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

We discuss the impact of the uncertainty ($\pm 8$ keV) in the excitation energy of the astrophysically important 6.356 MeV $1\mathrm{/}{2}_2^{+}$ 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}$} + \alpha \right>$ 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 $E_{\mathrm{e}\mathrm{x}}=6.356$ – $6.348$ 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 $E_{\mathrm{e}\mathrm{x}}$ is reduced.