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 $⟨{}^{17}\mathrm{O}(1/2_2^{+})\mid \text{protect}{}^{13}\mathrm{C}+\alpha ⟩$ 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.