Investigating $\gamma$-ray decay of excited ${}^{12}\mathrm{C}$ levels with a multifold coincidence analysis

Background: The $\gamma$ decay of ${}^{12}\mathrm{C}$ levels above the particle emission threshold plays a crucial role in the production of ${}^{12}\mathrm{C}$ in astrophysical environments. The Hoyle state is fundamental in the helium-burning phase of red giant stars, while the 9.64-MeV level can be involved in higher temperature explosive environments.

Purpose: The aim of this work was to explore the feasibility of measuring the $\gamma$-decay widths of the 9.64-MeV state. The experiments were performed at Laboratori Nazionali del Sud of INFN (INFN-LNS), in Catania, using $\alpha$ and proton beams impinging on a carbon target.

Methods: The method used consists in the detection of all charged products and $\gamma$ rays emitted in the reaction, in order to strongly reduce the background.

Results: Few events of $\gamma$ decay of the 9.64-MeV level were observed in the reaction $\alpha +{}^{12}\mathrm{C}$. Also the decay yield of the Hoyle state was measured in both the measured reactions $\alpha +{}^{12}\mathrm{C}$ and $p+{}^{12}\mathrm{C}$.

Conclusions: The $\gamma$ decay of the 9.64-MeV level is, inside error bars, in reasonable agreement with the yield recently reported in literature by measuring the ${}^{12}\mathrm{C}$ residue. The observed yield is larger than previously accepted lower limit. Also, the decay yield of the Hoyle state seems larger than the one reported in literature, even if the limited statistics do not allow a definite conclusion.

Figure 1

Fast vs slow identification plot obtained in the reaction $\alpha +{}^{12}\mathrm{C}$ at 64 MeV with GET electronics [35].

Figure 2

(a) $\gamma$-ray energy spectrum for peaks at different energies, measured with the CsI(Tl) of the CHIMERA multidetector using the $\alpha +{}^{12}\mathrm{C}$ reaction. See text for details. (b) $\gamma$-ray energy spectrum, collected using a CsI(Tl) crystal with $p$ $+{}^{12}\mathrm{C}$ reaction.

Figure 3

(a) Identification plot $\mathrm{\Delta }E-E$ measured for the reaction $\alpha +{}^{12}\mathrm{C}$ at ${34}^{\circ }$. The peaks relative to elastic, inelastic, and transfer channels can be observed. (b) Similar plot taken at ${58}^{\circ }$ for the reaction $p$ $+{}^{12}\mathrm{C}$. Protons and few deuterons can be observed.

Figure 4

Mass spectrum obtained through the measurement of the particle time of flight.

Figure 5

Kinematic $Q_K$ spectra in the reaction $p$ $+{}^{12}\mathrm{C}$ at 24 MeV for ${66}^{\circ }$ (filled spectrum) and ${58}^{\circ }$ (blue spectrum multiplied by 5). The observed excited levels are marked in the figure.

Figure 6

Comparison of kinematic $Q$ value measured in single (green filled spectrum) and one $\gamma$-ray coincidence events (red filled spectrum). A background spectrum evaluated for the 9.64-MeV level is also shown (dot yellow histogram).

Figure 7

Kinematic $Q$ value evaluated for events in coincidence with two $\gamma$ rays, with the expected total energy. Dot spectra are the background evaluated by looking at spurious coincidences with elastic peak.

Figure 8

Green filled spectrum is the $Q_{ME}$, obtained by evaluating the missing energy, as discussed in detail in the text. The blue spectrum is the $Q_K$, obtained considering the scattered $\alpha$ beam angle using Eq. (1). No conditions were imposed on this spectrum.

Figure 9

(a) Missing energy $Q$-value spectrum measured in coincidence with one $\gamma$ ray. The energy conservation is applied requiring $\gamma$-ray energy equal to the missing energy of charged particles. (b) $\gamma$-ray energy spectrum for the events of panel (a).

Figure 10

(a) $Q_{ME}$ and (b) total detected $\gamma$-ray energy in two $\gamma$-ray coincidence events (green filled spectrum). The red and blue histograms are background evaluations; see Appendix pp1-s2.

Figure 11

Kinematic plot obtained with the energy of recoiling carbon plotted against the energy of scattered $\alpha$ particles. The green, black, purple, blue, and red lines correspond to the ground, 4.44-, 7.65-, 9.64-, and 12.7-MeV states; (b) events selected in coincidence with two $\gamma$ rays.

Figure 12

Distribution of the relative angle between the two detected $\gamma$-rays from the Hoyle level. Counts were normalized to solid angle and detector efficiency evaluations.

Figure 13

Excitation energy calculated for events in which 3-$\alpha$ particles (filled green spectrum) or an $\alpha$ particle and a ${}^8\mathrm{Be}$ events (blue dots) were detected in coincidence with the scattered beam $\alpha$ particle.

Figure 14

Excitation energy spectrum of the Hoyle state (filled green spectrum) compared to simulations, red histogram with 2% of energy resolution and blue histogram with 5% of energy resolution. The ratio of experimental data and simulations with 2% of energy resolution is also plotted as purple histogram.

Figure 15

(a) Observed angular distribution of scattered $\alpha$ particles populating the Hoyle state (filled green spectrum) compared to filtered simulations assuming 2% energy resolution shown as filled triangles and to not filtered angular distribution shown as blue histogram. The ratio of filtered over not filtered distributions is also plotted, multiplied by 100 as purple histogram showing the efficiency; (b) same as panel (a) but for the 9.64-MeV level.

Figure 16

$Q$ value (filled green histogram) and corresponding $\gamma$-ray energy spectrum (red empty histogram) selected for the 4.44-MeV level in the $\alpha +{}^{12}\mathrm{C}$ reaction.

Figure 17

Missing energy $Q$-value spectra for the reactions $\alpha +{}^{13}\mathrm{C}$ (red histogram) and $\alpha {+}^{12}\mathrm{C}\to {}^3\mathrm{He}+{}^{13}\mathrm{C}$ (blue histogram) compared to the spectrum $\alpha +{}^{12}\mathrm{C}\to {}^4\mathrm{He}+{}^{12}\mathrm{C}$ (green filled histogram), shown also in Fig. 8.