A Study of the $^{13}$C($\alpha $,n) Reaction Rate Through the ANC Technique

The $^{13}$C($\alpha $,n) reaction is the main source of neutrons for the s-process. Currently the adopted rate has an uncertainty of $\sim $300{\%}[C. Angulo et al., Nucl. Phys. A656, 3 (1999)] at the relevant stellar temperatures($\sim $10$^{8}$ K). This leads to a large uncertainty in the modeling of AGB stars, which is where the s-process occurs. Recently, we measured the ANC of the $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} ^{+}$, 6.356 MeV, near threshold state in $^{17}$O. This was done via the $\alpha $-transfer reaction $^{13}$C($^{6}$Li,d)$^{17}$O($\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} ^{+}$, 6.356) at sub-Coulomb energies. Using this information we were able to calculate the contribution of the $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} ^{+}$ state to the astrophysical S-factor. From our S-factor curve we calculated that the $^{13}$C($\alpha $,n) reaction rate is reduced by a factor of 3, also the associated uncertainty is improved to $\sim $15{\%}[E.D. Johnson et al., currently under review with PRL].