A Cautionary Tale: The Coulomb Modified ANC for the $1/2_2^{+}$ State in ${}^{17}$O

Abstract

We discuss the impact of the uncertainty ($\pm 8$ keV) in the excitation energy of the astrophysically important 6.356 MeV $1/2_2^{+}$ state of ${}^{17}$O on the precision with which the Coulomb reduced ANC ($\tilde{C}$) for the $\left<^{17}\mathrm{O}(1/2^+_2) \mid \protect{^{13}\mathrm{C}} + α\right>$ overlap can be extracted from direct reaction data. We find a linear dependence of ${\tilde{C}}^2$ on the binding energy, the value extracted varying by a factor of 4 over the range $E_{\mathrm{ex}}=6.356$ -- $6.348$ MeV. This represents an intrinsic limit on the precision with which ${\tilde{C}}^2$ can be determined which cannot be improved unless or until the uncertainty in $E_{\mathrm{ex}}$ is reduced.

References in corpus (1)

• New $\alpha$ ANC measurement of the 1/2${}^{+}$ state in ${}^{17}$O at 6.356 MeV, that dominates the ${}^{13}$C($\alpha$,n)${}^{16}$O reaction rate at temperatures relevant for the s-process

Cited by in corpus (2)

• Direct measurement of the 13C(α,n)16O cross section into the s-process Gamow peak
• Asymptotic normalization coefficients from transfer reaction and R-martix analysis of direct capture in ${}^{22}$Ne(p,$\gamma$)${}^{23}$Na reaction