Neutron pulse height analysis (R405n)

Neutron pulse height analysis (R405n) Y. Satou April 6, 2011 Abstract A pulse height analysis was made for the neutron counter hodoscope used in R405n. By normalizing the pulse height distributions measured for cosmic ray muons in individual bars, to the calculated Landau distribution, gain parameters were deduced, with which the ADC values in ch are transformed into energy loss values in MeVee. 1 Introduction The neutron detection relies on energy transfer to a charged particle capable of ionizing and exciting scintillator material. In R405n, fast neutrons were detected by measuring light pulses generated by recoil protons produced mainly through the (n, p) reaction in the scintillator material. The scintillation light was converted to an electric current by a photomultiplier tube (PMT), and the total charge was digitized by an ADC to be stored in a media in the data acquisition system. The charge information (also mentioned as the pulse height information) is preferably expressed in terms of energy: MeVee (MeV electron equivalent), from the following reasons: This allows to make a direct comparison of results obtained with different PMT high voltage settings, This also allows to compare experimentally determined efficiencies with those calculated by Monte Carlo simulations. The pulse height information given in ch unit can be converted to values given in energy unit by using special sets of data recording detector responses to particular types of radiations for which the amount of energy lost inside the detector is known or calculable. Examples of these radiations are, Cosmic ray muons (µ), High energy γ rays emitted from the α+ 9 Be 12 C+n+γ (4.44 MeV) reaction in an 241 Am Be source. In the R405n experiment, both cosmic ray and γ ray measurements were performed to allow energy (pulse height) calibration of the neutron hodoscope. This report deals with the analysis of the calibration data based on the cosmic ray measurement. The trigger http://rarfaxp.riken.jp/ ysatou/r405n/neutron ph.pdf 1

condition was such that more than three hits were required in either of the four neutron walls to start data acquisition (RUN203, RUN204). The analysis was done in the following three steps: Eliminating the position dependence of scintillator light output Tracking of cosmic ray muons (identifying an angle of incidence) Normalization of the experimental pulse height distribution to the Landau distribution A description for each of the three steps is given below. 2 Eliminating the position dependence of scintillator light output The scintillation light produced in a long scintillator rod suffers from various effects which cause light attenuation, such as self absorption inside the scintillator and losses when the light is reflected on the material surface. In order to set a universal threshold value over the whole effective volume of the detector, it is important to have an indicator for the light output which does not depend on the hit position. In Fig. 1, examples are shown how the light amount recorded for cosmic ray muons by either left or right PMT in a rod depends on the hit position. Events which are near to the peaks in the muon energy loss distributions are pre-selected in the figure. The ADC value in the figure is corrected for the effect due to different incident angles of cosmic ray muons by making a tracking analysis as described in Sect. 3. Note that the larger the incident angle with respect to the vertical direction, muons lose more energy. In the present analysis, the position dependence in the pulse height was eliminated (1) by determining parameters which describe the measured position dependence and (2) by normalizing the pulse height by the fitted curve. The light amount recorded in the left A L or right A R PMT was found to be well fitted as a superposition of two exponential curves as given below: Wall 1,2 Wall 3,4 A L = p 1 exp( X X +90.0 [cm] )+p 3 exp( ), (1) p 2 p 4 A R = p 5 exp( X p 6 )+p 7 exp( X 90.0 [cm] p 8 ), (2) A L = p 9 exp( X X +40.0 [cm] )+p 11 exp( ), (3) p 10 p 12 A R = p 13 exp( X p 14 )+p 15 exp( X 40.0 [cm] p 16 ). (4) Different fit functions were used for long (wall-1,2) and short (wall-3,4) counters. The parameters p 1 through p 16 were determined by a chi-square minimization procedure. In Fig. 1, the results of the fit are shown as solid red lines. The extracted attenuation length, as given in the first terms in Eqs. (1) (4), is summarized in Fig. 2. For long counters (ID:1-12,21-32) the values of around 200 cm were obtained, while for short counters (ID:41-52,61-72) these were found to be around 100 cm. 2

In Figs. 3, 4, 5, and 6, correlations between normalized pulse height and hit position obtainedforcosmicraymuonsareshownforeachcounterinwalls-1, 2, 3, and4, respectively. In these figures, the pulse height is re-defined as a geometric mean of normalized heights in both left and right PMTs. It is seen that this does not depends on the detected position. 3 Tracking of cosmic ray muons (identifying an angle of incidence) A tracking analysis was done for cosmic ray muons using the hit position information in each counter. Twelve-fold coincidence events, in which all counters in a wall had a hit, were selected, and the muon tracks were determined by fitting using a straight line: X = a 1 +a 2 Y. In Fig. 7, two dimensional X Y position distributions and X position distributions at the top (Y=34.25 cm), middle (Y=0.0 cm), and bottom (Y= 32.85 cm) of a wall are shown for each wall. The X position distributions at the middle of a wall were found to have less pronounced edge boundaries. This is due to the requirement of twelve-fold coincidence for tacking. Since the edge locations in the cosmic ray position distributions are used to determine position parameters of a counter, it would be important to take cosmic ray data with a lower multiplicity trigger condition for position calibrations. InFig. 8, theincident angle (a 2 = tanθ) distributionsareshownfor each wall. Although the muon flux is the highest at a 2 = 0 (the vertical direction), it is seen that tracks with incident angles larger than θ = 45 ( a 2 > 1) are still non-negligible. The information on the incident angle provided by the tracking analysis can be used to correct for the angle dependence of the scintillator light output. The tracking analysis also yields an estimate for the position resolution in the X direction. This is provided by the width of the distribution of the fit residue, the difference between the measured hit position and the position inferred by the track. By fitting the residue distributions by a Gaussian function, position resolutions (in σ) of 1.61, 1.59, 1.64, and 1.58 cm were deduced for walls- 1, 2, 3, and 4, respectively. For this analysis a special set of tracks having small incident angles was selected. The Y position was provided by the location of the hit counter. The position uncertainty is thus given by the counter height (6.1 cm in full width). 4 Normalization of the experimental pulse height distribution to the Landau distribution The cosmic ray data allow to fix gain parameters, with which the pulse height given in ADC ch (or equivalent) is translated into energy in MeVee. For neutron detection with a plastic scintillation counter, a software threshold is set offline on the pulse height distribution to avoid unwanted background hits with lower depositing energies. Since the energy of a charged particle struck by an incident neutron distributes from zero to a certain maximum energy, the neutron detection efficiency depends on the threshold value. To allow comparisons in detection efficiency among different measurements, and to compare the efficiency value with the result from a Monte Carlo simulation, it is important to give the threshold value in an energy unit: MeVee. In the present analysis, the energy calibration of the scintillator light output was made by normalizing the pulse height distributions of cosmic ray muons to the calculated Landau distribution. The procedure is given below. 3

Figure 1: The position dependence of the scintillator light output for some of the counters in a neutron wall. The correlation plots, separately shown for left and right channels, were made based on cosmic ray muon data. The effect of finite incident angles of muons on the scintillator light output is corrected. The results of the fit using Eqs. (1) and (2) are overlaid as red lines. Figure 2: A summary of extracted attenuation lengths (absolute values) of all channels in the neutron hodoscope. The values were deduced using cosmic ray data by fitting the correlation between pulse height and hit position using curves in Eqs. (1) (4). The results are given separately for left and right channels. 4

Figure 3: Correlations between the normalized pulse height and the hit position, measured for cosmic ray muons with counters of the neutron wall-1. 5

Figure 4: Correlations between the normalized pulse height and the hit position, measured for cosmic ray muons with counters of the neutron wall-2. 6

Figure 5: Correlations between the normalized pulse height and the hit position, measured for cosmic ray muons with counters of the neutron wall-3. 7

Figure 6: Correlations between the normalized pulse height and the hit position, measured for cosmic ray muons with counters of the neutron wall-4. 8

Figure 7: Hit position distributions of cosmic ray muons for each wall obtained by requiring twelve-fold coincidence in a wall: two dimensional position distributions and horizontal position distributions at the top, middle, and bottom in a wall. The horizontal position distributions were deduced by using the fitted track information. 9

Figure 8: The incident angle distributions for all walls obtained by a tracking analysis of the cosmic ray muons. The abscissa is the tangent of the incident angle measured from the vertical direction (a 2 = tanθ). The energy loss caused by the passage of a charged particle through matter is distributed around an average, given by the Bethe-Bloch formula, due to statistical fluctuations in the number of collisions with electrons and in the amount of energy transferred to the electron in each collision (energy straggling). If the stopping material is thin enough for a charged particle having a particular energy that the statistical processes become important, the energy loss distribution can be treated with the theory of Landau (the Landau distribution) [1]. A brief explanation is given below on the Landau distribution and on the related parameters. This is based on the description in appendices D and E in Ref. [2]. The energy loss distribution (the struggling function) for a particle with velocity βc and charge ze traveling through an absorber with a thickness of t is given by the following relationship: f(t,,δ 2 ) = 1 πe M e κ(1+β2 Γ) Here is the total energy deposit, and 0 exp[κf 1 (y)]cos[λ 1 y +κf 2 (y)]dy. (5) f 1 (y) = β 2 [lny Ci(y)] cos(y) ysi(y), (6) f 2 (y) = y[lny Ci(y)]+sin(y)+β 2 Si(y), (7) λ 1 = κλ+κlnκ. (8) Si(y) and Ci(y) are the integral functions of sin and cos. And λ = λ +, (9) ξ e 4 ( ) z 2 Z ξ = 2πN a mc 2 ρx, (10) β A λ = (1 Γ) β 2 lnκ, (11) ξ κ =, (12) E M E M = Mc 2 β 2 γ 2 M 2m +γ + m. (13) 2M Here E M is the maximum possible energy transfer to an electron in one collision, M and m are the rest masses respectively of the charged particle and an electron, and Γ is the 10

Euler s constant (Γ = 0.577215). The average of the total energy deposit is given by the Bethe-Bloch formula: [ = ξ ln 2mc2 β 2 γ 2 ] E M I 2 2β 2 δ. (14) By neglecting higher order terms not shown in Eq. (14), such as the shell correction term, Barkas effect term, Bloch correction term, and so on, the total energy deposit is expressed by using λ as follows: = ξ[λ+ln(ξ/ε)+1 Γ δ]. (15) Here lnε is defined by lnε = ln I 2 2mc 2 β 2 γ 2 +β2. (16) Figure 9 shows the Landau distributions calculated for 10 GeV µ particles passing through a 6.1 cm-thick plastic scintillator. This energy gives κ = 0.0001 (generally if the κ value is less than 0.01, the energy loss distribution is expected to follow the Landau distribution [1]). The upper panel of the figure shows the result obtained by taking λ as an independent parameter, while the lower panel shows the result obtained by letting the total energy deposit [Eq. (15)] an independent parameter. For the calculation, the weighted random number generator ranlan [3] in the CERN Program Library was used. For energy loss distributions of µ particles calculated with different kinetic energies, the most probable energy loss values, mp, at which the Landau distribution reaches the maximum, were deduced. The results are shown as open squares in Fig. 10. The thickness of the plastic scintillator was taken to be 6.1 cm. For muons with energies greater than 1 GeV, the mp value was found not to depend heavily on the incident muon energy; for muons with energies greater that 10 GeV, mp converged to 11.030 MeV. The red line in the figure is a prediction of the following formula given in the Leo s textbook [1]: mp = ξ[ln(ξ/ε)+0.198 δ)]. (17) The mp values calculated with this equation well describes the peak positions of the Landau distributions (open squares). The mean energy loss given by the Bethe-Bloch formula is also plotted in the figure as a black line. The energy independence of mp at high energies mainly comes from the energy dependence of the density (δ) term. The energy calibration of the scintillator light output was made by normalizing the cosmic ray energy loss distributions to the calculated Landau distribution. The gain parameters were deduced for each counter. It is implicit that the pedestal correction is made so that the ADC 0 ch corresponds to 0 MeVee. The normalized pulse height distributions of walls-1, 2, 3, and 4 are shown in Figs. 11, 12, 13, and 14, respectively. In the figures, the red (green) lines refer to the Landau distributions calculated for 10 GeV muons by taking into account an energy resolution of E = 0.0 MeV (0.25 MeV) in σ. The resolution value for the green curves was determined so as to reproduce the rising edge and the peak position of the cosmic ray energy distributions. The calculated Landau distributions were scaled appropriately. In the measured pulse height distributions, the effect of varying counter thickness due to finite angular range in the incident muon track was corrected. It is seen that the energy calibrated pulse height distributions are well described by the Landau distributions taking into account the energy resolution. The µ particles with energies 11

less than 300 MeV lose more energy on average than higher energy muons; contributions from the low energy muons will shift the energy loss distribution towards the higher energy side. The observed slight enhancements in the measured pulse height distribution over the calculated Landau distribution at the higher energy tail of the peak might be explained as due to contributions from the low energy µ particles. References [1] W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, (Springer-Verlag, Berlin, 1994). [2] H. Bichsel, Rev. Mod. Phys., Vol. 60, No. 3, July 1988. [3] http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/g110/top.html 12

Figure 9: The Landau distribution functions calculated for 10 GeV muons incident on a plastic scintillation counter with a thickness of 6.1 cm. The upper (lower) figure refers to the distribution plotted as a function of λ ( : the total energy deposit given in Eq. (15)). 13

Figure 10: The incident energy dependence of the most probable energy loss value, mp, for cosmic ray muons penetrating a plastic scintillator with a thickness of 6.1 cm. The open squares are the mp values read from the Landau distributions calculated for various muon incident energies. The red line is the prediction of Eq. (17) given in the Leo s textbook [1]. It is seen that the red line gives a good description of mp read from the calculated Landau distributions (open squares). The black line refers to the mean energy loss value,, obtained from the Bethe-Bloch formula (shown for reference). 14

Figure 11: The normalized pulse height distribution for cosmic ray muons measured with the neutron wall-1. The Landau distribution assuming an energy resolution of E(σ) =0.0 MeV (0.25 MeV) is shown as a red (green) line. The effect of varying counter thicknesses due to different incident angles is corrected. Figure 12: The normalized pulse height distribution for cosmic ray muons measured with the neutron wall-2. The Landau distribution assuming an energy resolution of E(σ) =0.0 MeV (0.25 MeV) is shown as a red (green) line. The effect of varying counter thicknesses due to different incident angles is corrected. 15

Figure 13: The normalized pulse height distribution for cosmic ray muons measured with the neutron wall-3. The Landau distribution assuming an energy resolution of E(σ) =0.0 MeV (0.25 MeV) is shown as a red (green) line. The effect of varying counter thicknesses due to different incident angles is corrected. Figure 14: The normalized pulse height distribution for cosmic ray muons measured with the neutron wall-4. The Landau distribution assuming an energy resolution of E(σ) =0.0 MeV (0.25 MeV) is shown as a red (green) line. The effect of varying counter thicknesses due to different incident angles is corrected. 16