Evidence against the Efimov effect in C 12 from spectroscopy and astrophysics

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 C12 at 7.458-MeV excitation energy, comprising a loose structure of three α 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 γ 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 α decay and the other with Gammasphere to measure γ decay of states in C12 populated by N12 and B12β decay, respectively, we achieve high sensitivity to states in close proximity to the α threshold in C12. Results: No evidence of a state at 7.458 MeV is seen in either data set. Using a likelihood method, the 95% confidence limit γ-decay branching ratio is determined as a function of the β-decay feeding strength relative to the Hoyle state. In parallel, calculations of the 3α reaction rate show the inclusion of the Efimov corresponds to a large increase in the reaction rate around 5×107 K. Conclusion: From decay spectroscopy - at the 95% confidence limit, the Efimov state cannot exist at 7.458 MeV with any γ-decay branching ratio unless the β 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 C12. Furthermore, the 3α 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.