Abstract
The inelastic excitations and cluster decay of $^{13}$C have been measured using the reaction, $^9$Be($^{13}$C,$^{13}$C* $\rightarrow$ $^9$Be + $\alpha$ )$^9$Be. We observe strong excitation to the 14.3-MeV (1/2$^-$) resonant state from the cluster-decay channel, leading to an enhanced monopole matrix element of (6.3 $\pm$ 0.6) fm$^2$. This large cluster-related monopole strength is a clear indication of the cluster-structure domination of this state and is consistent with the recent prediction of the orthogonality condition model (OCM). It would be interesting to further explore the three-center molecular rotational band that is initiated from the observed band-head.
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