The chronicles of the $3_{1}^{-}$ total width in $\mathrm{^{12}C}$: the formal, the observed and the FWHM

K. C. W. Li, R. Neveling, P. Adsley, H. Fujita, P. Papka, F. D. Smit, J. W. Brümmer, L. M. Donaldson, M. N. Harakeh, Tz. Kokalova, E. Nikolskii, W. Paulsen, L. Pellegri, S. Siem, M. Wiedeking
Nuclear Experiment, Nuclear Experiment (nucl-ex), Nuclear Theory (nucl-th)
2023-07-15 16:00:00
Recent measurements indicate that the previously established upper limit for the $\gamma$-decay branch of the $3_{1}^{-}$ resonance in $^{12}\textrm{C}$ at $E_{x} = 9.641(5)$ MeV may be incorrect. The $3_{1}^{-}$ resonance has thus been touted as a significant resonance for mediating the triple-$\alpha$ reaction at high temperatures above 2 GK. Accurate estimations of the $3_{1}^{-}$ contribution to the triple-$\alpha$ 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 $\gamma$-decay branch of the $3_{1}^{-}$ state, the objective of this work is to accurately determine the total width of the $3_{1}^{-}$ state. An evaluation was performed on all previous results considered in the current ENSDF average for the $3_{1}^{-}$ total width of 46(3) keV. A new R-matrix analysis for the $3_{1}^{-}$ state was performed with a self-consistent, simultaneous fit of several high-resolution $\mathrm{^{12}C}$ excitation-energy spectra populated with direct reactions. The global analysis performed in this work yields a formal total width of $\Gamma(E_{r}) = 46(2)$ keV and an observed total width of $\Gamma_{\textrm{obs}}(E_{r}) = 38(2)$ keV for the $3_{1}^{-}$ state. Significant unaccounted-for uncertainties and/or formalism errors were discovered in the previous results employed in the ENSDF for the observed total width of the $3_{1}^{-}$ state. These previously reported widths are fundamentally different quantities, leading to an invalid ENSDF average. An observed total width of $\Gamma_{\textrm{obs}}(E_{r}) = 38(2)$ keV is recommended for the $3_{1}^{-}$ state in $\mathrm{^{12}C}$. This total width should be employed for future evaluations of the radiative width for the $3_{1}^{-}$ state and its contribution to the high-temperature triple-$\alpha$ reaction rate.
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