${}^{12}$C and $\hat{I}\pm$-clusters, $0^{+}$ spectrum, and Hoyle-state candidates in ${}^{24}$Mg

Abstract

Background: A recent inelastic alpha-scattering experiment [Phys. Rev. Lett. 129, 102701 (2022)] found $0^{+}$ resonances in ${}^{24}$Mg on and above the ${}^{12}$C+${}^{12}$C break-up threshold. It has been conjectured that the states have a ${}^{12}$C+${}^{12}$C cluster structure, and play a similar role in accelerating ${}^{12}$C+${}^{12}$C fusion to the manner in which the Hoyle state accelerates production of ${}^{12}$C in massive stars. Purpose: We wish to build up a quantitative theoretical basis for the considerations of the Hoyle-state paradigm, by calculating the distribution of the $0^{+}$ states in the shell, as well as in the relevant cluster models. Methods: We determine the spectrum of excited $0^{+}$ states in ${}^{24}$Mg nucleus using multiconfigurational dynamical symmetry calculations leading to a unified description of the quartet (or shell), ${}^{12}$C+${}^{12}$C and ${}^{20}$Ne+${}^4$He cluster configurations. Results: The density of $0^{+}$ states in the quartet spectrum is comparable to that found in experiment; however, the density of cluster states is considerably less. Conclusions: The recently observed alpha-scattering resonances do not seem to be simple ${}^{12}$C+${}^{12}$C cluster states, but are more plausibly interpreted as fragmented cluster states due to coupling to quartet excitations, as background states.

7 pages, 6 figures