Emissions of Hydrogen Isotopes from the Nuclear Muon Capture Reaction in nat Si

. The energy spectra of protons, deuterons and tritons produced by the nuclear muon capture reaction in nat Si were measured at the M1 beam line of Muon Science Innovative Channel (MuSIC) in Research Center for Nuclear Physics (RCNP) using a counter telescope consisting of a Si detector and a CsI(Tl) scintillation detector. The measured energy spectra were consistent with the previous ones. The experimental energy spectra were compared with theoretical model calculations using the Particle and Heavy Ion Transport code System (PHITS). In PHITS, both the dynamical and statistical processes in the nuclear muon capture reaction are described by the Quantum Molecular Dynamics (QMD) or the modified QMD and the Generalized Evaporation Model (GEM), respectively. The PHITS simulation reproduced generally well the measured proton spectrum at emission energies below 20 MeV, while underestimation was seen at emission energies above 20 MeV. The PHITS simulation underestimates remarkably the measured energy spectra of light complex particles (deuterons, tritons, and alpha particles) in the high energy region.


Introduction
The main threat to electronics at ground level is wellknown as secondary-cosmic-ray-induced soft errors. The soft error is caused by an upset of the memory information due to the energy deposition by energetic cosmic-rays. Among the cosmic-ray species, the muon has recently drawn attention as a new cause of the soft error due to reduction of the critical charge of the static random-access memory. Several previous works [1][2][3][4][5][6] reported that negative muons have much more serious effect on the occurrence of soft errors compared to positive ones because of the emission of light ions (i.e., hydrogen and helium) from the nuclear muon capture (μNC) reaction in silicon nuclei.
Several works were devoted to investigation on the emissions of charged particles from the μNC reaction. Sobottka and Wills conducted a measurement of the energy spectra of the ions from the μNC reaction in silicon [7]. A 3-mm thick Si(Li) detector was irradiated by a muon beam, and the spectrum of emitted light ions and recoiled nuclei in the detector was measured. They estimated the charged-particle emission probability per muon capture of 15±2 %. However, the particle identification (PID) of each emitted ion was not * Corresponding author: s-manabe@aist.go.jp performed in their experiment. Budyashov et al. measured the energy spectra of protons and deuterons in the emission energy range above 15 and 18 MeV, respectively [8]. A 50 mg/cm 2 -thick Si detector and a 2.2-cm thick CsI(Tl) detector were used as a ΔE-E counter telescope. The authors investigated the atomic number dependence of the emission probability of charged particles. Thus, the experimental proton and deuteron spectra in the energy range from 15 to 50 MeV were available prior to the present experiment.
In the present work, we have performed an experiment to accumulate the basic data of the fundamental physical process of muon-induced soft errors, i.e., energy spectra of light ions in the μNC reaction, to improve the simulation accuracy for prediction of muon-induced soft errors. In a lowerenergy region, the emission probability of the light ions is relatively high, which is expected to have a large impact on the occurrence of the soft errors. Thus, the present experiment was conducted to measure the energy spectra of protons, deuterons, and tritons in the emission energy region from 8 to 35 MeV lower than the previous experiment [8]. In addition, validation of the reaction model implemented in Particle and Heavy Ions Transport code System (PHITS) ver. 3.17 [9] was made by comparison of the experimental data with the model calculations.

Experiment
The experiment was performed at the M1 beam line of the MuSIC [10] at the RCNP, Osaka University, Japan. The facility produces pions through the nuclear reaction between a 392-MeV proton beam and a graphite target. The produced pions decay into muons in superconducting solenoid magnets and the muons are transported to the beam exit of the M1 beam line. During the experiment, the average current of the proton beam was 1.1 μA. The average muon momentum was chosen to be 36 MeV/c to maximize the numbers of stopping muons at a target in an experimental setup mentioned below. Figure 1 shows the experimental setup in a vacuum chamber located at the M1 beam exit. Two plastic scintillators (pla. 1 and 2) whose size was 50 mm × 70 mm × 0.5 mm t were used as an incident muon counter. The thickness of pla. 1 and 2 was so thin that the incident muons could pass through the incident muon counter. According to the muon transport simulation with PHITS, the average momentum of the muos after passing through pla. 1 and 2 was estimated to be about 32 MeV/c. The target was mounted at the center of the chamber. Two silicon detectors denoted as tgt. 1 and 2 in Fig. 1 were used as active targets. The sensitive area of each detector was 50 mm × 50 mm, and the thickness was 0.1 mm. The fraction of the muons stopping at the target relative to the muons detected by pla. 1 and pla. 2 was roughly expected to be less than 10%. The two telescopes were mounted in parallel to the target at both upstream and downstream of the target to detect the emitted ions to measure their kinetic energy. The distance between the target and the telescope was 150 mm. The counter telescope consisted of a 0.325-mm thick silicon detector and a 25-mm thick CsI(Tl) detector. The sensitive area of both the detectors was 50 mm × 50 mm. An additional plastic scintillator denoted as 'veto' in Fig. 1 was placed downstream of the target to reject the events that the incident muons pass through the target. The size of the plastic scintillator was 150 mm × 150 mm × 15 mm t .
The scintillation lights of the plastic scintillators and the CsI(Tl) crystals were read through photomultiplier tube and silicon photo diodes, respectively. The signals from the photo diodes and the Si detectors were amplified by preamplifiers. Each output from the preamplifiers and the photomultipliers was divided into two analogue signals. One of the divided signals of all detectors were fed into an analog-to-digital convertor module (A3400 manufactured by NIKI GLASS) after shaping and amplifying by shaping amplifiers. The other divided output signals from Si and CsI(Tl) detectors were processed by a timing filter amplifier (model 474 manufactured by ORTEC) and a constant fraction discriminator (model 934 manufactured by ORTEC), and then fed into a timing-to-digital converter (TDC) module (V1290N manufactured by CAEN). The divided outputs from the plastic scintillators were fed into the TDC module through the discriminators. During the experiment, the coincidence events of the pla.1 and pla.2 were used as the trigger for the data acquisition (DAQ) system. The above DAQ system was controlled by the babirlDAQ program [11]. The average trigger rate was approximately 1000 s -1 . The total beam time was 48 h,    including 26 h irradiation to the silicon target and 7 h irradiation without the target to confirm the background. Figure 2 shows a ΔE-E plot of the telescope 1 for all the events accumulated during the experiment. The separate bands corresponing to protons, deuterons, and tritons were observed in the plot. The energy spectra of those ions were derived after the energy calibration of Si and CsI(Tl) detectors. In total, 1290 protons, 289 deuterons, and 62 tritions were observed in the two telescopes. We examined the time distribution of events in the E silicon detector of telescope 1 with respect to the timing when the incident muon arrived at pla. 1. A negative muon captured by an atom decays or is absorbed by a nucleus with a specific lifetime. The lifetime of the muonic silicon atom is known to be 758 ns [12]. Figure 3 depicts the time distribution of the events from the ΔE detector of the telescope 1. The distribution was fitted with an exponential function. The decay time was found to be 778±30 ns which is consistent with the lifetime of the muons captured on silicon atoms within the uncertainty. Therefore, it was concluded that the telescope successfully measured the ions emitted from the silicon targets and the other background noises did not significantly affect the experimental results. Note that only the data for the telescope 1 are shown here in Figs. 2 and 3, but similar data were obtained for the telescope 2 using the same analysis method.

Comparison with existing experimental data
The data of telescopes 1 and 2 were summed to make a comparison. The present experimental data were normalized to the previous proton data [8] at 17 MeV. The measured spectra are compared to those in [8]. More recently, new experimental data have been published by Edmonds et al. (AlCap Collaboration) in 2022 [13]. Figure 4 shows the energy spectra of protons, deuterons, and tritons measured in the present and previous works. The error bars include only the statistical uncertainty. As shown in Fig. 4, the triton spectrum in the range from 19 MeV to 32 MeV was newly measured in the present experiment. The spectra measured in the present work are smoothly connected to the higher and lower energy region. Moreover, the emission ratio of deuteron and triton to proton generally agreed with that of the previous data. Thus, it was confirmed that the present data are consistent with the previous data.

Comparison with model calculation
When a muon is captured by a nucleus, a proton in the nucleus is converted to a neutron by the following weak interaction: In Monte Carlo simulation with PHITS, a proton in the nucleus is randomly selected and changed to a neutron with the added excitation energy of the nucleus [13]. The time evolution of the highly-excited nucleons is simulated by the quantum molecular dynamics (QMD) model [15]. The sequential evaporation process is described by the generalized evaporation model (GEM) [16]. We have performed a benchmark test of the reaction models implemented in PHITS by comparisons of the measured data with the simulated ones. So far, some studies have been devoted to charged-particle production in neutron-induced nuclear reactions using the QMD plus GEM. In Ref. [17], the QMD was improved by using the surface coalescence model (SCM) to reproduce the experimental results, and the SCM implementation to the QMD (hereafter referred to as modified-QMD, MQMD) led to the enhancement of the production of light complex particles (i.e., deuteron, triton, alpha particle, and 3 He). The agreement with the experimental data was improved by consideration of the surface coalescence process. Therefore, the MQMD plus GEM is also used in the present benchmark test. The values of adjustable parameters used in SCM were the same as in [17].
The simulation was performed with a total of 5 × 10 6 events for nat Si. The muons were stopped uniformly in the 0.1-mm thick silicon to reproduce the experimental condition. Then, the emitted particles (i.e., protons, deuterons, tritons, and alpha particles) from silicon were tallied. The emission probability per the NC reaction was derived by dividing the number of the tallied particles by the capture rate for the silicon nucleus (= 0.66 in the PHITS simulation) and the energy bin width in units of MeV. Figure 5 shows the PHITS simulation results with the experimental data. As for the proton spectrum, the Fig. 4. Comparison of the measured spectra of proton, deuteron, and triton from the μNC reaction on silicon measured in the present and previous works [8,13]. The red, blue, and green symbols denote proton, deuteron, and triton spectra, respectively. The closed circle represents the measured spectra in the present work. The open circle and square are the measured spectra in [13] and [8], respectively. results calculated by the QMD plus GEM and MQMD plus GEM are almost identical. Both the models reproduce the experimental data generally well in the emission energy region below 20 MeV, while the simulation underestimates the experimental data in the higher energy region. For the spectra of light complex particles (LCPs: deuterons, tritons, and alpha particles), the MQMD results in enhancement of the production of LCPs as in the case of neutron reactions. The simulation with MQMD plus GEM reasonably reproduces the deuteron spectrum around 10 MeV. However, the MQMD simulation still underpredicts the emission of all light ions, especially in the relatively higher emission energy region.

Conclusion
We have measured the energy spectra of protons, deuterons, and tritons from the nuclear muon capture (μNC) reaction on nat Si. The measured spectra were compared to those measured in the previous works. The consistency between the present and previous data was confirmed. In addition, the benchmark test of the QMD plus GEM and the MQMD plus GEM implemented in the PHITS code was performed. The test indicated that the MQMD plus GEM provides higher yields of light charged particles compared to the QMD plus GEM due to implementation of the surface coalescence model as in the simulation of neutron-induced nuclear reactions. However, both the models still significantly underestimated the energy spectra of all light ions in the high emission energy region.
As a next step, we plan to measure the energy spectrum of the alpha particles emitted from the μNC reaction in silicon, which is expected to provide predominant influence on the muon-induced soft error occurrence among the secondary ions produced by the μNC reaction [1].

Fig. 5.
Comparison of the measured and simulated energy spectra of proton, deuteron, tritons, and alpha particle from the μNC reaction on silicon. The orange open circle denotes the energy spectrum of alpha particle measured in [13]. The other markers denote the experimental spectra in the same manner as in Fig. 4. The red, blue, orange, and green lines represent the energy spectra of proton, deuteron, alpha particle, and triton simulated by PHITS, respectively. The dashed and solid lines are the simulated spectra with QMD plus GEM and MQMD plus GEM, respectively.