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The β decays of 12 N and 12 B have been studied at KVI and JYFL to resolve the composition of the broad and interfering 0 + and 2 + strengths in the triple-α continuum. For the first time a complete treatment of 3α 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 β strength up to the 12 N Q-value window suggests the presence of additional 0 + and 2 + components in the 12 C structure at energies above 12.7 MeV.

Two complementary experimental techniques have been used to extract precise branching ratios to unbound states in 12 C from 12 N and 12 B β-decays. In the first the three α-particles emitted after βdecay are measured in coincidence in separate detectors, while in the second method 12 N and 12 B are implanted in a detector and the summed energy of the three α-particles is measured directly. For the narrow states at 7.654 MeV (0 +) and 12.71 MeV (1 +) the resulting branching ratios are both smaller than previous measurements by a factor of 2. The experimental results are compared to no-core shell model calculations with realistic interactions from chiral perturbation theory, and inclusion of three-nucleon forces is found to give improved agreement.

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