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

TL;DR

This paper examines how the uncertainty in the excitation energy of a specific state in $^{17}$O affects the precision of Coulomb reduced ANC extraction from reaction data, highlighting an intrinsic limit on accuracy.

Contribution

It demonstrates a linear dependence of the Coulomb reduced ANC on the excitation energy, revealing a fundamental limit on precision due to energy uncertainty.

Findings

$ ilde{C}^2$ varies by a factor of 4 within the energy range

Intrinsic limit on ANC precision due to excitation energy uncertainty

Reducing energy uncertainty is necessary for improved ANC accuracy

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 ($\widetilde{C}$) 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 $\widetilde{C}^2$ 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 $\widetilde{C}^2$ can be determined which cannot be improved unless or until the uncertainty in $E_{\mathrm{ex}}$ is reduced.