Radiative decay branching ratio of the Hoyle state

Background: The triple-alpha process is a vital reaction in nuclear astrophysics, characterized by two consecutive reactions [$2\alpha \leftrightarrows {}^8\mathrm{Be}(\alpha ,\gamma ){}^{12}\mathrm{C}$] that drive carbon formation. The second reaction occurs through the Hoyle state, a 7.65 MeV excited state in ${}^{12}\mathrm{C}$ with $J^{\pi }=0^{+}$. The rate of the process depends on the radiative width, which can be determined by measuring the branching ratio for electromagnetic decay. Recent measurements by Kibédi et al. conflicted with the adopted value and resulted in a significant increase of nearly 50% in this branching ratio, directly affecting the triple-alpha reaction.

Purpose: This work aims to utilize charged-particle spectroscopy with magnetic selection as a means to accurately measure the total radiative branching ratio (${\mathrm{\Gamma }}_{\mathrm{rad}}/\mathrm{\Gamma }$) of the Hoyle state in ${}^{12}\mathrm{C}$.

Methods: The Hoyle state in ${}^{12}\mathrm{C}$ was populated via ${}^{12}\mathrm{C}(\alpha ,{\alpha }^{\prime }){}^{12}{\mathrm{C}}^{*}$ inelastic scattering. The scattered $\alpha$-particles were detected using a $\mathrm{\Delta }E-E$ telescope, while the recoiled ${}^{12}\mathrm{C}$ ions were identified in a magnetic spectrometer.

Results: A radiative branching ratio value of ${\mathrm{\Gamma }}_{\mathrm{rad}}/\mathrm{\Gamma }\times {10}^4=4.0\pm 0.3\left(\mathrm{stat}.\right)\pm 0.16\left(\mathrm{syst}.\right)$ was obtained.

Conclusions: The radiative branching ratio for the Hoyle state obtained in this work is in agreement with the original adopted value. Our result suggests that the proton-$\gamma -\gamma$ spectroscopy result reported by Kibédi et al. may be excluded.

Figure 1

Summary of ${\mathrm{\Gamma }}_{\mathrm{rad}}/\mathrm{\Gamma }$ measurements from Alburger (1961) [3], Seeger (1963) [4], Hall (1964) [5], Chamberlin (1974) [6], Davids (1975) [7], Mak (1975) [8], Markham (1976) [9], Obst (1976) [10], Kibédi (2020) [2], Tsumura (2021) [12], and this work. The black diamonds and circles represent measurements conducted using charged-particle spectroscopy with and without magnetic selection, respectively, while the white boxes represent measurements employing $\gamma$-particle coincidence methods. The value from Ref. [4] has been excluded from the adopted value by Kelly (2016) [11] as it is considered a statistical outlier.

Figure 2

Schematics of the experimental setup.

Figure 3

Charge state fraction distribution of ${}^{12}\mathrm{C}$ ions leaving the target.

Figure 4

Timing difference between the first PPAC and the DSSD ($T_1-T_{\mathrm{Si}}$) vs excitation energy in ${}^{12}\mathrm{C}$. See the text for details.

Figure 5

Measurement conducted with ${}^{13}\mathrm{C}$ target under the same experimental conditions as for the Hoyle state. (a) Plot of $T_2-T_{\mathrm{Si}}$ vs excitation energy for measurement conducted using the ${}^{13}\mathrm{C}$ target. (b) Excitation energy spectrum obtained from measurement using the ${}^{13}\mathrm{C}$ target. The labels adjacent to each peak indicate their corresponding origins. The black dashed lines outline the energy range for the Hoyle state. The excitation energy values in both figures were calculated using the mass of ${}^{12}\mathrm{C}$.

Figure 6

ToF between the two PPACs vs excitation energy in ${}^{12}\mathrm{C}$. The black polygon represents the cut applied to select ${}^{12}\mathrm{C}$ events.

Figure 7

Excitation-energy spectra of ${}^{12}\mathrm{C}$ for (a) the singles events and (b) the coincidence with ${}^{12}\mathrm{C}$ events in the inelastic $\alpha$ scattering.

Figure 8

Excitation-energy spectra of ${}^{12}\mathrm{C}$ around the Hoyle state for (a) the singles events and (b) the coincidence events in the inelastic $\alpha$ scattering. The thick solid lines represent the fitted Gaussian functions for the $0_2^{+}, 3_1^{-}, 2_2^{+}, 1_1^{-}$ states in ${}^{12}\mathrm{C}$ and the $1_3^{-}$ state in ${}^{16}\mathrm{O}$. The states are labeled near each peak. The gray solid line corresponds to the fitted Gaussian function for the shoulder around $E_x=6$ MeV. The black dash-dotted lines represent the background, and the thin solid line represents the sum of these functions.