Understanding the total width of the $3_1^{-}$ state in ${}^{12}\mathrm{C}$

Abstract

Recent measurements indicate that the previously established upper limit for the ${\hat{I}}^3$-decay branch of the $3_1^{-}$ resonance in ${}^{12}\text{C}$ at $E_x=9.641(5)$ MeV may be incorrect. As a result, the $3_1^{-}$ resonance has been suggested as a significant resonance for mediating the triple-$\hat{I}\pm$ reaction at high temperatures above 2 GK. Accurate estimations of the $3_1^{-}$ contribution to the triple-$\hat{I}\pm$ reaction rate require accurate knowledge of not only the radiative width, but also the total width. In anticipation of future measurements to more accurately determine the ${\hat{I}}^3$-decay branch of the $3_1^{-}$ resonance, the objective of this work is to accurately determine the total width of the $3_1^{-}$ resonance. An evaluation was performed on all previous results considered in the current ENSDF average of 46(3) keV for the physical total width (FWHM) of the $3_1^{-}$ resonance in ${}^{12}\text{C}$. Significant unaccounted-for uncertainties and a misstated result were discovered in these previous results, leading to an invalid ENSDF average. In this work, the new global \textbf{R}-matrix analysis performed on direct-reaction data yields a formal total width of $\hat{I}“(E_r)=46(2)$ keV and an observed total width of $\hat{I}{“}_{\text{obs}}(E_r)=38(2)$ keV for the $3_1^{-}$ resonance. An observed total width of $\hat{I}{“}_{\text{obs}}(E_r)=38(2)$ keV is recommended for the $3_1^{-}$ resonance in ${}^{12}\mathrm{C}$. This observed total width should be employed for future evaluations of the observed total radiative width for the $3_1^{-}$ resonance and its contribution to the high-temperature triple-$\hat{I}\pm$ reaction rate.