Evidence against the Efimov effect in $^{12}\mathrm{C}$ from spectroscopy and astrophysics

TL;DR

This study uses spectroscopy and astrophysical data to test for the existence of an Efimov state in carbon-12 at 7.458 MeV, finding no evidence for such a state and challenging its hypothesized properties.

Contribution

The paper provides the first experimental constraints on the Efimov state in $^{12}$C, combining decay spectroscopy and astrophysical reaction rate calculations to disprove its existence at the proposed energy.

Findings

No evidence of the Efimov state at 7.458 MeV in $^{12}$C.

The Efimov state cannot have a gamma-decay branching ratio above 0.7%.

Including such a state in models increases the triple-alpha reaction rate beyond stellar requirements.

Abstract

Background: The Efimov effect is a universal phenomenon in physics whereby three-body systems are stabilized via the interaction of an unbound two-body sub-systems. A hypothetical state in $^{12}\mathrm{C}$ at 7.458 MeV excitation energy, comprising of 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. Method: Using the combined data sets from two recent experiments, one with the TexAT TPC 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\% C.L. $\gamma$-decay branching ratio is determined as a function of the $\beta$-decay feeding strength relative to the Hoyle state. In parallel, calculations of the triple-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\% C.L., 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 triple-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.