High-Precision Probe of the Fully Sequential Decay Width of the Hoyle State in ${}^{12}\mathrm{C}$

The decay path of the Hoyle state in ${}^{12}\mathrm{C}$ ($E_x=7.654\mathrm{MeV}$) has been studied with the ${}^{14}\mathrm{N}(d,{\alpha }_2){}^{12}\mathrm{C}(7.654)$ reaction induced at 10.5 MeV. High resolution invariant mass spectroscopy techniques have allowed us to unambiguously disentangle direct and sequential decays of the state passing through the ground state of ${}^8\mathrm{Be}$. Thanks to the almost total absence of background and the attained resolution, a fully sequential decay contribution to the width of the state has been observed. The direct decay width is negligible, with an upper limit of 0.043% (95% C.L.). The precision of this result is about a factor 5 higher than previous studies. This has significant implications on nuclear structure, as it provides constraints to $3\alpha$ cluster model calculations, where higher precision limits are needed.

Figure 1

${}^{12}\mathrm{C}$ excitation energy spectrum reconstructed from the measured momentum of particles detected by the $\mathrm{\Delta }E-E$ anticoincidence telescope (blue line). Labels are used to indicate the energy and spins of well-known states of ${}^{12}\mathrm{C}$. (filled histogram) Same spectrum obtained by selecting four-particle coincidences.

Figure 2

Three-particle invariant mass spectrum (${}^{12}\mathrm{C}$ $E_x$) gated on the Hoyle peak of Fig. 1. Experimental points are compared with the result of a Monte Carlo simulation of the ${}^{14}\mathrm{N}(d,{\alpha }_2){}^{12}\mathrm{C}(7.654)$, details are explained in the text. Events under the peak centered at 7.654 MeV are due to the decay of the Hoyle state. The evaluated background level is about 0.036%.

Figure 3

Experimental symmetric Dalitz plot (a) compared with Monte Carlo simulations of (b) 100% SD and (c) 100% $\mathrm{DD}\mathrm{\Phi }$. Further details on the simulation procedure are explained in the text. Simulated SD events result in a horizontal band and the effect of our experimental apparatus is expected to not introduce any significant contamination outside this band, as instead observed in previous works [27, 32].

Figure 4

${\epsilon }_i$ distribution, i.e., the largest energy among the normalized decay energy of the three $\alpha$ particles in their emitting reference frame. Experimental data (green circles) are compared with the result of a Monte Carlo simulation (red dashed line) where we assumed a 100% sequential decay (SD).