Radiative Width of the Hoyle State from $\gamma$-Ray Spectroscopy

The cascading 3.21 and 4.44 MeV electric quadrupole transitions have been observed from the Hoyle state at 7.65 MeV excitation energy in ${}^{12}\mathrm{C}$, excited by the ${}^{12}\mathrm{C}(p,p^{\prime })$ reaction at 10.7 MeV proton energy. From the proton-$\gamma \text{−}\gamma$ triple coincidence data, a value of ${\mathrm{\Gamma }}_{\mathrm{rad}}/\mathrm{\Gamma }=6.2(6)\times {10}^{-4}$ was obtained for the radiative branching ratio. Using our results, together with ${\mathrm{\Gamma }}_{\pi }^{E0}/\mathrm{\Gamma }$ from Eriksen et al. [Phys. Rev. C 102, 024320 (2020)] and the currently adopted ${\mathrm{\Gamma }}_{\pi }(E0)$ values, the radiative width of the Hoyle state is determined as ${\mathrm{\Gamma }}_{\mathrm{rad}}=5.1(6)\times {10}^{-3}\mathrm{eV}$. This value is about 34% higher than the currently adopted value and will impact models of stellar evolution and nucleosynthesis.

Figure 1

Singles proton events recorded in the SiRi $E$ (horizontal axis) versus $\mathrm{\Delta }E$ (vertical axis) telescopes using the ${\mathrm{SiO}}_2$ plus carbon target. Events corresponding to the excitation of the 4.98 MeV $0^{+}$ state are indicated by the ellipse. The inset shows $\mathrm{\Delta }E+E$ total energy spectrum around the proton group of the 4.98 MeV $0^{+}$ state, together with the energy gate (dashed lines).

Figure 2

Singles spectra of (a) protons and (b) $\gamma$ rays using the ${}^{12}\mathrm{C}(p,p^{\prime })$ reaction. The proton ($7.65_p$) and $\gamma$-ray energy ($3.21_{\gamma }$ and $4.44_{\gamma }$) gates used for the analysis are indicated by red lines.

Figure 3

Time differences between protons exciting the Hoyle state and 3.21 and 4.44 MeV $\gamma$ rays. The prompt (pr) and four background gates on each side (bgLx, bgRx) are marked in red. The average counts in the background peaks is 318(18).

Figure 4

Protons in prompt coincidence with the 3.21 and 4.44 MeV $\gamma$-rays cascade. (a) Both $\gamma$ rays observed in the prompt (“pr-pr”) TDC window, and (b) random events from the “pr-bgLx” and “pr-bgRx” TDC gates (Fig. 3) are subtracted.

Figure 5

$\gamma$-ray energy versus summed $\gamma$-ray energy matrix constructed from $\gamma \text{−}\gamma$ coincidence events gated by protons exciting the Hoyle state. Random events have been removed. The gate representing the 3.21 plus 4.44 MeV summed energy ($7.65_{\mathrm{sum}}$) is indicated with red horizontal lines. The inset shows the region around the 3.21 and 4.44 MeV transitions in 3D. Data have been compressed by factor 4. The location of the random coincidences of the 4.44 MeV $\gamma$ ray with itself is also marked.

Figure 6

Random subtracted $\gamma$ rays from the Hoyle state. The fit to the spectrum including the 3.21 and 4.44 MeV transitions is shown in red.