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Influence of light output calibration on neutron energy spectrum unfolding up to 300 MeV using liquid organic scintillator
Nuclear Inst. and Methods in Physics Research B 445 (2019) 26–33
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Influence of light output calibration on neutron energy spectrum unfolding up to 300 MeV using liquid organic scintillator
T
Eunji Leea, , Nobuhiro Shigyoa, Tsuyoshi Kajimotob, Toshiya Sanamic, Naruhiro Matsufujid, Shogo Izumitania, Naoki Tokunagaa, Mamoru Kiyotaa ⁎
a
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan Quantum Energy Applications, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8527, Japan c High Energy Accelerator Research Organization (KEK)/The Graduate University for Advanced Studies (SOKENDAI), Oho, Tsukuba 305-0801, Japan d National Institute of Radiation Sciences, Inage-ku, Chiba 263-8555, Japan b
ARTICLE INFO
ABSTRACT
Keywords: Neutron spectrum Time-of-flight Unfolding Light output Liquid organic scintillator
The influence from uncertainty on light output calibration was studied experimentally for neutron energy spectra up to 300 MeV obtained by an unfolding method using a liquid organic scintillator. The neutrons were generated from the interactions of 100 and 290 MeV/u 28Si ion beams on thick silicon targets at a 75° direction with respect to the beam axis. The light output calibration determined by using Compton edges of γ-rays from 60 Co and 241Am-Be sources was used for the unfolding method. The uncertainty of the calibration points at the Compton edges was estimated to be within 3%. Two calibration lines which connected the 3% larger light output point of the Compton edge of the γ-ray from 60Co and that the 3% lower light output point of that from 241Am-Be and vice versa were examined for influence on variation of calibration line. The unfolded spectra using the two calibration lines were compared with one using the calibration line connecting light output points of Compton edges from both γ-ray sources. The comparison indicates the uncertainty of calibration line influences the neutron light output spectrum within order of several %. The all unfolded spectra generally reproduced one by the time-of-flight (TOF) method in the same experiment. The difference between TOF and unfolded spectra were 17 and 8% for 100 and 290 MeV/u data, at maximum.
1. Introduction Information on energy spectrum and intensity of neutrons is important for shielding design of high-energy accelerators. They enable us to estimate precisely the neutron dose, amount of activity induced in devices and materials placed around the accelerator. They also give an estimation of radiation effects on electronic components installed in an accelerator tunnel and spaceships with considering mechanism and materials [1,2]. In addition to these, the neutron energy spectrum can be used to validate the nuclear reaction model imprinted in particle transport codes based on the Monte Carlo technique, that are used in the design of accelerators and the evaluation of radiation effects mentioned above. Until now, many experiments were performed to measure high-energy neutron spectrum using various techniques, such as Bonner spheres [3–7], time-of-flight (TOF) method with an NE213 liquid scintillator [8–10], and an unfolding method with an NE213 liquid scintillator [11,12]. Bonner spheres have sensitivity from thermal to
⁎
GeV neutron energy range but low energy resolutions. TOF method provides precise neutron energy spectrum from MeV to GeV; however, it is only applicable to neutron source measurement using a beam trigger. Unfolding method using NE213 liquid scintillator delivers neutron energy spectrum from a few to several hundreds of MeV with higher energy resolution. The unfolding method can be used in some situations (both for the source and transmitted neutron measurements) without the beam trigger signal. However, this method has raised arguments in terms of the uncertainty in the unfolding process as it depends on process of unfolding, uncertainty of detector response function, uncertainty of light output calibration and statistical data binning. Several codes have been developed to unfold the neutron energy spectrum from a pulse height distribution [13–16]. In the unfolding process, the neutron energy spectrum is unfolded using the detector response function, which have been obtained through calculation or experiment [17,18]. The unfolded energy spectrum is sensitive to calibration of light output because the pulse height distribution and response function matrix are
Corresponding author. E-mail address: [email protected] (E. Lee).
https://doi.org/10.1016/j.nimb.2019.02.024 Received 19 December 2018; Received in revised form 24 February 2019; Accepted 26 February 2019 Available online 05 March 2019 0168-583X/ © 2019 Elsevier B.V. All rights reserved.
Nuclear Inst. and Methods in Physics Research B 445 (2019) 26–33
E. Lee, et al.
changed by light output calibration. Radioactive γ-ray sources are often used for the light output calibration, i.e., energies from these sources which cover only equivalent to the low light output region. Kajimoto et al. [19] recently proposed the use of cosmic-ray muons for calibration in a relatively high light output region, it may have large uncertainty due to broad peak and dependency of detector structure and orientation. Thus, in most of the case, detector calibration is performed only using the radioactive γ-ray sources. It is necessary to accurately assess the uncertainty associated with calibration using radioactive γ-ray sources for relatively high-energy neutron spectrum. In this study, the influence from the uncertainty of light output calibration at low light output region was examined experimentally in the unfolding method. Four kinds of calibration points were used to obtain calibration lines that were used to generate unfolded neutron spectra. Neutron energy spectra determined by TOF method for reactions of 100 and 290 MeV/u 28Si beam on thick silicon targets were used as a reference in evaluating the unfolded spectra with four different light output calibrations.
Table 1 Ion energy and target thicknesses.
n=
2.1. Experimental setup The experimental procedure was the same as a previous experiment by D. Satoh et al. [8]. Only the outline of the experiment is described in this section. Fig. 1 illustrates the experimental setup at the PH2 beam line of NIRS-HIMAC. Beams extracted from the synchrotron had a pulse width of about 1 s. The pulse had a repetition rate of 0.3 Hz. The beams of Si ions were set at energies of 100 and 290 MeV/u. The average beam intensity was 1 × 105 ions/3.3 s. The beam spot size was less than 10 mm in diameter at the target position. The beam passed through a 0.5-mm-thick NE102A plastic scintillator as a beam pick-up detector that individually counted incident ions. The output signal of this scintillator was used as a stop signal for the TOF measurement. The beam then hit a silicon target. The target had a section size of 50 × 50 mm2 and a density of 2.34 g/cm3. Table 1 shows the thickness of the targets that is enough to stop the beam traveling through the target. To determine the thickness of the targets, the energy loss of the incident beam in the target and its range were calculated using Bethe–Bloch formula. For a particle with speed v, charge z, and energy E, traveling a distance x into a target of electron density of material n and mean excitation potential I, the relativistic version of the formula is given by the following equation:
=
4 nz 2 e2 · 2 · 2 me c 4 0
2
· In
2me c 2 2 2) I ·(1
2
,
(1)
Liquid organic scintillator NE213 (12.7 cm thick and diameter)
ax is
Veto detector NE102A (6 mm thick)
75 Si Target Beam pick up detector NE102A (0.5 mm thick)
25.0 mm 50.0 mm
NA ·Z · , A·Mu
(2)
Fig. 2 shows the simplified block diagram of electronic circuit used in the experiment; it consisted of standard NIM and VME modules. Inverse-TOF method was adopted in this experiment. The electronic circuit was also similar in reference 8. The signals from the NE213 scintillator were divided by a divider (DIV) and sent to two branches. One branch was fed into a constant fraction discriminator (CFD) to generate a 40 ns long logic pulse that was then sent to a coincidence module (Coin (1)). The number of events detected on the neutron detector was counted here and referred to as a real event. If the logic pulse from CFD reached Coin (1) and overlapped either the 300 ns long logic pulse from the beam pick-up detector (B0), the coincidence module generated an output logic pulse that was sent to a Fan-in/out module. The pulse passing through the Fan-in/out module fed into one of gate generators (G.G.4), and then it generated 1.2 µs long gate to count events transferred to the computer. A time-to-digital convertor (TDC) was used to obtain the time difference between signals of the B0 and the NE213 scintillators for TOF measurement. The start signal of the TOF measurement was taken from the NE213 scintillator. The stop signal came from the B0 with a 40 ns width and 380 ns delay, which is coincident at Coin (2) with the logic pulse of the NE213 with 300 ns length. The other outputs of CFD were fed into G.G.5 and G.G.6 to generate total gate and slow gate. Two values obtained by integrating a signal from the NE213 scintillator in the gates were acquired using charge-todigital convertors (QDCs). The total gate, whose width was 200 ns, contained whole components of the signal, and the slow gate with 160 ns length and 40 ns delay was mostly the tail component of the signal. Signals integrated with a specific gate for the NE213, the veto and the beam pick-up detectors, and time difference between the NE213 and the beam pick-up detectors were recorded event-by-event. Neutron and γ-ray events were separated using QDC values of the NE213 scintillator with two gate lengths [20]. The more than 99.9% of coincident events were transferred to the computer in data-acquisition.
2.4 74 m
Be am
100 MeV/u 290 MeV/u
2.2. Electronic circuit
where c is the speed of light and ε0 is the vacuum permittivity, β = v/c, e and me are the electron charge and rest mass, respectively. Here, the electron density of the material can be calculated by equation (2): Beam Dump
Target thickness
where ρ is the density of the material, Z is its atomic number, A is its relative atomic mass, NA is the Avogadro number and Mu is the molar mass constant. The beam dump was located at 700 cm downstream from the target. The beam dump was made of an aluminum plate (30 cm × 30 cm × 15 cm) and iron block (100 cm × 100 cm × 155 cm). Neutrons produced as a result of the nuclear reaction of ions and target nuclei were measured using a 12.7 cm long NE213 liquid organic scintillator (diameter: 12.7 cm). The NE213 scintillator is widely used for neutron measurements due to its good pulse shape discrimination and time resolution. The NE213 scintillator was placed at 2.474 m away from the target and in 75° direction to the beam axis. A veto detector, a 6 mm thick NE102A plastic scintillator, was placed in front of the NE213 scintillator to tag events of charged particles. Background neutrons produced due to room-scattering were measured separately using an iron bar (15 × 15 × 110 cm3), referred as shadow bar, that was placed between the target and the NE213 scintillator. The length of the shadow bar was chosen in order to reduce neutrons to less than 1/1000 based on the Monte Carlo simulation.
2. Experiment
dE dx
Ion energy
Silicon ions
Fig. 1. Experimental setup of the PH2 beam line of HIMAC. 27
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Fig. 2. Schematic of the electric circuit for acquiring measurement data.
3. Data analysis
factor. The geometrical component ΔL was derived from the thickness of the target and the NE213 scintillator, Δt is the uncertainty in the flight time, and t is the TOF. The Δt was the sigma of a Gaussian function, which was used for fitting the prompt γ-ray peak on the TOF spectrum. The Δt was to be 0.5 ns for 100 MeV/u incidence and 0.4 ns for 290 MeV/u incidence, respectively. Fig. 3 shows two results of the energy resolution for 100 and 290 MeV/u Si ion beams. The energy resolution at 100 MeV was about 12%. The minimum bin width of neutron spectra was set to be equal to or greater than the energy resolution. Neutron energy spectra were converted to thick target neutron yield (TTNY) using the following equation:
3.1. Neutron spectrum by TOF method Analysis on the experimental data was also basically the same as the one in the previous experiment [8]. Only the outline of data analysis is described in this section. To determine the number of heavy ions bombarding the target during measurement, the number of signal particle events were obtained according to light output spectrum of the B0 detector. Light output distribution of the veto detector was used to extract uncharged particles, i.e., neutron and γ-ray events. Then, neutron events were separated from γ-ray against each other using a ratio of QDC values with the total and slow gates. The time response is a function of the amplitude and rise time of the input pulse. The time constant at the output of signal became different due to variations in amplitude and rise time of input pulse, and it leads to time walk. For this reason, time walk correction was performed using the scatter plot of TDC value against QDC value with the total gate to improve the time resolution. According to this analysis, the events with the larger QDC value shifted to the lower TDC value. The threshold level distinguishing neutron events from γ-ray events was set to 1.072 MeVee (MeVee: MeV electron equivalent) that was determined through measurement of the Compton edge of γ-ray from a 60 Co source which corresponding to 2.81 MeV in proton energy. The neutron kinetic energy En was determined using the following equation:
1
En = mn c 2 1
(
L ctn
+L
)
TTNY =
Nn (En) , Nion· (En)· · E
where Nn is the number of detected neutrons at the energy En, Nion is the number of incident ions, ε(En) is the neutron detection efficiency obtained by using a computer simulation code program called SCINFULQMD [21], ΔΩ is the solid angle of the detector, and ΔE is the energy
1 ,
2
(3)
2
where mnc is the rest mass of neutron, L is the distance from the center of the target to the center of the NE213 scintillator, and tn-γ is the difference between the flight times of the prompt γ-ray and neutron. The energy resolution of the TOF measurement depends on geometric and time components. It is given by the following equation:
En = ( + 1) En
L L
2
+
t t
2
,
(5)
(4) Fig. 3. Energy resolutions of the TOF measurement.
where ΔEn/En denotes the energy resolution, γ refers to the Lorentz 28
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Fig. 5. QDC distributions of total gate measured by sources.
60
Co and for
241
Am-Be
Counts (log scale)
3%
Fig. 4. QDC distribution of total gate for neutron events from 100-MeV/nucleon (a) and 290-MeV/nucleon (b) silicon ion incidence.
bin width. The SCINFUL-QMD code can simulate the deposition energy imparted by the charged particles produced from reactions between neutrons and nuclei in the scintillator. A scoring region with the same shape and size as the NE213 scintillator was set in the calculation. The TTNY obtained from the background data measured with the shadow bar derived by subtraction of ones from the foreground data measured without the shadow bar.
Maximum, N0 2/3 N0 Half maximum, 1/2 N0 1/3 N0
Compton peak
X0
QDC [ch] Fig. 6. The uncertainty determination of the half maximum position X0 in schematic Compton spectrum.
3.2. Neutron spectrum by unfolding method The same dataset used for the TOF data analysis were processed according to the following procedures to obtain neutron spectrum by unfolding method: 1) extraction of neutron events for a single ion incidence using the same procedure described in section 3.1; 2) calibration of QDC value with the total gate to light output; 3) spectrum unfolding using the RooUnfold package [16] based on an iterative Bayesian algorithm. The QDC distribution of total gate for neutron events was shown in Fig. 4(a) for 100 MeV/u incidence and (b) for 290 MeV/u incidence, respectively. The QDC values were converted into light output in MeVee before the unfolding process. For the channel to light output conversion, four calibration methods described below were available. Fig. 5 shows QDC distributions obtained by measuring γ-rays from 60 Co and 241Am-Be sources for the light output calibration. We can observe Compton edges of γ-rays. The calibration points were given by the QDC value of half height of the Compton edge on the QDC distribution and the energy of Compton edge for the γ-rays [8]. The dashed line in Fig. 5 indicates uncertainties in the determination of Compton edges according to the following procedure. The simplified illustration for the determination of the QDC value is shown in Fig. 6. N0 is the maximum counts around a Compton edge, referred as Compton peak, and X0 is the channel at the half counts to that around the Compton
peak. The number of events in the distribution changes from 2/3N0 to 1/3N0 when the channel changes 3% from X0 in case of γ-rays from 241 Am-Be source in Fig. 5. Thus, we assumed the maximum uncertainty in determination of X0 is 3% in this study. For the sufficient statistics, more than 1000 events at the Compton peak were accumulated to suppress the statistical fluctuation in the determination of the Compton edge position. The Compton edges of γ-rays have energies of approximately 1.253 MeV (average of 1.173 and 1.333 MeV) of 60Co and 4.439 MeV of 241Am-Be sources. The peak of cosmic-ray muons in the natural background was also used as a calibration point of for 20.5 ± 1.0 MeVee of the NE213 with a thickness of 12.7 cm and a diameter of 12.7 cm [19]. The QDC distribution of total gate in the natural background obtained after the experiment is shown in Fig. 7. To reduce statistical fluctuation for finding the peak positions, data for more than 100 events at the peak channel were accumulated for 13 h. The peak position was determined by fitting the spectrum with the Gaussian function. The uncertainty for cosmic-ray muon peak was estimated to be 5.8% from error propagation with independent uncertainty values for light output of muon and peak determination. The uncertainty of light output of muon was 4.9% 29
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Fig. 9. Two-dimensional QDC plot of the total gate and the veto detector in the case of 290 MeV/u Si incidence on a Si thick target. Fig. 7. QDC distribution of total gate measured by cosmic-ray muon sources.
for calibration point when high-energy protons are observed in the dataset. Fig. 9 shows a two-dimensional QDC plot of the total gate and veto detector for the dataset of 290 MeV/u Si ions. The boundary around 4240 ch indicates the maximum energy deposition of protons. The maximum energy deposition shows when the proton range in the scintillator is equal to the length. The maximum energy deposition was calculated to be 124 MeV using the SRIM code [23] for NE213 scintillator with a thickness of 12.7 cm. The light output of the maximum energy deposition became to be 98 MeVee by Equation (6). The QDC value of this event was obtained from the half maximum of the proton edge in the QDC distribution of the total gate. The uncertainty was to be estimated at 6.5% which were derived from standard deviation of the Gaussian function for proton edges spectra. Fig. 10 shows a relationship between the QDC value and light output for the data points obtained using the four methods; Compton edges of γ-rays, peak of cosmic-ray muons, recoil proton edges and maximum energy deposition of protons. The black line (a) was obtained from the two data points for Compton edges of 60Co and 241Am-Be sources. The data point of cosmic-ray muon peak was not used in determination of the black line. As can be seen in Fig. 10, the black line is in agreement with the point of muon within the uncertainty limit. The red line (b) was obtained by connecting 3% larger light output point of the Compton edge of the γ-ray from 60Co and 3% lower light output point of that from 241Am-Be as shown in inner panel of Fig. 10. The blue
[19]. The uncertainty of peak determination was estimated from intrinsic energy resolution to be 3.2% by interpolating widths of Compton edges of the two γ-ray sources and the peak of maximum energy deposition protons at 124 MeV. In addition to these two calibration methods, recoil proton edges can be used as calibration points for this dataset since the TOF data were available. Fig. 8 displays a two-dimensional plot of TDC value against QDC one with the total gate for neutron events of 290 MeV/u Si ion data. The red curved line in the figure indicates recoil proton edges that correspond to the maximum energy of recoil protons for neutron energies. The neutron energies were derived from the TOF method. Thus, the light output, Le (MeVee), for the channel of recoil proton edges can be obtained using the equation formulated by Nakao et al. [22]:
Le = 0. 81Ep
2. 8(1. 0
exp( 0. 20Ep)),
(6)
where Ep is deposition energy of recoil protons. Eighteen points were selected from 1 MeVee to 70 MeVee for the 290 MeV/u Si ions dataset as shown in Fig. 8. The events for maximum energy deposition of protons can be used
Fig. 8. TOF & QDC total gate histogram of neutron events from the thick Si target bombarded by 290-MeV/nucleon.
Fig. 10. Calibration lines and curve of channels vs. light output. 30
Nuclear Inst. and Methods in Physics Research B 445 (2019) 26–33
E. Lee, et al.
Fig. 11. Example of response function. Fig. 12. Thick target neutron yield for 100-MeV/u Si incidence on Si thick target. Black circle and solid lines indicate TOF method, Unfolding method, respectively.
line (c) was obtained in the same manner as the red line using the opposite side of uncertainties. The area surrounded by the (b) and (c) lines is probable area of the calibration line (a) connecting light output points of Compton edges from both γ-ray sources. As shown in the Fig. 10, the difference between the two lines, the uncertainty of calibration, increases as the QDC value increases. The dotted line (d) was obtained using the data points of recoil proton edge and maximum energy deposition. The difference between the black and the dotted lines, the non-linearity of calibration [18], increases as the channel value increases. Fig. 11 shows examples of the response functions obtained using the SCINFUL-QMD code, which was modified by Kajimoto et al. [18]. Neutrons isotropically emitted from a point source 3 m away from the scintillator surface were used as incident neutrons. The neutron energy region between 0 and 1 GeV was divided into 200 steps in a linear interval. The scoring region is same as when calculating the detection efficiency for TOF method. The TTNYs were derived from Eq. (5). The N(Lj) was obtained by unfolding the neutron light output spectrum using the response functions. The neutron energy spectrum Φ(Ei) at i-th energy bin Ei is expressed using a simple equation as follows:
N (Lj ) =
Rij (Ei ),
(7)
i
where N(Lj) is the recorded count in the j-th light output Lj on the neutron light output spectrum. Rij is the response at i-th energy bin and the j-th light output bin. The distribution of N(Lj) is the neutron light output spectrum, which was obtained by analyzing event-by-event data. For the unfolding process, the iterative Bayesian algorithm in the RooUnfold package [16] was used. The response Rij can be represented as a conditional probability P(Lj|Ei). The Bayesian formula is the following equation by conditional probability equation P(Lj|Ei):
P (Lj |Ei ) =
P (Ei |Lj ) P (Ei ) nE i=1
P (Ei |Ej ) P (Ei )
,
Fig. 13. Thick target neutron yield for 290-MeV/u Si incidence on Si thick target. Black circle and solid lines indicate TOF method, Unfolding method, respectively.
4. Results and discussions The experimental TTNYs from 3 to 300 MeV range were obtained by the RooUnfold code and SCINFUL-QMD response for light output spectrum of NE213 scintillator. Figs. 12 and 13 show TTNYs for thick silicon targets bombarded by 100 and 290 MeV/u Si ions. The unfolded TTNYs show only uncertainty originating in the RooUnfold package during unfolding [16]. Black circles denote the results of TOF method. Statistical uncertainties are only shown in the figures. The neutron yield for 290 MeV/u Si ion incidence is larger than the neutron yield for 100 MeV/u. As shown in Fig. 13, a considerable amount of high-energy neutron components above 100 MeV was observed from the data of
(8)
where P(Ei) is the probability of the incident neutron number in the i-th energy bin to that in all energy bins while nE is the number of energy bins. The regularization parameter, i.e., iteration number, was chosen in a way that fulfils the condition χ2 ≈ 0.9 (100 MeV/u TTNY) and 0.1 (290 MeV/u TTNY) for best fit with TOF results. The regularization parameters were 10 (100 MeV/u TTNY) and 50 (290 MeV/u TTNY). 31
Nuclear Inst. and Methods in Physics Research B 445 (2019) 26–33
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the radioisotope sources and background muon became applicable. Further study is required using the same technique but for higher energy neutron data.
Table 2 The neutron yields for 100 MeV/u Si incidence were obtained by integrating the TTNY from 3 to 300 MeV range, and the ratio of each case yield to the TOF yield.
TOF Case Case Case Case
(a) (b) (c) (d)
Yield [n/sr/incidence]
Ratio
6.29 5.45 5.23 5.83 5.42
0.87 0.83 0.93 0.86
E−03 E−03 E−03 E−03 E−03
5. Conclusion The influence from uncertainty of light output calibration was experimentally checked by comparing the thick target neutron yields (TTNYs) using unfolding method and the TOF method. TTNYs were for neutrons from the thick Si targets bombarded with 100 and 290 MeV/u 28 Si ions. The energy range of TTNYs was from 3 to 300 MeV. Four unfolded TTNYs were obtained by using different calibration lines each other. The shapes of unfolded TTNYs with linear calibration line obtained from two γ-ray sources generally agree with the results obtained using the TOF method. When the calibration line was varied from uncertainty for finding the half maximum counts of Compton edges of radioisotope sources, the indicative difference was observed for the neutron component above 100 MeV as well as for neutron component below 7 MeV. The difference shows that the calibration causes the shape change of the neutron light output spectrum due to the influence of the calibration line for the neutron component above 100 MeV as well as below 7 MeV. Thus, unfolded TTNYs with different calibration lines were changed each other. To reduce the effect, calibration point of 20.5 MeVee for cosmic-ray muon peak could be used. Because there was no neutron component above 50 MeVee due to lack of high light output events, a large uncertainty of the light output calibration affects neutron energy spectrum obtained using the unfolding process, especially above the 50 MeVee region. Calibration points from the maximum energy deposition of the proton should be taken into account in calibration curve determination. A further experimental study is required to cover higher energy region.
Table 3 The neutron yields for 290 MeV/u Si incidence were obtained by integrating the TTNY from 3 to 300 MeV range, and the ratio of each case yield to the TOF yield.
TOF Case Case Case Case
(a) (b) (c) (d)
Yield [n/sr/incidence]
Ratio
6.31 6.49 6.66 6.79 6.29
1.03 1.06 1.08 0.99
E−02 E−02 E−02 E−02 E−02
290 MeV/u Si ions. No peak structure was observed in both spectra that looks like the spectrum usually obtained from shielding experiments. Solid lines show the results for unfolded TTNYs with four calibration lines in Fig. 10. The shapes of unfolded TTNYs with four calibration lines generally agree with the results obtained using the TOF method in both figures. (Note: case (a) in Fig. 12 is completely overlapped by case (d) above 20 MeV.) Tables 2 and 3 list the neutron yields obtained by integrating the TTNYs from 3 to 300 MeV range, and the ratio of each case yield to one by the TOF method for 100 and 290 MeV/u Si ions, respectively. The difference among integrated values for different calibrations was within 6%. The difference between TOF and unfolded results were 17 and 8% for 100 and 290 MeV/u data, at maximum. It indicates uncertainty of calibration affects neutron yield within order of several %. As shown in Fig. 13, the differences among unfolded TTNYs with different calibration curves became larger in the energy region above 100 MeV. The differences came from a large difference of (b) and (c) calibration in a relatively high light output region. In the inner panel of Fig. 10, the red line (b) and blue line (c) cross each other at the intersection of 165 ch. In the region below 165 ch, the calibration line of (b) is lower than that of (c). Inversely, in the higher region above the channel, the calibration line of (b) is upper than that of (c). This phenomenon has been reflected in unfolded TTNYs. As can be seen from the blue line in Fig. 13, a significant decrease in events above 100 MeV region was compensated by an increase of less than 7 MeV. This shows that the difference of the calibration line influences the neutron light output spectrum. It can be seen conspicuously both in the lowest and the highest regions. In this study, the linear calibration line obtained from only the radioisotope sources with the RooUnfold code and SCINFUL-QMD response gives reasonable neutron energy spectrum below 300 MeV while taking into consideration of the uncertainty in the calibration data. Although the uncertainty in the low light output region is less than 3%, the uncertainty in the high light output region could be larger than that as shown in Fig. 10. Thus, the deviation of the neutron spectrum in Fig. 13 is therefore larger in the high-energy region. In the present data analysis, the light output corresponding to the neutron component was up to about 50 MeVee. When the region of light output is lower than 50 MeVee, the dotted line (d) from recoil proton edges follows a straight line (a) as shown in Fig. 10. Since the relationship between the channel and light output is proportional below the 50 MeVee region, the linear calibration line determined from only
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E. Lee, et al. facility, Nucl. Instrum. Methods Phys. Res., Sect. B 266 (2008) 93–106. [12] T. Kajimoto, T. Sanami, N. Nakao, et al., Reproduction of neutron fluence by unfolding method with an NE213 scintillator, Nucl. Instr. Meth. Phys. Res., Sect. A 906 (2018) 141–149. [13] W.N. McElroy, S. Berg, A computer-automated iterative method for neutron flux spectra determination by foil activation, Vol. II: SAND II (Spectrum Analysis by Neutron Detectors II) and associated codes, AFWL, Technical Report AFWL-TR-6741, 1967. [14] R.H. Johnson, D.T. Ingersoll, B.W. Wehring, et al., NE-213 neutron spectrometry system for measurement from 1.0 to 20 MeV, Nucl. Instr. Meth. 145 (1977) 337–346. [15] M. Reginatto, The ‘‘multi-channel’’ Unfolding Programs in the UMG Package, UMG Package Version 3.3, Physikalisch Technische Bundesanstalt (PTB), 2003. [16] T. Adye, Unfolding algorithms and tests using RooUnfold, Proceedings of the PHYSTAT 2011 Workshop on Statistical Issues Related to Discovery Claims in Search Experiments and Unfolding, 2011, pp. 313–318. [17] D. Satoh, T. Sato, A. Endo, et al., J. Nucl. Sci. Technol. 43 (2006) 714.
[18] T. Kajimoto, N. Shigyo, T. Sanami, et al., Measurement of absolute response functions and detection efficiencies of an NE213 scintillator up to 600 MeV, Nucl. Instr. Meth. Phys. Res., Sect. A 665 (2011) 80–89. [19] T. Kajimoto, K. Tanaka, S. Endo, et al., Light output due to cosmic-ray muons for an EJ301 scintillator of 12.7 cm in diameter and length, Nucl. Instr. Meth. Phys. Res., Sect. A (2018) 53–57. [20] D. Satoh, T. Kajimoto, N. Shigyo, et al., Distributions of neutron yields and doses around a water phantom bombarded with 290-MeV/nucleon and 430-MeV/nucleon carbon ions, Nucl. Instr. Meth. Phys. Res., Sect. B 387 (2016) 10–19. [21] D. Satoh, S. Kunieda, Y. Iwamoto, et al., Development of SCINFUL-QMD code to calculate the neutron detection efficiencies for liquid organic scintillator up to 3 GeV, J. Nucl. Sci. Technol. 39 (Supp. 2) (2002) 657–660. [22] N. Nakao, T. Nakamura, M. Baba, et al., Measurements of response function of organic liquid scintillator for neutron energy range up to 135 MeV, Nucl. Instr.. Meth. Phys. Res., Sect. A 362 (1995) 454–465. [23] J.F. Ziegler, M.D. Ziegler, J.P. Biersack, SRIM–The stopping and range of ions in matter, Nucl. Instr. Meth. Phys. Res. Sect. B 268 (2010) (2010) 1818–1823.
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Influence of light output calibration on neutron energy spectrum unfolding up to 300 MeV using liquid organic scintillator
T
Eunji Leea, , Nobuhiro Shigyoa, Tsuyoshi Kajimotob, Toshiya Sanamic, Naruhiro Matsufujid, Shogo Izumitania, Naoki Tokunagaa, Mamoru Kiyotaa ⁎
a
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan Quantum Energy Applications, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8527, Japan c High Energy Accelerator Research Organization (KEK)/The Graduate University for Advanced Studies (SOKENDAI), Oho, Tsukuba 305-0801, Japan d National Institute of Radiation Sciences, Inage-ku, Chiba 263-8555, Japan b
ARTICLE INFO
ABSTRACT
Keywords: Neutron spectrum Time-of-flight Unfolding Light output Liquid organic scintillator
The influence from uncertainty on light output calibration was studied experimentally for neutron energy spectra up to 300 MeV obtained by an unfolding method using a liquid organic scintillator. The neutrons were generated from the interactions of 100 and 290 MeV/u 28Si ion beams on thick silicon targets at a 75° direction with respect to the beam axis. The light output calibration determined by using Compton edges of γ-rays from 60 Co and 241Am-Be sources was used for the unfolding method. The uncertainty of the calibration points at the Compton edges was estimated to be within 3%. Two calibration lines which connected the 3% larger light output point of the Compton edge of the γ-ray from 60Co and that the 3% lower light output point of that from 241Am-Be and vice versa were examined for influence on variation of calibration line. The unfolded spectra using the two calibration lines were compared with one using the calibration line connecting light output points of Compton edges from both γ-ray sources. The comparison indicates the uncertainty of calibration line influences the neutron light output spectrum within order of several %. The all unfolded spectra generally reproduced one by the time-of-flight (TOF) method in the same experiment. The difference between TOF and unfolded spectra were 17 and 8% for 100 and 290 MeV/u data, at maximum.
1. Introduction Information on energy spectrum and intensity of neutrons is important for shielding design of high-energy accelerators. They enable us to estimate precisely the neutron dose, amount of activity induced in devices and materials placed around the accelerator. They also give an estimation of radiation effects on electronic components installed in an accelerator tunnel and spaceships with considering mechanism and materials [1,2]. In addition to these, the neutron energy spectrum can be used to validate the nuclear reaction model imprinted in particle transport codes based on the Monte Carlo technique, that are used in the design of accelerators and the evaluation of radiation effects mentioned above. Until now, many experiments were performed to measure high-energy neutron spectrum using various techniques, such as Bonner spheres [3–7], time-of-flight (TOF) method with an NE213 liquid scintillator [8–10], and an unfolding method with an NE213 liquid scintillator [11,12]. Bonner spheres have sensitivity from thermal to
⁎
GeV neutron energy range but low energy resolutions. TOF method provides precise neutron energy spectrum from MeV to GeV; however, it is only applicable to neutron source measurement using a beam trigger. Unfolding method using NE213 liquid scintillator delivers neutron energy spectrum from a few to several hundreds of MeV with higher energy resolution. The unfolding method can be used in some situations (both for the source and transmitted neutron measurements) without the beam trigger signal. However, this method has raised arguments in terms of the uncertainty in the unfolding process as it depends on process of unfolding, uncertainty of detector response function, uncertainty of light output calibration and statistical data binning. Several codes have been developed to unfold the neutron energy spectrum from a pulse height distribution [13–16]. In the unfolding process, the neutron energy spectrum is unfolded using the detector response function, which have been obtained through calculation or experiment [17,18]. The unfolded energy spectrum is sensitive to calibration of light output because the pulse height distribution and response function matrix are
Corresponding author. E-mail address: [email protected] (E. Lee).
https://doi.org/10.1016/j.nimb.2019.02.024 Received 19 December 2018; Received in revised form 24 February 2019; Accepted 26 February 2019 Available online 05 March 2019 0168-583X/ © 2019 Elsevier B.V. All rights reserved.
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changed by light output calibration. Radioactive γ-ray sources are often used for the light output calibration, i.e., energies from these sources which cover only equivalent to the low light output region. Kajimoto et al. [19] recently proposed the use of cosmic-ray muons for calibration in a relatively high light output region, it may have large uncertainty due to broad peak and dependency of detector structure and orientation. Thus, in most of the case, detector calibration is performed only using the radioactive γ-ray sources. It is necessary to accurately assess the uncertainty associated with calibration using radioactive γ-ray sources for relatively high-energy neutron spectrum. In this study, the influence from the uncertainty of light output calibration at low light output region was examined experimentally in the unfolding method. Four kinds of calibration points were used to obtain calibration lines that were used to generate unfolded neutron spectra. Neutron energy spectra determined by TOF method for reactions of 100 and 290 MeV/u 28Si beam on thick silicon targets were used as a reference in evaluating the unfolded spectra with four different light output calibrations.
Table 1 Ion energy and target thicknesses.
n=
2.1. Experimental setup The experimental procedure was the same as a previous experiment by D. Satoh et al. [8]. Only the outline of the experiment is described in this section. Fig. 1 illustrates the experimental setup at the PH2 beam line of NIRS-HIMAC. Beams extracted from the synchrotron had a pulse width of about 1 s. The pulse had a repetition rate of 0.3 Hz. The beams of Si ions were set at energies of 100 and 290 MeV/u. The average beam intensity was 1 × 105 ions/3.3 s. The beam spot size was less than 10 mm in diameter at the target position. The beam passed through a 0.5-mm-thick NE102A plastic scintillator as a beam pick-up detector that individually counted incident ions. The output signal of this scintillator was used as a stop signal for the TOF measurement. The beam then hit a silicon target. The target had a section size of 50 × 50 mm2 and a density of 2.34 g/cm3. Table 1 shows the thickness of the targets that is enough to stop the beam traveling through the target. To determine the thickness of the targets, the energy loss of the incident beam in the target and its range were calculated using Bethe–Bloch formula. For a particle with speed v, charge z, and energy E, traveling a distance x into a target of electron density of material n and mean excitation potential I, the relativistic version of the formula is given by the following equation:
=
4 nz 2 e2 · 2 · 2 me c 4 0
2
· In
2me c 2 2 2) I ·(1
2
,
(1)
Liquid organic scintillator NE213 (12.7 cm thick and diameter)
ax is
Veto detector NE102A (6 mm thick)
75 Si Target Beam pick up detector NE102A (0.5 mm thick)
25.0 mm 50.0 mm
NA ·Z · , A·Mu
(2)
Fig. 2 shows the simplified block diagram of electronic circuit used in the experiment; it consisted of standard NIM and VME modules. Inverse-TOF method was adopted in this experiment. The electronic circuit was also similar in reference 8. The signals from the NE213 scintillator were divided by a divider (DIV) and sent to two branches. One branch was fed into a constant fraction discriminator (CFD) to generate a 40 ns long logic pulse that was then sent to a coincidence module (Coin (1)). The number of events detected on the neutron detector was counted here and referred to as a real event. If the logic pulse from CFD reached Coin (1) and overlapped either the 300 ns long logic pulse from the beam pick-up detector (B0), the coincidence module generated an output logic pulse that was sent to a Fan-in/out module. The pulse passing through the Fan-in/out module fed into one of gate generators (G.G.4), and then it generated 1.2 µs long gate to count events transferred to the computer. A time-to-digital convertor (TDC) was used to obtain the time difference between signals of the B0 and the NE213 scintillators for TOF measurement. The start signal of the TOF measurement was taken from the NE213 scintillator. The stop signal came from the B0 with a 40 ns width and 380 ns delay, which is coincident at Coin (2) with the logic pulse of the NE213 with 300 ns length. The other outputs of CFD were fed into G.G.5 and G.G.6 to generate total gate and slow gate. Two values obtained by integrating a signal from the NE213 scintillator in the gates were acquired using charge-todigital convertors (QDCs). The total gate, whose width was 200 ns, contained whole components of the signal, and the slow gate with 160 ns length and 40 ns delay was mostly the tail component of the signal. Signals integrated with a specific gate for the NE213, the veto and the beam pick-up detectors, and time difference between the NE213 and the beam pick-up detectors were recorded event-by-event. Neutron and γ-ray events were separated using QDC values of the NE213 scintillator with two gate lengths [20]. The more than 99.9% of coincident events were transferred to the computer in data-acquisition.
2.4 74 m
Be am
100 MeV/u 290 MeV/u
2.2. Electronic circuit
where c is the speed of light and ε0 is the vacuum permittivity, β = v/c, e and me are the electron charge and rest mass, respectively. Here, the electron density of the material can be calculated by equation (2): Beam Dump
Target thickness
where ρ is the density of the material, Z is its atomic number, A is its relative atomic mass, NA is the Avogadro number and Mu is the molar mass constant. The beam dump was located at 700 cm downstream from the target. The beam dump was made of an aluminum plate (30 cm × 30 cm × 15 cm) and iron block (100 cm × 100 cm × 155 cm). Neutrons produced as a result of the nuclear reaction of ions and target nuclei were measured using a 12.7 cm long NE213 liquid organic scintillator (diameter: 12.7 cm). The NE213 scintillator is widely used for neutron measurements due to its good pulse shape discrimination and time resolution. The NE213 scintillator was placed at 2.474 m away from the target and in 75° direction to the beam axis. A veto detector, a 6 mm thick NE102A plastic scintillator, was placed in front of the NE213 scintillator to tag events of charged particles. Background neutrons produced due to room-scattering were measured separately using an iron bar (15 × 15 × 110 cm3), referred as shadow bar, that was placed between the target and the NE213 scintillator. The length of the shadow bar was chosen in order to reduce neutrons to less than 1/1000 based on the Monte Carlo simulation.
2. Experiment
dE dx
Ion energy
Silicon ions
Fig. 1. Experimental setup of the PH2 beam line of HIMAC. 27
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Fig. 2. Schematic of the electric circuit for acquiring measurement data.
3. Data analysis
factor. The geometrical component ΔL was derived from the thickness of the target and the NE213 scintillator, Δt is the uncertainty in the flight time, and t is the TOF. The Δt was the sigma of a Gaussian function, which was used for fitting the prompt γ-ray peak on the TOF spectrum. The Δt was to be 0.5 ns for 100 MeV/u incidence and 0.4 ns for 290 MeV/u incidence, respectively. Fig. 3 shows two results of the energy resolution for 100 and 290 MeV/u Si ion beams. The energy resolution at 100 MeV was about 12%. The minimum bin width of neutron spectra was set to be equal to or greater than the energy resolution. Neutron energy spectra were converted to thick target neutron yield (TTNY) using the following equation:
3.1. Neutron spectrum by TOF method Analysis on the experimental data was also basically the same as the one in the previous experiment [8]. Only the outline of data analysis is described in this section. To determine the number of heavy ions bombarding the target during measurement, the number of signal particle events were obtained according to light output spectrum of the B0 detector. Light output distribution of the veto detector was used to extract uncharged particles, i.e., neutron and γ-ray events. Then, neutron events were separated from γ-ray against each other using a ratio of QDC values with the total and slow gates. The time response is a function of the amplitude and rise time of the input pulse. The time constant at the output of signal became different due to variations in amplitude and rise time of input pulse, and it leads to time walk. For this reason, time walk correction was performed using the scatter plot of TDC value against QDC value with the total gate to improve the time resolution. According to this analysis, the events with the larger QDC value shifted to the lower TDC value. The threshold level distinguishing neutron events from γ-ray events was set to 1.072 MeVee (MeVee: MeV electron equivalent) that was determined through measurement of the Compton edge of γ-ray from a 60 Co source which corresponding to 2.81 MeV in proton energy. The neutron kinetic energy En was determined using the following equation:
1
En = mn c 2 1
(
L ctn
+L
)
TTNY =
Nn (En) , Nion· (En)· · E
where Nn is the number of detected neutrons at the energy En, Nion is the number of incident ions, ε(En) is the neutron detection efficiency obtained by using a computer simulation code program called SCINFULQMD [21], ΔΩ is the solid angle of the detector, and ΔE is the energy
1 ,
2
(3)
2
where mnc is the rest mass of neutron, L is the distance from the center of the target to the center of the NE213 scintillator, and tn-γ is the difference between the flight times of the prompt γ-ray and neutron. The energy resolution of the TOF measurement depends on geometric and time components. It is given by the following equation:
En = ( + 1) En
L L
2
+
t t
2
,
(5)
(4) Fig. 3. Energy resolutions of the TOF measurement.
where ΔEn/En denotes the energy resolution, γ refers to the Lorentz 28
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Fig. 5. QDC distributions of total gate measured by sources.
60
Co and for
241
Am-Be
Counts (log scale)
3%
Fig. 4. QDC distribution of total gate for neutron events from 100-MeV/nucleon (a) and 290-MeV/nucleon (b) silicon ion incidence.
bin width. The SCINFUL-QMD code can simulate the deposition energy imparted by the charged particles produced from reactions between neutrons and nuclei in the scintillator. A scoring region with the same shape and size as the NE213 scintillator was set in the calculation. The TTNY obtained from the background data measured with the shadow bar derived by subtraction of ones from the foreground data measured without the shadow bar.
Maximum, N0 2/3 N0 Half maximum, 1/2 N0 1/3 N0
Compton peak
X0
QDC [ch] Fig. 6. The uncertainty determination of the half maximum position X0 in schematic Compton spectrum.
3.2. Neutron spectrum by unfolding method The same dataset used for the TOF data analysis were processed according to the following procedures to obtain neutron spectrum by unfolding method: 1) extraction of neutron events for a single ion incidence using the same procedure described in section 3.1; 2) calibration of QDC value with the total gate to light output; 3) spectrum unfolding using the RooUnfold package [16] based on an iterative Bayesian algorithm. The QDC distribution of total gate for neutron events was shown in Fig. 4(a) for 100 MeV/u incidence and (b) for 290 MeV/u incidence, respectively. The QDC values were converted into light output in MeVee before the unfolding process. For the channel to light output conversion, four calibration methods described below were available. Fig. 5 shows QDC distributions obtained by measuring γ-rays from 60 Co and 241Am-Be sources for the light output calibration. We can observe Compton edges of γ-rays. The calibration points were given by the QDC value of half height of the Compton edge on the QDC distribution and the energy of Compton edge for the γ-rays [8]. The dashed line in Fig. 5 indicates uncertainties in the determination of Compton edges according to the following procedure. The simplified illustration for the determination of the QDC value is shown in Fig. 6. N0 is the maximum counts around a Compton edge, referred as Compton peak, and X0 is the channel at the half counts to that around the Compton
peak. The number of events in the distribution changes from 2/3N0 to 1/3N0 when the channel changes 3% from X0 in case of γ-rays from 241 Am-Be source in Fig. 5. Thus, we assumed the maximum uncertainty in determination of X0 is 3% in this study. For the sufficient statistics, more than 1000 events at the Compton peak were accumulated to suppress the statistical fluctuation in the determination of the Compton edge position. The Compton edges of γ-rays have energies of approximately 1.253 MeV (average of 1.173 and 1.333 MeV) of 60Co and 4.439 MeV of 241Am-Be sources. The peak of cosmic-ray muons in the natural background was also used as a calibration point of for 20.5 ± 1.0 MeVee of the NE213 with a thickness of 12.7 cm and a diameter of 12.7 cm [19]. The QDC distribution of total gate in the natural background obtained after the experiment is shown in Fig. 7. To reduce statistical fluctuation for finding the peak positions, data for more than 100 events at the peak channel were accumulated for 13 h. The peak position was determined by fitting the spectrum with the Gaussian function. The uncertainty for cosmic-ray muon peak was estimated to be 5.8% from error propagation with independent uncertainty values for light output of muon and peak determination. The uncertainty of light output of muon was 4.9% 29
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Fig. 9. Two-dimensional QDC plot of the total gate and the veto detector in the case of 290 MeV/u Si incidence on a Si thick target. Fig. 7. QDC distribution of total gate measured by cosmic-ray muon sources.
for calibration point when high-energy protons are observed in the dataset. Fig. 9 shows a two-dimensional QDC plot of the total gate and veto detector for the dataset of 290 MeV/u Si ions. The boundary around 4240 ch indicates the maximum energy deposition of protons. The maximum energy deposition shows when the proton range in the scintillator is equal to the length. The maximum energy deposition was calculated to be 124 MeV using the SRIM code [23] for NE213 scintillator with a thickness of 12.7 cm. The light output of the maximum energy deposition became to be 98 MeVee by Equation (6). The QDC value of this event was obtained from the half maximum of the proton edge in the QDC distribution of the total gate. The uncertainty was to be estimated at 6.5% which were derived from standard deviation of the Gaussian function for proton edges spectra. Fig. 10 shows a relationship between the QDC value and light output for the data points obtained using the four methods; Compton edges of γ-rays, peak of cosmic-ray muons, recoil proton edges and maximum energy deposition of protons. The black line (a) was obtained from the two data points for Compton edges of 60Co and 241Am-Be sources. The data point of cosmic-ray muon peak was not used in determination of the black line. As can be seen in Fig. 10, the black line is in agreement with the point of muon within the uncertainty limit. The red line (b) was obtained by connecting 3% larger light output point of the Compton edge of the γ-ray from 60Co and 3% lower light output point of that from 241Am-Be as shown in inner panel of Fig. 10. The blue
[19]. The uncertainty of peak determination was estimated from intrinsic energy resolution to be 3.2% by interpolating widths of Compton edges of the two γ-ray sources and the peak of maximum energy deposition protons at 124 MeV. In addition to these two calibration methods, recoil proton edges can be used as calibration points for this dataset since the TOF data were available. Fig. 8 displays a two-dimensional plot of TDC value against QDC one with the total gate for neutron events of 290 MeV/u Si ion data. The red curved line in the figure indicates recoil proton edges that correspond to the maximum energy of recoil protons for neutron energies. The neutron energies were derived from the TOF method. Thus, the light output, Le (MeVee), for the channel of recoil proton edges can be obtained using the equation formulated by Nakao et al. [22]:
Le = 0. 81Ep
2. 8(1. 0
exp( 0. 20Ep)),
(6)
where Ep is deposition energy of recoil protons. Eighteen points were selected from 1 MeVee to 70 MeVee for the 290 MeV/u Si ions dataset as shown in Fig. 8. The events for maximum energy deposition of protons can be used
Fig. 8. TOF & QDC total gate histogram of neutron events from the thick Si target bombarded by 290-MeV/nucleon.
Fig. 10. Calibration lines and curve of channels vs. light output. 30
Nuclear Inst. and Methods in Physics Research B 445 (2019) 26–33
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Fig. 11. Example of response function. Fig. 12. Thick target neutron yield for 100-MeV/u Si incidence on Si thick target. Black circle and solid lines indicate TOF method, Unfolding method, respectively.
line (c) was obtained in the same manner as the red line using the opposite side of uncertainties. The area surrounded by the (b) and (c) lines is probable area of the calibration line (a) connecting light output points of Compton edges from both γ-ray sources. As shown in the Fig. 10, the difference between the two lines, the uncertainty of calibration, increases as the QDC value increases. The dotted line (d) was obtained using the data points of recoil proton edge and maximum energy deposition. The difference between the black and the dotted lines, the non-linearity of calibration [18], increases as the channel value increases. Fig. 11 shows examples of the response functions obtained using the SCINFUL-QMD code, which was modified by Kajimoto et al. [18]. Neutrons isotropically emitted from a point source 3 m away from the scintillator surface were used as incident neutrons. The neutron energy region between 0 and 1 GeV was divided into 200 steps in a linear interval. The scoring region is same as when calculating the detection efficiency for TOF method. The TTNYs were derived from Eq. (5). The N(Lj) was obtained by unfolding the neutron light output spectrum using the response functions. The neutron energy spectrum Φ(Ei) at i-th energy bin Ei is expressed using a simple equation as follows:
N (Lj ) =
Rij (Ei ),
(7)
i
where N(Lj) is the recorded count in the j-th light output Lj on the neutron light output spectrum. Rij is the response at i-th energy bin and the j-th light output bin. The distribution of N(Lj) is the neutron light output spectrum, which was obtained by analyzing event-by-event data. For the unfolding process, the iterative Bayesian algorithm in the RooUnfold package [16] was used. The response Rij can be represented as a conditional probability P(Lj|Ei). The Bayesian formula is the following equation by conditional probability equation P(Lj|Ei):
P (Lj |Ei ) =
P (Ei |Lj ) P (Ei ) nE i=1
P (Ei |Ej ) P (Ei )
,
Fig. 13. Thick target neutron yield for 290-MeV/u Si incidence on Si thick target. Black circle and solid lines indicate TOF method, Unfolding method, respectively.
4. Results and discussions The experimental TTNYs from 3 to 300 MeV range were obtained by the RooUnfold code and SCINFUL-QMD response for light output spectrum of NE213 scintillator. Figs. 12 and 13 show TTNYs for thick silicon targets bombarded by 100 and 290 MeV/u Si ions. The unfolded TTNYs show only uncertainty originating in the RooUnfold package during unfolding [16]. Black circles denote the results of TOF method. Statistical uncertainties are only shown in the figures. The neutron yield for 290 MeV/u Si ion incidence is larger than the neutron yield for 100 MeV/u. As shown in Fig. 13, a considerable amount of high-energy neutron components above 100 MeV was observed from the data of
(8)
where P(Ei) is the probability of the incident neutron number in the i-th energy bin to that in all energy bins while nE is the number of energy bins. The regularization parameter, i.e., iteration number, was chosen in a way that fulfils the condition χ2 ≈ 0.9 (100 MeV/u TTNY) and 0.1 (290 MeV/u TTNY) for best fit with TOF results. The regularization parameters were 10 (100 MeV/u TTNY) and 50 (290 MeV/u TTNY). 31
Nuclear Inst. and Methods in Physics Research B 445 (2019) 26–33
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the radioisotope sources and background muon became applicable. Further study is required using the same technique but for higher energy neutron data.
Table 2 The neutron yields for 100 MeV/u Si incidence were obtained by integrating the TTNY from 3 to 300 MeV range, and the ratio of each case yield to the TOF yield.
TOF Case Case Case Case
(a) (b) (c) (d)
Yield [n/sr/incidence]
Ratio
6.29 5.45 5.23 5.83 5.42
0.87 0.83 0.93 0.86
E−03 E−03 E−03 E−03 E−03
5. Conclusion The influence from uncertainty of light output calibration was experimentally checked by comparing the thick target neutron yields (TTNYs) using unfolding method and the TOF method. TTNYs were for neutrons from the thick Si targets bombarded with 100 and 290 MeV/u 28 Si ions. The energy range of TTNYs was from 3 to 300 MeV. Four unfolded TTNYs were obtained by using different calibration lines each other. The shapes of unfolded TTNYs with linear calibration line obtained from two γ-ray sources generally agree with the results obtained using the TOF method. When the calibration line was varied from uncertainty for finding the half maximum counts of Compton edges of radioisotope sources, the indicative difference was observed for the neutron component above 100 MeV as well as for neutron component below 7 MeV. The difference shows that the calibration causes the shape change of the neutron light output spectrum due to the influence of the calibration line for the neutron component above 100 MeV as well as below 7 MeV. Thus, unfolded TTNYs with different calibration lines were changed each other. To reduce the effect, calibration point of 20.5 MeVee for cosmic-ray muon peak could be used. Because there was no neutron component above 50 MeVee due to lack of high light output events, a large uncertainty of the light output calibration affects neutron energy spectrum obtained using the unfolding process, especially above the 50 MeVee region. Calibration points from the maximum energy deposition of the proton should be taken into account in calibration curve determination. A further experimental study is required to cover higher energy region.
Table 3 The neutron yields for 290 MeV/u Si incidence were obtained by integrating the TTNY from 3 to 300 MeV range, and the ratio of each case yield to the TOF yield.
TOF Case Case Case Case
(a) (b) (c) (d)
Yield [n/sr/incidence]
Ratio
6.31 6.49 6.66 6.79 6.29
1.03 1.06 1.08 0.99
E−02 E−02 E−02 E−02 E−02
290 MeV/u Si ions. No peak structure was observed in both spectra that looks like the spectrum usually obtained from shielding experiments. Solid lines show the results for unfolded TTNYs with four calibration lines in Fig. 10. The shapes of unfolded TTNYs with four calibration lines generally agree with the results obtained using the TOF method in both figures. (Note: case (a) in Fig. 12 is completely overlapped by case (d) above 20 MeV.) Tables 2 and 3 list the neutron yields obtained by integrating the TTNYs from 3 to 300 MeV range, and the ratio of each case yield to one by the TOF method for 100 and 290 MeV/u Si ions, respectively. The difference among integrated values for different calibrations was within 6%. The difference between TOF and unfolded results were 17 and 8% for 100 and 290 MeV/u data, at maximum. It indicates uncertainty of calibration affects neutron yield within order of several %. As shown in Fig. 13, the differences among unfolded TTNYs with different calibration curves became larger in the energy region above 100 MeV. The differences came from a large difference of (b) and (c) calibration in a relatively high light output region. In the inner panel of Fig. 10, the red line (b) and blue line (c) cross each other at the intersection of 165 ch. In the region below 165 ch, the calibration line of (b) is lower than that of (c). Inversely, in the higher region above the channel, the calibration line of (b) is upper than that of (c). This phenomenon has been reflected in unfolded TTNYs. As can be seen from the blue line in Fig. 13, a significant decrease in events above 100 MeV region was compensated by an increase of less than 7 MeV. This shows that the difference of the calibration line influences the neutron light output spectrum. It can be seen conspicuously both in the lowest and the highest regions. In this study, the linear calibration line obtained from only the radioisotope sources with the RooUnfold code and SCINFUL-QMD response gives reasonable neutron energy spectrum below 300 MeV while taking into consideration of the uncertainty in the calibration data. Although the uncertainty in the low light output region is less than 3%, the uncertainty in the high light output region could be larger than that as shown in Fig. 10. Thus, the deviation of the neutron spectrum in Fig. 13 is therefore larger in the high-energy region. In the present data analysis, the light output corresponding to the neutron component was up to about 50 MeVee. When the region of light output is lower than 50 MeVee, the dotted line (d) from recoil proton edges follows a straight line (a) as shown in Fig. 10. Since the relationship between the channel and light output is proportional below the 50 MeVee region, the linear calibration line determined from only
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