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

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 $\hat{I}\pm$-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 $\hat{I}\pm$-decay and the other with Gammasphere to measure ${\hat{I}}^3$-decay of states in ${}^{12}\mathrm{C}$ populated by ${}^{12}\mathrm{N}$ and ${}^{12}\mathrm{B}$ ${\hat{I}}^2$-decay respectively, we achieve high sensitivity to states in close-proximity to the $\hat{I}\pm$-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. ${\hat{I}}^3$-decay branching ratio is determined as a function of the ${\hat{I}}^2$-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 ${\hat{I}}^3$-decay branching ratio unless the ${\hat{I}}^2$-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.

Submitted to PRL