The $\beta$ decays of ${}^{12}\mathrm{N}$ and ${}^{12}\mathrm{B}$ have been studied at KVI and JYFL to resolve the composition of the broad and interfering $0^{+}$ and $2^{+}$ strengths in the triple-$\alpha$ continuum. For the first time a complete treatment of $3\alpha$ decay is presented including all major breakup channels. A multilevel, many-channel $R$-matrix formalism has been developed for the complete description of the breakup in combination with the recently published separate analysis of angular correlations. We find that, in addition to the Hoyle state at 7.65 MeV, more than one $0^{+}$ and $2^{+}$ state is needed to reproduce the spectra. Broad $0_3^{+}$ and $2_2^{+}$ states are found between 10.5 and 12 MeV in this work. The presence of $\beta$ strength up to the ${}^{12}\mathrm{N}$ $Q$-value window suggests the presence of additional $0^{+}$ and $2^{+}$ components in the ${}^{12}\mathrm{C}$ structure at energies above 12.7 MeV.

• Received 30 November 2009

DOI:https://doi.org/10.1103/PhysRevC.81.024303