two $4^{+}$ states (at $E_x=10.35\mathrm{} \mathrm{and} 11.096$ MeV) are populated with relative strengths of $\frac{\sigma \mathrm{}\left(11.096\right)\mathrm{}}{\sigma \mathrm{}\left(10.35\right)\mathrm{}}\approx 0.5$ even though their reduced $\alpha$-particle widths to the g.s. of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are in the ratio $\frac{S_{\alpha }\mathrm{}\left(11.096\right)\mathrm{}}{S_{\alpha }\mathrm{}\left(10.35\right)\mathrm{}}<{10}^{-2\mathrm{}}$. A two-step process proceeding through the first excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ offers a likely mechanism of the enhanced feeding of the 11.096-MeV state.