Extracting ANCs in neutron transfer reactions to determine proton capture reaction rates

The high temperatures ( $>$10$^{8}$ K) in novae outbursts enable unstable nuclei to leak out from the hot CNO cycle to the rp-process, where heavier nuclei such as $^{18}$F and $^{22}$Na are synthesized and might be ejected. Their abundances can be influenced by the $^{17}$F(p,$\gamma )^{18}$Ne and $^{22}$Mg(p,$\gamma )^{23}$Al reactions respectively. The first reaction connects the CNO and NeNa cycles, while the second may explain the unobserved $\gamma $-ray emission from $^{22}$Ne due to the $\beta $ decay in $^{22}$Na. We have applied an indirect technique to determine the above reaction rates at stellar energies. We have measured the neutron transfer reactions $^{13}$C($^{17}$O,$^{18}$O)$^{12}$C and $^{13}$C($^{22}$Ne,$^{23}$Ne)$^{12}$C to determine the asymptotic normalization coefficients (ANCs) for the ground and first excited states in $^{18}$O and $^{23}$Ne. These ANCs can be transposed to the corresponding states in the mirror nuclei $^{18}$Ne and $^{23}$Al respectively. As a part of these experiments, we have measured the elastic scattering data to obtain the optical model parameters that are used in DWBA calculations, and hence to extract the ANCs.