Shapes of (Li6,d) Angular Distributions as Signatures of Rotational Bands inSi29

Angular distributions obtained in a study of the ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, d)$ reaction at $E_{\mathrm{Li}}=36\mathrm{}$ MeV are characterized by the lowest allowed $L$ transfers for cluster transitions to the members of the ground-state rotational band of ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, while a mixture of $L$ values is required for states of the $K={\frac{3}{2}}^{+}$ excited band. This demonstrates that an $\alpha$-transfer reaction can probe the internal structure of the nucleus in a way that can be deciphered.