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Measurement of 12 C(n,n’) reaction cross section to determine triple-alpha reaction rate in high-density environments
Tatsuya Furuno1,∗ , Takanobu Doi2 , Kanako Himi1 , Takahiro Kawabata1 , Satoshi Adachi1 ,Hidetoshi Akimune3 , Shiyo Enyo2 , Yuki Fujikawa2 , Yuto Hijikata2,4 , Kento Inaba5 , Masatoshi
Itoh6 , Shigeru Kubono4 , Yohei Matsuda3 , Isao Murata7 , Motoki Murata8 , Shintaro Okamoto2 ,Kosuke Sakanashi1 , and Shingo Tamaki7
1

Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
Department of Physics, Kyoto University, Sakyo, Kyoto 606-8502, Japan3
Department of Physics, Konan University, Kobe, Hyogo 658-8501, Japan
4
RIKEN Nishina Center, Wako, Saitama 351-0198, Japan
5
Institute for Advanced Synchrotron Light Source, Quantum Scinence and Technology, Sendai, Miyagi
980-8579, Japan
6
Cyclotron and Radio Isotope Center (CYRIC), Tohoku University, Sendai, Miyagi 980-8578, Japan
7
Division of Sustainable Energy and Environmental Engineering, Osaka University, Suita, Osaka 5650871, Japan
8Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-0047, Japan
2Abstract. The reaction rate of the triple-alpha reaction can be enhanced in hotand dense environments due to the deexcitation of the Hoyle state in 12 C byneutrons. The cross section of the deexcitation should be determined for theenhanced reaction rate. We plan to obtain the cross section by measuring the inverse reaction using a neutron beam around 10 MeV and an active target system.
In the present paper, we report a proof-of-principle experiment using a neutron
beam at 14 MeV. The obtained cross section is consistent with a previous result,demonstrating the validity of our method.

1 Introduction
The triple-alpha reaction is one of the most crucial nucleosynthesis reactions because it isthe doorway reaction from A < 5 nuclei to heavier elements. In this reaction, the groundstate of 12 C nucleus is populated from three alpha particles via the two alpha and three alpharesonance states in 8 Be and 12 C, followed by the gamma decay of the resonance state in 12 C.
The resonance state in 12 C, known as Hoyle state, is located at E x = 7.65 MeV with the spinparity of 0+2 .
Since the triple-alpha reaction proceeds via the Hoyle state, its branching ratio to theground state is directly related to the reaction rate. The probability of the gamma decay isexperimentally determined as (4.16±0.11)×10−4 [1]. Recently, it is pointed out that in hot anddense environments, the branching ratio of the Hoyle state to the ground state can be greatlyenhanced due to the deexcitation scattering with the surrounding nuclei [2]. Because the∗ e-mail: furuno@ne.phys.sci.osaka-u.ac.jp© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative
Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).

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neutrons are not obstructed by the Coulomb barrier, the scattering with the neutrons increases
the reaction rate the most by a factor of about 40 at the density of 106 g/cm3 and temperatureof 109 K.
In order to determine the enhanced reaction rate by the neutrons, it is necessary to measure
the deexcitation cross section of the Hoyle state and neutrons. However, it is almost impossible to perform such an experiment because the life time of the Hoyle state is extremely short
to use as a target. Instead of measuring the direct process, the deexcitation cross section canbe obtained on the basis of the detailed balance principle by measuring the inverse reaction,i.e., the inelastic scattering of the ground state in 12 C and the neutron beam at about 10 MeV.
We will reconstruct the excitation energy of 12 C by detecting the three alpha particles
emitted from the Hoyle state, and calculating the invariant mass. The energy of the alpha particles, however, is extremely small (∼100 keV), thus they cannot be detected with a normal
detector system. In our experiment, the low-energy alpha particles will be detected using anactive target system MAIKo [3]. The MAIKo active target is based on a gaseous time projection chamber (TPC) and capable of recording three-dimensional trajectories of the incident
charged particles. In MAIKo, the detection gas of the TPC plays also as the target gas of thescattering. Since the scattering occurs inside the sensitive volume of the TPC, the detection
threshold is lowered.
In the present article, we report the proof-of-principle experiment using MAIKo to detect
the low-energy alpha particles emitted from the Hoyle state and reconstruct the invariant massof 12 C.

2 Experiment
The experiment was carried out at the intense deuterium-tritium neutron source facility (OKTAVIAN) of Osaka University. The mono-energetic neutron beam at 14 MeV was producedby the DT fusion reaction of a tritium target bombarded by a deuteron beam at 300 keV from a
Cockcroft-Walton accelerator. Figure 1 shows the setup of the experiment. The neutron beam
was collimated by a polyethylene collimator with a diameter of 20 mm installed inside theconcrete wall of 1-m thick. The MAIKo active target was installed just behind the collimator.
The number of the incident neutron beam was monitored with a BC501 liquid scintillator.
The intensity of the neutron beam at MAIKo was approximately 10k cps in average.
The MAIKo TPC was operated with the iso-C4 H10 (10%)+H2 (90%) gas at 100 hPa. The
iso-C4 H10 gas was used as the carbon target and the H2 gas was added to suppress the diffusion of the drift electrons and improve the track reconstruction efficiency. The effective lengthof the target gas was 92.4 mm. When the inelastic scattering of carbon with neutron occurs
and the excited carbon nucleus decay into three alpha particles, the alpha particles ionize theTPC gas. The electrons produced in the ionization drift along the electric field formed by theTPC field cage. The drift electrons are multiplied by a gas electron multiplier. The electrons
are further amplified and detected by a micro pixel chamber (µ-PIC) [4]. The µ-PIC consistsof 256 anode strips and 256 cathode strips with a pitch of 400 µm. The cathode strips are
orthogonal to the anode strips. The sensitive area of the µ-PIC is 102.4 × 102.4 mm2 . Each
strip of the µ-PIC is connected to the readout circuits which record the electron drift time.
The drift time as a function of anode and cathode strip number provides the two-dimensional
projection of the trajectories of the charged particles.

3 Data analysis and results
Figure 2 shows an example of the TPC track of the signal events in which the excited 12 C nucleus decay into three alpha particles. The left and right images show the anode and cathode2EPJ Web of Conferences 260, 11010 (2022)
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neutron beam
BC501
MAIKo

1m

CH2 collimator
deuteron beamtritium target

Figure 1. Experimental setup at OKTAVIAN.

projections, respectively. In addition to the signal events, many background events were acquired during the measurement. The background events consist of the elastic scattering withthe hydrogen or 12 C, and the 12 C+n →13 C*→9 Be+4 He reaction. The signal events can be
distinguished from the background events according to the number of trajectories containedin the TPC images. The signal events contain three trajectories whereas the elastic scattering
events contain only one trajectory and the 13 C* events contain two trajectories of 9 Be and4He.

10

Kinetic energy (MeV)

Cathode image
8

Drift time (µs)

8Drift time (µs)

310Anode image

64642200 50 100 150 200 25000 50 100 150 200 250

Strip number

2.521.5
10.5005 10 15 20 25 30 35 40 45

Recoil angle (deg)Strip number

Figure 2. Example of the TPC track of threealpha decay from 12 C event. The left and rightpanels shows the anode and cathode iamges, respectively.

Figure 3. Scatter plot of the kinetic energy andangle of the recoil 12 C. The solid line represents
the calculated energy and angle for the 0+2 state.

We performed an eye scan analysis to categorize the TPC images according to the numberof trajectories. About 63,000 events were analyzed by 10 eye scanners. For events that were3

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Table 1. Summary of the experimental results.

YNbNtσ (Present)
σ (Previous [7])6 ± 2(stat.)[4.5 ± 0.3(syst.)] × 108
9.2 × 1018 /cm2
0.104 ± 0.014(syst.)
14 ± 6(stat.) ± 2(syst.) mb
8.4 mbcategorized as a candidate of the signal event, the eye scanner recorded the coordinates of thevertex position of three alpha trajectories and the end points of the trajectories in the anodeand cathode images by mouse clickings. The kinetic energy and momentum of each alphaparticle were calculated from the vector between the vertex position and the end point using
a computer program SRIM [5]. The kinetic energy, recoil angle, and excitation energy of the12
C nucleus were calculated with the invariant mass spectroscopy method.
Figure 3 represents the correlation between the reconstructed kinetic energy and recoil
angle of 12 C. The calculated energies and angles for the 0+2 state in 12 C are plotted with thesolid line. The events which lie around the solid line correspond to the inelastic scattering inwhich the 12 C was excited to the 0+2 state.
The detection and analysis efficiency of the inelastic scattering events to the 0+2 state wasestimated by a Monte-Carlo simulation. In the simulation, the inelastic scattering eventswere generated along the beam region. The decay three alpha particles were then generated
from the interaction point. The ionization of the TPC gas by the alpha particles was calculated using SRIM. The electrons due to the ionization were transported towards the µ-PIC
plane taking into account for the drift speed and diffusion of the electrons in the gas. Theanalog signal from the µ-PIC for a single electron was simulated with the computer code
Garfield++ [6]. The arrival time of the electrons at the µ-PIC was folded by the analog
signal for a single electron. The simulated signals were virtually processed to generate theanode and cathode images. The generated images were analyzed by the eye scanner in thesame manner as the experimental data. The detection and analysis efficiency was obtainedby the number of events in which three alpha particles stopped inside the sensitive volumeof the TPC and the eye scanner identified as the signal event, divided by the number of total
generated signal events.
The cross section if the inelastic scattering to the 0+2 state was obtained by σ = Y/(Nb Nt ).
Y, Nb , Nt , and  are the yield of the signal events reconstructed in the analysis, number ofincident neutrons, number of target nuclei for the unit area, and the detection and analysis efficiency, respectively. These values are summarized in Table 1. The cross section determinedby the present measurement is, σ = 14 ± 6(stat.) ± 2(syst.) mb. This cross section is consistent
with the previous one of σ = 8.4 mb reported by Kondo et al. [7], demonstrating the validityof our method using the MAIKo active target.

4 Future perspectives
We are now constructing a larger active target called MAIKo+ that has a sensitive volume of
300 × 300 × 300 mm3 to increase the statistics by 10 times from the present MAIKo. The
MAIKo+ system will be commissioned at OKTAVIAN in 2022 to measure the same reaction
as the present paper. After the commissioning experiment, the physics measurement using
the neutron beam at around 10 MeV will be performed at CYRIC, Tohoku University.

4

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References[1] J. Kelly et al., Nucl. Phys. A 968, 71 (2017)[2] M. Beard et al., Phys. Rev. Lett. 119, 112701 (2017)[3] T. Furuno et al., Nucl. Instrum. Methods Phys. Res. A 908, 215 (2018)[4] A. Ochi et al., Nucl. Instrum. Methods Phys. Res. A 471, 264 (2001)[5] J. Ziegler et al., Nucl. Instrum. Methods Phys. Res. B 268, 1818 (2010)[6] https://garfieldpp.web.cern.ch/garfieldpp/[7] K. Kondo et al., J. Nucl. Sci. Tech. 45, 103 (2008)5