Background: The Efimov effect is a universal phenomenon in physics whereby three-body systems are stabilized via the interaction of an unbound two-body subsystems. A hypothetical state in ${}^{12}\mathrm{C}$ at 7.458-MeV excitation energy, comprising a loose structure of three $\alpha$ particles in mutual two-body resonance, has been suggested in the literature to correspond to an Efimov state in nuclear physics. The existence of such a state has not been demonstrated experimentally.

Purpose: Using a combination of $\gamma$ spectroscopy, charged-particle spectroscopy, and astrophysical rate calculations allowing for strict limits on the existence of such a state to been established here.

Method: Using the combined data sets from two recent experiments, one with the TexAT (Texas Active Target) TPC (Time Projection Chamber) to measure $\alpha$ decay and the other with Gammasphere to measure $\gamma$ decay of states in ${}^{12}\mathrm{C}$ populated by ${}^{12}\mathrm{N}$ and ${}^{12}\mathrm{B}\beta$ decay, respectively, we achieve high sensitivity to states in close proximity to the $\alpha$ threshold in ${}^{12}\mathrm{C}$.

Results: No evidence of a state at 7.458 MeV is seen in either data set. Using a likelihood method, the 95% confidence limit $\gamma$-decay branching ratio is determined as a function of the $\beta$-decay feeding strength relative to the Hoyle state. In parallel, calculations of the $3\alpha$ reaction rate show the inclusion of the Efimov corresponds to a large increase in the reaction rate around $5\times {10}^7$ K.

Conclusion: From decay spectroscopy—at the 95% confidence limit, the Efimov state cannot exist at 7.458 MeV with any $\gamma$-decay branching ratio unless the $\beta$ strength is less than 0.7% of the Hoyle state. This limit is evaluated for a range of different excitation energies and the results are not favorable for existence of the hypothetical Efimov state in ${}^{12}\mathrm{C}$. Furthermore, the $3\alpha$ reaction rate with the inclusion of a state between 7.43 and 7.53 MeV exceeds the rate required for stars to undergo the red giant phase.

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• Efimov states
• Few-body systems
• Nuclear astrophysics
• Nuclear forces
• Nuclear structure & decays
• 6 ≤ A ≤ 19