Further Improvement of the Upper Limit on the Direct $3\alpha$ Decay from the Hoyle State in ${}^{12}\mathrm{C}$

The direct $3\alpha$ decay branch from the $0_2^{+}$ state at $E_x=7.65\mathrm{MeV}$ in ${}^{12}\mathrm{C}$, which is known as the Hoyle state, is considered to affect the triple-$\alpha$ reaction rate strongly and to give crucial information on its structure. We have performed a high-precision measurement of the $3\alpha$ decay from this state using the ${}^{12}\mathrm{C}({}^{12}\mathrm{C},3\alpha ){}^{12}\mathrm{C}$ reaction at $E_{{}^{12}\mathrm{C}}=110\mathrm{MeV}$. The branching ratio of the direct $3\alpha$ decay was under the detection limit in the present experiment. By comparing with Monte Carlo simulations for three decay mechanisms as the sequential decay through the ground state of ${}^8\mathrm{Be}$, the direct decay with equal energies of three $\alpha$ particles, and the direct decay to the phase space uniformly, we have obtained the upper limit of 0.2% on the direct $3\alpha$ decay.

Figure 1

(a) The kinematics of the ${}^{12}\mathrm{C}({}^{12}\mathrm{C},{}^{12}{\mathrm{C}}^{*}[3\alpha ]){}^{12}\mathrm{C}$ reaction. Those of the 4.44 MeV, $2_1^{+}$ state, the 7.65 MeV, $0_2^{+}$ state, and the 9.64 MeV, $3^{-}$ state are drawn by thin solid, thick solid, and dotted lines, respectively. The dashed line shows the kinematics in the case in which both the beam and the target ${}^{12}\mathrm{C}$ are excited to the $2_1^{+}$ state. The hatched region indicates the acceptance of the silicon detector for the recoiling ${}^{12}\mathrm{C}$. (b) Energy spectra of the recoiling ${}^{12}\mathrm{C}$ at 67° are shown. The thin solid and thick solid lines show the energy spectrum of the singles trigger and the coincidence spectrum with the breakup three $\alpha$ particles, respectively.

Figure 2

The total kinetic energy spectrum in the ${}^{12}{\mathrm{C}}^{*}$ rest frame. The peak at 0.38 MeV corresponds to the Hoyle state. The result of the Monte Carlo simulation for the 100% sequential decay is drawn by the solid line. The dotted line shows the background level which we assumed.

Figure 3

Symmetric Dalitz plots for (a) the experimental data, Monte Carlo simulations of (b) the sequential decay (SD), (c) the direct decay with an equal energy of three $\alpha$ particles (DDE), and (d) the direct decay to the phase space uniformly ($\mathrm{DD}\mathrm{\Phi }$) (see text).

Figure 4

${ϵ}_i$ distribution. ${ϵ}_i$ is the highest energy among the decay $3\alpha$ particles from the Hoyle state (see text). The solid circles show the experimental data. The solid line shows the ${ϵ}_i$ distribution obtained by the fit with the result of the Monte Carlo simulation for the sequential decay (SD). The dashed, dotted, and dashed-dotted lines indicate the distributions for DDE, $\mathrm{DD}\mathrm{\Phi }$, and the sum of these two direct decays reported in Ref. [21]