Discussion
5.3 Neutron beam simulation
Cathode hit weighted mean position [mm]
-100 -50 0 50 100
Entry
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Neutron beta decay
Cathode hit weighted mean position [mm]
-100 -50 0 50 100
Entry
0 200 400 600 800 1000 1200 1400 1600 1800 2000 He absorption
3
Fig. 5.3 Weighted mean x position distribution of neutron beta decay (left red histogram) and 3He absorption (right blue histogram) at 600 mT. Both signals are confined in the signal region of±30 mm.
Cathode hit weighted mean position [mm]
-100 -50 0 50 100
Entry
0 2 4 6 8 10 12 14 16 18 20
Neutron-induced background
Fig. 5.4 Weighted mean x position distribution of neutron-induced background at 600 mT. The histogram has an asymmetry distribution because the electrons are shifted −x direction during drift with the Lorentz angle. The Y-axis (Entry) is normalized by beta decay signals.
Figure 5.5 shows the count rate of the remaining neutron-induced γ-ray in the signal region without (dark green) and with (light green) magnetic field by simulation. The remaining background is estimated to be (2.3 ± 3.2)% compared to no magnetic field.
This corresponds to (0.12 ± 0.17)% for the beta decay electron.
5.3 Neutron beam simulation
We should confirm whether we calculate all possible reactions induced by neutron beam injection. Therefore, a full simulation of the neutron beam was performed by shooting a neutron from the upstream of the LiNA detector system. Figure 5.6 shows the clas-sification of neutron-induced events. The most of the neutrons (97%) are transported
Anode pulse height maximum [ch]
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
103
×
Entry [cps]
0 0.05 0.1 0.15 0.2 0.25
−3
×10
Gamma ray source Neutron-induced Gamma Gamma ray source Neutron-induced Gamma
Anode pulse height maximum [ch]
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
103
×
Entry [cps]
−7
10
−6
10
−5
10
−4
10
Gamma ray source Neutron-induced Gamma
Fig. 5.5 Count rate of neutron-induced γ-ray at the signal region without (dark green) and with (light green) magnetic field by the simulation. The left figure is linear scale and the right is log scale. The remaining background is (2.3 ± 3.2)%
compared to no magnetic field.
and absorbed at the beam dump, and only a small fraction of neutrons decay (0.0001%), absorption (0.002%), or scatter (3%). The top two events in Fig. 5.6, the beta decay and
3He absorption, are signals of this experiment. The other events are classified as beta de-cay background, 3He absorption background, or undetected. The reaction AX(n, γ)A+1X indicates that arbitral nucleus AX captures the scattered neutron and emits γ-ray.
This full simulation requires huge calculation cost, hence it takes time to get a sufficient amount of signals. It takes twelve hours to simulate 108 neutrons using one CPU. There-fore, the data set of 1011 neutrons, which corresponds to two-day measurement at BL05, were generated for the analysis. The energy of the neutron is fixed at 7.2 meV, which is the fastest bunch from the SFC. In the following signal selection, only the detectable information is used and the Monte Carlo true information is never used.
The selection of the neutron beta decay signal is the following five cuts. “Time of flight cut” requires that event trigger time is the neutron bunch completely inside the TPC (−400 mm< z <+400 mm). “Weighted meanx position cut” requires that the weighted mean x position of the track is located around the beam axis (−30 mm < x < +30 mm). “Layer cut” requires that no tracks are detected at the upper and lower detection volume. “Low energy cut” requires that total deposit energy exceeds the threshold (> 3 keV) to eliminate 99.99% of the recoiled 13C (see Section 2.5.3). “Time over threshold cut” requires that time width while the waveform is over threshold is shorter than 30 µs.
Figure 5.8 shows the definition of the time over threshold with the typical waveforms of beta decay and 3He absorption by the simulation. Figure 5.9 shows distributions of time over threshold for the two signals.
The selection of the 3He absorption signal is the following three cuts. “Time of flight cut” and “weighted mean x position cut” are the same as the beta decay signal. An
5.3 Neutron beam simulation 85
3He absorption BG Beta decay BG
17O(n,α)14N
12C(n,γ)13C
Neutron
Decay
Scatter Absorption
Transport
3He(n,p)3H
14N(n,p)14C
6Li(n,α)3H
AX(n,γ)A+1X Absorption
Escape
Beta decay signal
Decay
3He(n,p)3H
3He absorption signal
Compton
Undetected Absorption
3He absorption BG
3He absorption BG Undetected Beta decay BG
Beta decay BG Undetected Escape
γ n
n n
e -e
-e
-γ
γ 0.0001%
1.3%
98.7%
0.002%
1.1%
0.1%
n
Fig. 5.6 Neutron-induced event classification. The most of the neutrons are trans-ported and absorbed in the beam dump, some of them decay, absorbed, or scattered.
The reactionAX(n, γ)A+1X indicates arbitral nucleusAX captures the scattered neu-tron and emitsγ-ray.
inversion of “time over threshold cut” requires the time length is longer than 30 µs.
The number of selected signal candidates from the simulation data is 76,611 events for beta decay and 1,915,609 events for 3He absorption. The cut efficiencies were eval-uated using the individual simulation to εβ = (99.90 ± 0.01)% for beta decay and εHe = (100 − 0.01)% for3He absorption. All cut efficiencies are summarized in Table 5.1 together with their errors including the simulation statistics and cut value fluctuation
±5%. The efficiency of “Time of flight cut” is not listed in Table 5.1 because this effi-ciency cancel out for beta decay and 3He absorption in Eq. 2.1. The lost event in εβ is 0.035% for the low energy cut and 0.065% for the layer cut. Some neutrons decay with the emission of a photon in a branching ratio of 1%. If these photons deposit energy at the outside of the signal region, the layer cut rejects these events. The number of background contamination for beta decay candidates is 163 events which correspond to 0.21% and their components are summarized in Table 5.2. All backgrounds are (n, γ) reaction. Some scattered neutrons escape from the gap of6LiF tiles, and they are captured at the printed circuit board or iron shield. The number of admixtured 3He gas is calculated from the
Energy [keV]
0 5 10 15 20 25 30 35 40 45 50
Entry
1 10 102
103
104
105
Carbon neutron capture and Beta decay
Fig. 5.7 Energy deposit of carbon neutron capture and beta decay. The green histogram is 12C neutron capture recoil 1 keV. The red histogram is beta decay energy deposit distribution.
Time [us]
20 25 30 35 40 45 50 55 60 65 70
Pulse Height [ch]
0 500 1000 1500 2000
Time [us]
20 25 30 35 40 45 50 55 60 65 70
Pulse Height [ch]
0 500 1000 1500
2000 Beta decay 3He absorption
Time over threshold
Threshold Threshold
Fig. 5.8 Definition of time over threshold with the typical waveforms of beta decay and3He absorption by the Monte Carlo simulation.
Time over threshold [us]
0 5 10 15 20 25 30 35 40
Entry
1 10 102
103
104
105
106
Time over threshold
Fig. 5.9 Time over threshold distribution. The beta decay (red histogram) is dis-tributed to 28 µs. The3He absorption (blue histogram) is distributed over 30µs.
5.3 Neutron beam simulation 87
Cut name Efficiency [%]
Weighted mean x position 99.991± 0.002
Layer 99.935± 0.003
Low energy 99.965± 0.005
Time over threshold 99.999± 0.001
ALL 99.90 ± 0.01
Table 5.1 Cut efficiency for the beta decay signal. The errors includes the simulation statistic and cut position fluctuation ±5%.
Event Number Location
1H(n, γ)2H 61 Printed circuit board
6Li(n, γ)7Li 13 Beam dump and detector wall
12C(n, γ)13C 13 TPC operation gas
13C(n, γ)14C 26 TPC operation gas
16O(n, γ)17O 18 TPC operation gas
28Si(n, γ)29Si 12 Printed circuit board
56Fe(n, γ)57Fe 18 Iron shield
57Fe(n, γ)58Fe 2 Iron shield
Total 163
Table 5.2 Components of the background contamination by Monte Carlo true.
simulation input value of 100 mPa. The all results in Eq. 2.1 are summarized in Table 5.3 and the obtained neutron lifetime from the simulation data is
τn(MC) = 887.0±3.3 (stat)±1.2 (syst) sec = 887.0±3.5 sec. (5.1) Note that, the neutron lifetime imported in Geant4.9.6.p03 is 885.7 sec that is the PDG average value in 2010. The result is consistent with the Monte Carlo true value.
Value Result Correction Uncertainty
ρ (2.396 ± 0.003) ×1019/m3 0 0.13%
σ0v0 (5333 ± 7) barn × 2200 m/s 0 0.13%
SHe (1915609 ± 1384) event (9578 ± 575) event 0.07%
Sβ (76611 ± 276) event (163 ± 12) event 0.36%
εHe (100 − 0.01)% (0−0.01)% 0.01%
εβ (99.90 ± 0.01)% (+0.10 ±0.01)% 0.01%
Table 5.3 Results and uncertainties for the simulation data analysis.
Fig. 5.10 Neutron lifetime expected accuracy using the LiNA system. The red cross-shaped point is the result from the simulation data analysis.