Evidence against the Efimov effect in 12 C 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 $^{12}\mathrm{C}$ at 7.458-MeV excitation energy, comprising a loose structure of three $\ensuremath{\alpha}$ 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 $\ensuremath{\gamma}$ 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 $\ensuremath{\alpha}$ decay and the other with Gammasphere to measure $\ensuremath{\gamma}$ decay of states in $^{12}\mathrm{C}$ populated by $^{12}\mathrm{N}$ and $^{12}\mathrm{B}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$ decay, respectively, we achieve high sensitivity to states in close proximity to the $\ensuremath{\alpha}$ 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 $\ensuremath{\gamma}$-decay branching ratio is determined as a function of the $\ensuremath{\beta}$-decay feeding strength relative to the Hoyle state. In parallel, calculations of the $3\ensuremath{\alpha}$ reaction rate show the inclusion of the Efimov corresponds to a large increase in the reaction rate around $5\ifmmode\times\else\texttimes\fi{}{10}^{7}$ K.Conclusion: From decay spectroscopy---at the 95% confidence limit, the Efimov state cannot exist at 7.458 MeV with any $\ensuremath{\gamma}$-decay branching ratio unless the $\ensuremath{\beta}$ 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 $3\ensuremath{\alpha}$ 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.