$\alpha$-cluster ANCs for nuclear astrophysics

Background. Many important $\alpha$-particle induced reactions for nuclear astrophysics may only be measured using indirect techniques due to small cross sections at the energy of interest. One of such indirect technique, is to determine the Asymptotic Normalization Coefficients (ANC) for near threshold resonances extracted from sub-Coulomb $\alpha$-transfer reactions. This approach provides a very valuable tool for studies of astrophysically important reaction rates since the results are practically model independent. However, the validity of the method has not been directly verified. Purpose. The aim of this letter is to verify the technique using the $^{16}$O($^6$Li,$d$)$^{20}$Ne reaction as a benchmark. The $^{20}$Ne nucleus has a well known $1^-$ state at excitation energy of 5.79 MeV with a width of 28 eV. Reproducing the known value with this technique is an ideal opportunity to verify the method. Method. The 1$^-$ state at 5.79 MeV is studied using the $\alpha$-transfer reaction $^{16}$O($^6$Li,$d$)$^{20}$Ne at sub-Coulomb energies. Results. The partial $\alpha$ width for the $1^-$ state at excitation energy of 5.79 MeV is extracted and compared with the known value, allowing the accuracy of the method to be evaluated. Conclusions. This study demonstrates that extracting the Asymptotic Normalization Coefficients using sub-Coulomb $\alpha$-transfer reactions is a powerful tool that can be used to determine the partial $\alpha$ width of near threshold states that may dominate astrophysically important nuclear reaction rates. \end{description}