Decay Modes of the Hoyle State in $^{12}C$

TL;DR

This paper investigates the decay modes of the Hoyle state in carbon-12, combining experimental limits with theoretical tunneling calculations to estimate decay ratios and explore connections to Bose-Einstein Condensates and hypothetical Efimov states.

Contribution

The study provides new theoretical estimates of decay ratios of the Hoyle state, compares them with experimental limits, and discusses potential experimental tests and implications for nuclear structure.

Findings

Theoretical decay ratio estimates are more than an order of magnitude smaller than experimental upper limits.

Decay modes of high excitation states could reach a 10 ext{ extperthousand} ratio at 10.3 MeV excitation energy.

A hypothetical Efimov state would be extremely unlikely, at least 8 orders of magnitude less probable than the Hoyle state.

Abstract

Recent experimental results give an upper limit less than 0.043\% (95\% C.L.) to the direct decay of the Hoyle state into 3$\alpha$ respect to the sequential decay into $^8${Be}+$\alpha$. We performed one and two-dimensional tunneling calculations to estimate such a ratio and found it to be more than one order of magnitude smaller than experiment depending on the range of the nuclear force. This is within high statistics experimental capabilities. Our results can also be tested by measuring the decay modes of high excitation energy states of $^{12}$C where the ratio of direct to sequential decay might reach 10\% at $E^*$($^{12}$C)=10.3 MeV. The link between a Bose Einstein Condensate (BEC) and the direct decay of the Hoyle state is also addressed. We discuss a hypothetical `Efimov state' at $E^*$($^{12}$C)=7.458 MeV, which would mainly {\it sequentially} decay with 3$\alpha$ of {\it equal energies}: a counterintuitive result of tunneling. Such a state, if it would exist, is at least 8 orders of magnitude less probable than the Hoyle's, thus below the sensitivity of recent and past experiments.