A stringent upper limit on the direct 3$\hat{I}\pm$ decay of the Hoyle State in ${}^{12}$C

Abstract

We investigate an implication of the most recent observation of a second $J^{\ddot{I}}€=2^{+}$ state in ${}^{12}$C, which was measured using the ${}^{12}$C(${\hat{I}}^3$,$\hat{I}\pm$)${}^8$Be${}_{\text{(g.s.)}}$ reaction. In addition to the dissociation of ${}^{12}$C to an $\hat{I}\pm$-particle and ${}^8$Be in its ground state, a small fraction of events (2%) were identified as direct decays and decays to excited states in ${}^8$Be. This allowed a limit on the direct 3$\hat{I}\pm$ partial decay width to be determined as $\hat{I}{“}_{3\hat{I}\pm }<32(4)$ keV. Since this 2${}^{+}$ state is predicted by all theoretical models to be a collective excitation of the Hoyle state, the 3$\hat{I}\pm$ partial width of the Hoyle state is calculable from the ratio of 3$\hat{I}\pm$ decay penetrabilities of the Hoyle and 2${}^{+}$ states. This was calculated using the semi-classical WKB approach and we deduce a stringent upper limit for the direct decay branching ratio of the Hoyle state of $\frac{\hat{I}{“}_{3\hat{I}\pm }}{\hat{I}“}<5.7\times 10^{-6}$, over an order of magnitude lower than previously reported. This result places the direct measurement of this rare decay mode beyond current experimental capabilities.

Accepted for publication in Physical Review C (Rapid) on 01/16/2020