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Plastic scintillator response to relativistic nuclei, Z ≤ 28
Nuclear Instruments and Methods in Physics Research A242 (1985) North-Holland, Amsterdam
171-176
171
PLASTIC SCINTILLATOR RESPONSE TO RELATIVISTIC'NUCLEI, Z _< 28 Robert DWYER and Dazhuang ZHOU ** Enrico Fermi Institute, University
of Chicago,
Chicago, IL 60637, USA
Received 29 July 1985 This paper deals with the nonlinearity in the response of Pilot Y plastic scintillators to the energy loss of ionizing particles. The data on which the analysis is based are derived from a balloon-borne cosmic-ray experiment to investigate nuclei over the charge range from Z =1 through Z = 28 (nickel), and over an energy from 0.7 to 10 GeV/n. Comparison of the data is made with two variants of a simple core-halo model and good agreement between the measurements and the models is found for this charge and energy range. 1. Introduction Organic plastic scintillators have been widely used in the detection of charged particles since they have a fast response time, good light output, and are easily fabricated into a variety of forms useful for many experiments. In the design of a high altitude, balloon-borne instrument to measure relativistic cosmic-ray nuclei, we needed a detector sensitive to nuclear charge Z that had a large area, uniform response across its area and ample light yield and resolution such that each individual charge peak could be identified for all nuclei with atomic number up through nickel (Z = 28). Plastic scintillators are ideally suited for this task . However, plastic scintillators are nonlinear in their response . As the amount of energy lost by a penetrating particle increases, e.g . with increasing Z of relativistic cosmic ray nuclei, the light output is no longer proportional to the energy lost . The scintillation efficiency dL/dE decreases as the specific energy loss dE/dx increases. We found that this nonlinearity does not prevent good charge resolution of individual elements. In this paper we present data on the response of Pilot Y plastic scintillator [1] to relativistic nuclei with Z _< 28, In particular we discuss the form of this nonlinearity . For organic plastic scintillators like Pilot Y this "saturation" is gradual rather than abrupt so that charge information may still be extracted from the increase in the light signal with dE/dx. Although there has been much work done to define * This work was supported in part by the National Aeronautics and Space Administration under grant NGL 14-001-005. ** On leave from China University of Science and Technology, People's Republic of China. 0168-9002/85/$03 .30 © Elsevier Science Publishers B.V (North-Holland Physics Publishing Division)
this nonlinearity, it was mostly confined to either low Z and/or stopping particles. The data from, our balloon flights extend over .the entire charge range up through nickel and cover the-kinetic energy interval from 0.7 to 10 GeV/n . It is -of interest to investigate scintillator nonlinearity at relativistic energies "because the spatial distribution of energy deposited by knock-on electrons is quite different from lower energies due to the increase in the maximum transferable energy to an electron . In the next sections, we briefly describe the experiment and the analysis which gives us the data on scintillator nonlinearity . Then these data are compared with two versions of a simple model which divides the energy deposited into two regions - a "core" right around the particle track and a "halo" farther away and expected to become more important at higher energies . We give the parameters for our best fit to the data and find this simple model to be an excellent representation of the scintillator behavior over this charge and energy regime. 2. Instrumentation and balloon flights The instrument used for these measurements is shown in fig. 1. There are two identical plastic scintillators, T1 and T3, made of square sheets of Pilot Y, each of thickness 1 cm. These are enclosed in highly reflecting, white, light integration boxes and viewed by twelve RCA 4525 5" diameter photomultiplier tubes. This geometry produces higher uniformity of response across the scintillator area than a light pipe arrangement. Energy information over the range 0.7-10 GeV/n is derived from the 72 Cherenkov counter which contains a Freon fluorocarbon liquid type E-2 with refractive index n = 1.26. The multimire proportional chamber hodoscope (A, B, C) enables the trajectory of the penetrating
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei
172
Mw SCINTILLATION COUNTER T I LIQUID
CE RENKOV COUNTER T2
5"P M TUBES MWPC B
SCINTILLATION COUNTER T3
Fig. 1. Schematic cross section of the instrument used in these measurements. MWPC = multiwire proportional counter. Each MWPC measures both the x- and the y-coordinate of the traversing particle.
particle to be measured so that the zenith angle of incidence on the plane parallel detectors can be determined to correct each pulse height to that of normal incidence. For each event that triggers all the T counters, the pulse heights are all recorded in linear 2048channel analyzers along with the MWPC wire firings. The geometry factor of the instrument aperture is 0.25 in' sr. For more details on the instrument and on the data analysis the reader is referred to ref. [2]. The instrument has been flown successfully on four separate occasions from 20 .8 x 10 6 ft 3 balloons yielding over 150 h of exposure at a mean residual atmosphere of less than 4 g/cm2. These flights provided data of excellent statistical accuracy for the scintillation study considered here. 3. Data analysis Three corrections are applied to the raw pulse heights in the T counters . 1) A correction for path length through the detectors consisting of multiplication by the cosine of the zenith angle of incidence as measured by the MWPC hodoscope. 2) A correction for nonuniformity of response of each T counter depending on where the particle passes through each detector. This is generated from extensive "mapping" of each detector surface area using both sea level muons and in-flight oxygen nuclei. 3) A correction for gain drift of the electronics. In each case the residual error after correction amounts to at most a few tenths of a percent. Consistency requirements on the pulse heights are imposed in order to eliminate events in which a nuclear spallation interaction occurred with the matter of the
instrument . The three requirements we used were : 1) A straight line trajectory in the MWPC hodoscope. 2) Agreement between the T1 and T3 scintillator pulse heights. 3) Consistency between the two Cherenkov counters TO and 72 . This produced a sample of good noninteracting nuclei which could then be used to study the scintillator pulse height dependence on charge and velocity. Fig. 2 shows the charge resolution achieved in this data sample for Z = 14-28. This histogram is obtained from flight data after the corrections and selection criteria discussed above have been applied. Good separation of each element distribution is achieved over the entire charge range studied in these flights. The astrophysical aim of this work is a precision measurement of the elemental composition of cosmic rays [3]. Our data include the whole charge range from Z =1 up through Z = 28 in the following way. Extensive ground runs were done with sea level muons. Our first two fligths covered the charge range Z = 2 to about 14. Our latter two flights covered Z = 7 through 28 . The scintillator responds linearly at low Z, i.e. the mean pulse heights increase as Z2. Using the lower Z data from the first two flights we established the "unsaturated" response of the scintillation counters since the onset of the deviation of the mean pulse height from a pure Z2 response (for one velocity interval) can be easily seen. In this paper we use the data from the latter two flights (Z = 7-28) compared with the pure Z2 response derived from the lower Z data that would be expected if the scintillator exhibited no saturation . Fig. 3 shows the mean scintillator pulse height vs . charge for one sample velocity bin. The straight line drawn in shows the unsaturated, pure Z2 response . As can be seen the onset of nonlinearity is gradual although already occurring below Z = 7. However, the
Si }if
P
S
CI
A
K
Ca
Sc
T,
V
Cr
Mn
Fe
Co
M
800
600 z 6; z 400
ôU
200
0
.~ 14
L.I 15
16
I ~IIIt..) II 17
18
.IIII~ .I 19
II 20
~III, .IIIII,~IIII~ .IIIILfIIIIII 21
22
23
24
25
26
I~ . . . . fli . . 27
28
Fig. 2. Charge histogram for Z =14-28 for the energy range 1 .2-2.4 GeV/n obtained from flight data after application of the corrections and selection criteria discussed in the text .
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei 1 .2-1 .5 GeV/N
600
ô. 0
17 3
104
500
â â
400
w i 102
Z=14
â ô
300 200
â
100
c L U c
200
400 Z2
600
d
800
Fig. 3 . Mean pulse height in the average scintillator signal (T1+T3)/2 vs Z 2 for data in the 1 .2-1 .5 GeV/n bin. The straight line is extrapolated from lower Z data where an unsaturated (linear with Z2) dependence is observed . Each of the other energy intervals shows a similar behavior . slope of the response curve is still adequate to provide charge information sufficient to distinguish adjacent element distributions (fig . 2) . We show in table 1 the results of this data analysis, the mean pulse heights observed in the balloon flights for cosmic-ray elements nitrogen through nickel over six selected velocity intervals. These mean pulse heights are for the sum of the scintillator signals Tl + T3 since the TI/T3 consistency requirement has already been applied and summing reduces the statistical (Landau) fluctuations . We will work exclusively with the scintillator sum throughout this paper. The variation of pulse
100
98 0 .5
0 .7 1 2 3 6 Kinetic Energy, GeV/Nucleon
10
Fig. 4 . Variation of the average pulse height vs velocity for silicon (Z =14) . height with velocity for a given charge is shown in fig. 4. The features of the energy loss phenomenon, a decrease to the point of minimum ionization followed by the relativistic rise are readily observéd. Good statistical accuracy is reflected in the small error bars while the good energy resolution allows the detailed pulse height variation with velocity to be shown over the interval 0.7 to about 10 GeV/n. 4. Model for scintillator nonlinearity As a simple representation of the scintillation nonlinearity, we take a model in which the ionization en-
Table 1 Observed mean pulse height for the scintillation counter sum TI +T3 as a function of charge and energy Charge Z
k e) 7 8 10 12 14 16 18 20 22 24 26 28
Kinetic energy interval [GeV/n ] 0.7-1 .0
1 .0-1 .2
1 .2-1 .5
1 .5-2 .0
2.0-3.1
> 3 .1
1 .347
1 .320
1 .296
1 .274
1 .266
1 .285
61 .7±1 .7 75 .7±1 .9 106.5±2.5 139 .5±3 .1 176 .5±3 .6 217 .9±4 .0 263 .8±4 .4 312 .4±5 .7 364 .0±7 .1 419 .1±7 .3 478 .3±8 .5 544 .2±8 .6
60 .4±1.8 74 .3±2 .0 104 .2±2 .4 136 .7±2 .9 173 .5±3 .5 214 .0±3 .8 258 .7±3 .9 305 .6±4 .7 357 .0±6 .0 411 .8±6 .0 468 .8±6 .9 531 .9±6 .8
59 .3±2 .0 73 .1±2 .1 102 .8±2 .5 135 .5±3 .1 172 .0±3 .7 212.3±3 .8 256 .8±4.0 304.4±5 .1 355 .5±6 .4 407.7±6 .5 465 .6±7.5 528.0±5 .9
58 .3± 2 .1 72.2±2 .2 102.0± 2.7 134.8± 3 .4 171 .5± 4.0 212.2± 4.1 256.8± 4.5 304.1± 5 .3 355.5± 7.4 407 .8± 6.6 465 .4± 8.1 528 .1±10 .1
57 .9±2 .1 71 .9±2 .4 102 .3±3 .0 135 .4±3 .7 173 .1±4 .6 214 .7±5 .3 258 .8±5 .3 305 .9±6 .0 358 .9±7 .2 412 .7±6 .7 469 .7±8 .8 531 .5±8 .0
58 .8± 2 .5 73 .2± 2 .9 104.1± 3 .6 138 .6± 4 .3 177 .6± 5 .4 220.1± 5 .9 266.2± 6 .4 312.5± 7 .1 367.6± 8 .2 423.1± 6 .7 479.7±10.7 538.3±11 .3
e) The factor k is the slope of the "unsaturated" (linear with Z2) response derived from lower Z (Z < 7) data .
174
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei
ergy loss is divided into two regions depending on how far from the particle path the energy is deposited. An inner region of very dense ionization energy loss is called the "core" and the surrounding region farther away from the track is the "halo" . This division was first suggested by nuclear emulsion photographs showing the heavily darkened region directly around the particle path surrounded by a region of less dense ionization. For plastic scintillators the model is also reasonable if one considers that the scintillator nonlinearity results from a saturation or quenching of luminescence centers. This is most apt to happen nearest the particle path where the highest energy density is deposited. Farther from the track energy is deposited only by higher energy delta rays which represent the tail of the energy loss distribution and are rarer. Therefore it is in the inner or core region where all the saturation is assumed to occur. The scintillation efficiency in the halo is assumed to be linear. It is important to note that energy deposited in the core comes from the lowest energy delta rays arising from distant collisions between the primary and electrons in the medium . Electrons depositing energy in the halo are created with higher energy arising from close collisions. There has been much work on the saturation exhibited in the scintillation process but virtually all this work applies to slow or stopping particles of low Z. In the monograph by Birks [4], the following parametrization appears for the light output per unit path length _ dL _ A(dE/dx) dx 1 + B(dE/dx)
The interpretation of these models is straightforward . There are two terms: the first represents the saturating part of the light output from the core. The second is not saturated and represents the light contribution from the halo. The parameter fh represents the fraction of energy deposited in the halo and BS is a parameter governing the strength of the saturation . A is an overall gain normalization. We have fitted our data to both versions of the model using a least-squares fit to an arbitrary function [10] . We find that both versions give an excellent fit to our data over the charge and energy range covered here. Figs . 5a and 5b show examples of these fits for a particular velocity interval. Also shown, as in fig. 3, is the straight line representing a linear dependence on
(1)
In early work by Meyer and Murray [5] the core/halo distinction already appears. We compared our data to two variants of the core/halo model. Voltz et al . [6] discuss an equation for the specific luminescence of the form dx
-A
x 1 +fnl dx {( 1 - fh) exp[ - Bs(1 - fh) d
This formulation has also been discussed in Ahlen et al . [7]. We will refer to this as Model 1. Another form of this was given by Tarlé et al. [8]: _ dL _ A(1 -fh )dE/dx _ dE dx 1 + BS(1 - fh )dE/dx +Afh dx .
This will be referred to as Model 2. Salamon and Ahlen [9] also evaluated both these models in connection with accelerator data and found Model 2 to be favored. It is easily seen that the second form (eq. (3)) represents the first two terms after an expansion of the exponential in eq. (2). Thus mathematically it may be regarded as an approximation of eq. (2). Physically, however, we shall see that eq. (3) seems to reflect more accurately the physical processes involved.
Fig. 5. (a) Comparison of balloon flight data and curve fitted from Model 1 (eq. (2)) for one particular energy interval . The unsaturated response (straight line) is also shown. (b) Same as (a) for Model 2 (eq. (3)).
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei
Z2 , i.e . no saturation, derived from our lower Z data. When looking at the fits for all energy bins, both models are clearly within the error bars of all the data . However, there is some indication that the curvature of the Model 2 fit seems to provide a slightly better match to the trend of the data . The values of chi square are very low in both cases representing fluctuations among the velocity intervals considered . Table 2 gives the best fit parameters for each model with all energies observed in this experiment considered in one bin. There is a small variation with energy of these fit parameters . In particular, the values for fn found in both models increase slightly with energy. This is expected however since the spatial distribution of energy deposited is changing as the maximum transferable energy to a delta ray increases . Thus the contribution from the halo should be increasing with energy. It should also be noted that this core/halo distinction should not be expected to apply to low velocities of the primary particle . These models are specifically intended for relativistic energies . Shown in figs. 6a and 6b are the separate contribu1200 1000
175
Table 2 Parameters for best fit of models to data for all energies 0.7-10 GeV/n Bs !n Model 1 .22)X10-3 .35±0 (eq. (2)) 0.638±0 .005 0.527±0.005 (5 Model 2 (7 .30)X10-3 (eq. (3)) 0.729±0 .005 0.392±0.004 .71±0
tions from the core and halo to the total light signal. Here one notes the physical consequences of the mathematical difference between the two versions. In the expression with the full exponential, eq . (2), the core contribution increases, reaches a maximum and then decreases asymptotically to zero. This is not the case if one only takes the approximate expression, eq . (3). Here the core contribution increases to a maximum and gradually saturates. Physically, as the specific energy loss increases, the light from the core is apt to follow the behavior given by the approximate expression. It would never be expected to fall back towards zero. In this sense we might expect eq. (3) to be a better representation if extended to higher specific energy losses, e.g. to account for higher Z relativistic particles.
800
5. Conclusion
600
We have measured the response of plastic scintillator Pilot Y to relativistic nuclei of charge less than or equal to 28 (nickel) for six velocity intervals from 0.7 to 10 GeV/n . These measurements have then been fitted to two versions of a simple model of scintillator saturation . Both produce excellent fits over this charge and energy range although one is slightly favored due to its more realistic physical interpretation .
400 200 0
1200 1000 800 6 400 200 0 Fig. 6. (a) The individual contributions from the core and halo are shown for the fit to the data using Model 1 (eq. (2)) for one energy interval . (b) Same as (a) for Model 2 of eq . (3).
Acknowledgments The authors would like to thank Prof . P. Meyer for many helpful discussions and careful reading of the manuscript. The staff of the Laboratory for Astrophysics and Space Research at the University of Chicago, and in particular W. Johnson, G. Kelderhouse, W. Hollis, L. Glennie are thanked for instrument development. The staff of the National Scientific Balloon Facility in Palestine, Texas ably carried out balloon launch and recovery . References [11 Nuclear Enterprises, Inc., San Carlo, CA, USA . [21 R. Dwyer, S. Jordan and P. Meyer, Nucl . Instr. and Meth . 224 (1984) 247.
176
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei
[3] R. Dwyer and P. Meyer, Astrophys . 1294 (1985) 441 . [4] J .B . Birks, The Theory and Practice of Scintillation Counting (Pergamon, New York, 1964) . [5] A. Meyer and R.B. Murray, Phys. Rev. 128 (1962) 98 . [6] R. Voltz, J. Lopes da Silva, G. Lanstriat and A. Coche, J. Chem. Phys . 45 (1966) 3306 . [7] S.P. Ahlen, B .G. Cartwright and G . Tarlé, Nucl. Instr. and Meth. 147 (1977) 321 .
[8] G. Tarlé, S.P . Ahlen and B.G . Cartwright, Astrophys . J. 230 (1979) 607 . [9] M.H. Salomon and S .P . Ahlen, Nucl. Instr. and Meth . 195 (1982) 557 . [10] P.R. Bevington, Data Reduction and Error Analysis for the Physcial Sciences (McGraw-Hill, New York, 1969) ch. 11 .
171-176
171
PLASTIC SCINTILLATOR RESPONSE TO RELATIVISTIC'NUCLEI, Z _< 28 Robert DWYER and Dazhuang ZHOU ** Enrico Fermi Institute, University
of Chicago,
Chicago, IL 60637, USA
Received 29 July 1985 This paper deals with the nonlinearity in the response of Pilot Y plastic scintillators to the energy loss of ionizing particles. The data on which the analysis is based are derived from a balloon-borne cosmic-ray experiment to investigate nuclei over the charge range from Z =1 through Z = 28 (nickel), and over an energy from 0.7 to 10 GeV/n. Comparison of the data is made with two variants of a simple core-halo model and good agreement between the measurements and the models is found for this charge and energy range. 1. Introduction Organic plastic scintillators have been widely used in the detection of charged particles since they have a fast response time, good light output, and are easily fabricated into a variety of forms useful for many experiments. In the design of a high altitude, balloon-borne instrument to measure relativistic cosmic-ray nuclei, we needed a detector sensitive to nuclear charge Z that had a large area, uniform response across its area and ample light yield and resolution such that each individual charge peak could be identified for all nuclei with atomic number up through nickel (Z = 28). Plastic scintillators are ideally suited for this task . However, plastic scintillators are nonlinear in their response . As the amount of energy lost by a penetrating particle increases, e.g . with increasing Z of relativistic cosmic ray nuclei, the light output is no longer proportional to the energy lost . The scintillation efficiency dL/dE decreases as the specific energy loss dE/dx increases. We found that this nonlinearity does not prevent good charge resolution of individual elements. In this paper we present data on the response of Pilot Y plastic scintillator [1] to relativistic nuclei with Z _< 28, In particular we discuss the form of this nonlinearity . For organic plastic scintillators like Pilot Y this "saturation" is gradual rather than abrupt so that charge information may still be extracted from the increase in the light signal with dE/dx. Although there has been much work done to define * This work was supported in part by the National Aeronautics and Space Administration under grant NGL 14-001-005. ** On leave from China University of Science and Technology, People's Republic of China. 0168-9002/85/$03 .30 © Elsevier Science Publishers B.V (North-Holland Physics Publishing Division)
this nonlinearity, it was mostly confined to either low Z and/or stopping particles. The data from, our balloon flights extend over .the entire charge range up through nickel and cover the-kinetic energy interval from 0.7 to 10 GeV/n . It is -of interest to investigate scintillator nonlinearity at relativistic energies "because the spatial distribution of energy deposited by knock-on electrons is quite different from lower energies due to the increase in the maximum transferable energy to an electron . In the next sections, we briefly describe the experiment and the analysis which gives us the data on scintillator nonlinearity . Then these data are compared with two versions of a simple model which divides the energy deposited into two regions - a "core" right around the particle track and a "halo" farther away and expected to become more important at higher energies . We give the parameters for our best fit to the data and find this simple model to be an excellent representation of the scintillator behavior over this charge and energy regime. 2. Instrumentation and balloon flights The instrument used for these measurements is shown in fig. 1. There are two identical plastic scintillators, T1 and T3, made of square sheets of Pilot Y, each of thickness 1 cm. These are enclosed in highly reflecting, white, light integration boxes and viewed by twelve RCA 4525 5" diameter photomultiplier tubes. This geometry produces higher uniformity of response across the scintillator area than a light pipe arrangement. Energy information over the range 0.7-10 GeV/n is derived from the 72 Cherenkov counter which contains a Freon fluorocarbon liquid type E-2 with refractive index n = 1.26. The multimire proportional chamber hodoscope (A, B, C) enables the trajectory of the penetrating
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei
172
Mw SCINTILLATION COUNTER T I LIQUID
CE RENKOV COUNTER T2
5"P M TUBES MWPC B
SCINTILLATION COUNTER T3
Fig. 1. Schematic cross section of the instrument used in these measurements. MWPC = multiwire proportional counter. Each MWPC measures both the x- and the y-coordinate of the traversing particle.
particle to be measured so that the zenith angle of incidence on the plane parallel detectors can be determined to correct each pulse height to that of normal incidence. For each event that triggers all the T counters, the pulse heights are all recorded in linear 2048channel analyzers along with the MWPC wire firings. The geometry factor of the instrument aperture is 0.25 in' sr. For more details on the instrument and on the data analysis the reader is referred to ref. [2]. The instrument has been flown successfully on four separate occasions from 20 .8 x 10 6 ft 3 balloons yielding over 150 h of exposure at a mean residual atmosphere of less than 4 g/cm2. These flights provided data of excellent statistical accuracy for the scintillation study considered here. 3. Data analysis Three corrections are applied to the raw pulse heights in the T counters . 1) A correction for path length through the detectors consisting of multiplication by the cosine of the zenith angle of incidence as measured by the MWPC hodoscope. 2) A correction for nonuniformity of response of each T counter depending on where the particle passes through each detector. This is generated from extensive "mapping" of each detector surface area using both sea level muons and in-flight oxygen nuclei. 3) A correction for gain drift of the electronics. In each case the residual error after correction amounts to at most a few tenths of a percent. Consistency requirements on the pulse heights are imposed in order to eliminate events in which a nuclear spallation interaction occurred with the matter of the
instrument . The three requirements we used were : 1) A straight line trajectory in the MWPC hodoscope. 2) Agreement between the T1 and T3 scintillator pulse heights. 3) Consistency between the two Cherenkov counters TO and 72 . This produced a sample of good noninteracting nuclei which could then be used to study the scintillator pulse height dependence on charge and velocity. Fig. 2 shows the charge resolution achieved in this data sample for Z = 14-28. This histogram is obtained from flight data after the corrections and selection criteria discussed above have been applied. Good separation of each element distribution is achieved over the entire charge range studied in these flights. The astrophysical aim of this work is a precision measurement of the elemental composition of cosmic rays [3]. Our data include the whole charge range from Z =1 up through Z = 28 in the following way. Extensive ground runs were done with sea level muons. Our first two fligths covered the charge range Z = 2 to about 14. Our latter two flights covered Z = 7 through 28 . The scintillator responds linearly at low Z, i.e. the mean pulse heights increase as Z2. Using the lower Z data from the first two flights we established the "unsaturated" response of the scintillation counters since the onset of the deviation of the mean pulse height from a pure Z2 response (for one velocity interval) can be easily seen. In this paper we use the data from the latter two flights (Z = 7-28) compared with the pure Z2 response derived from the lower Z data that would be expected if the scintillator exhibited no saturation . Fig. 3 shows the mean scintillator pulse height vs . charge for one sample velocity bin. The straight line drawn in shows the unsaturated, pure Z2 response . As can be seen the onset of nonlinearity is gradual although already occurring below Z = 7. However, the
Si }if
P
S
CI
A
K
Ca
Sc
T,
V
Cr
Mn
Fe
Co
M
800
600 z 6; z 400
ôU
200
0
.~ 14
L.I 15
16
I ~IIIt..) II 17
18
.IIII~ .I 19
II 20
~III, .IIIII,~IIII~ .IIIILfIIIIII 21
22
23
24
25
26
I~ . . . . fli . . 27
28
Fig. 2. Charge histogram for Z =14-28 for the energy range 1 .2-2.4 GeV/n obtained from flight data after application of the corrections and selection criteria discussed in the text .
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei 1 .2-1 .5 GeV/N
600
ô. 0
17 3
104
500
â â
400
w i 102
Z=14
â ô
300 200
â
100
c L U c
200
400 Z2
600
d
800
Fig. 3 . Mean pulse height in the average scintillator signal (T1+T3)/2 vs Z 2 for data in the 1 .2-1 .5 GeV/n bin. The straight line is extrapolated from lower Z data where an unsaturated (linear with Z2) dependence is observed . Each of the other energy intervals shows a similar behavior . slope of the response curve is still adequate to provide charge information sufficient to distinguish adjacent element distributions (fig . 2) . We show in table 1 the results of this data analysis, the mean pulse heights observed in the balloon flights for cosmic-ray elements nitrogen through nickel over six selected velocity intervals. These mean pulse heights are for the sum of the scintillator signals Tl + T3 since the TI/T3 consistency requirement has already been applied and summing reduces the statistical (Landau) fluctuations . We will work exclusively with the scintillator sum throughout this paper. The variation of pulse
100
98 0 .5
0 .7 1 2 3 6 Kinetic Energy, GeV/Nucleon
10
Fig. 4 . Variation of the average pulse height vs velocity for silicon (Z =14) . height with velocity for a given charge is shown in fig. 4. The features of the energy loss phenomenon, a decrease to the point of minimum ionization followed by the relativistic rise are readily observéd. Good statistical accuracy is reflected in the small error bars while the good energy resolution allows the detailed pulse height variation with velocity to be shown over the interval 0.7 to about 10 GeV/n. 4. Model for scintillator nonlinearity As a simple representation of the scintillation nonlinearity, we take a model in which the ionization en-
Table 1 Observed mean pulse height for the scintillation counter sum TI +T3 as a function of charge and energy Charge Z
k e) 7 8 10 12 14 16 18 20 22 24 26 28
Kinetic energy interval [GeV/n ] 0.7-1 .0
1 .0-1 .2
1 .2-1 .5
1 .5-2 .0
2.0-3.1
> 3 .1
1 .347
1 .320
1 .296
1 .274
1 .266
1 .285
61 .7±1 .7 75 .7±1 .9 106.5±2.5 139 .5±3 .1 176 .5±3 .6 217 .9±4 .0 263 .8±4 .4 312 .4±5 .7 364 .0±7 .1 419 .1±7 .3 478 .3±8 .5 544 .2±8 .6
60 .4±1.8 74 .3±2 .0 104 .2±2 .4 136 .7±2 .9 173 .5±3 .5 214 .0±3 .8 258 .7±3 .9 305 .6±4 .7 357 .0±6 .0 411 .8±6 .0 468 .8±6 .9 531 .9±6 .8
59 .3±2 .0 73 .1±2 .1 102 .8±2 .5 135 .5±3 .1 172 .0±3 .7 212.3±3 .8 256 .8±4.0 304.4±5 .1 355 .5±6 .4 407.7±6 .5 465 .6±7.5 528.0±5 .9
58 .3± 2 .1 72.2±2 .2 102.0± 2.7 134.8± 3 .4 171 .5± 4.0 212.2± 4.1 256.8± 4.5 304.1± 5 .3 355.5± 7.4 407 .8± 6.6 465 .4± 8.1 528 .1±10 .1
57 .9±2 .1 71 .9±2 .4 102 .3±3 .0 135 .4±3 .7 173 .1±4 .6 214 .7±5 .3 258 .8±5 .3 305 .9±6 .0 358 .9±7 .2 412 .7±6 .7 469 .7±8 .8 531 .5±8 .0
58 .8± 2 .5 73 .2± 2 .9 104.1± 3 .6 138 .6± 4 .3 177 .6± 5 .4 220.1± 5 .9 266.2± 6 .4 312.5± 7 .1 367.6± 8 .2 423.1± 6 .7 479.7±10.7 538.3±11 .3
e) The factor k is the slope of the "unsaturated" (linear with Z2) response derived from lower Z (Z < 7) data .
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ergy loss is divided into two regions depending on how far from the particle path the energy is deposited. An inner region of very dense ionization energy loss is called the "core" and the surrounding region farther away from the track is the "halo" . This division was first suggested by nuclear emulsion photographs showing the heavily darkened region directly around the particle path surrounded by a region of less dense ionization. For plastic scintillators the model is also reasonable if one considers that the scintillator nonlinearity results from a saturation or quenching of luminescence centers. This is most apt to happen nearest the particle path where the highest energy density is deposited. Farther from the track energy is deposited only by higher energy delta rays which represent the tail of the energy loss distribution and are rarer. Therefore it is in the inner or core region where all the saturation is assumed to occur. The scintillation efficiency in the halo is assumed to be linear. It is important to note that energy deposited in the core comes from the lowest energy delta rays arising from distant collisions between the primary and electrons in the medium . Electrons depositing energy in the halo are created with higher energy arising from close collisions. There has been much work on the saturation exhibited in the scintillation process but virtually all this work applies to slow or stopping particles of low Z. In the monograph by Birks [4], the following parametrization appears for the light output per unit path length _ dL _ A(dE/dx) dx 1 + B(dE/dx)
The interpretation of these models is straightforward . There are two terms: the first represents the saturating part of the light output from the core. The second is not saturated and represents the light contribution from the halo. The parameter fh represents the fraction of energy deposited in the halo and BS is a parameter governing the strength of the saturation . A is an overall gain normalization. We have fitted our data to both versions of the model using a least-squares fit to an arbitrary function [10] . We find that both versions give an excellent fit to our data over the charge and energy range covered here. Figs . 5a and 5b show examples of these fits for a particular velocity interval. Also shown, as in fig. 3, is the straight line representing a linear dependence on
(1)
In early work by Meyer and Murray [5] the core/halo distinction already appears. We compared our data to two variants of the core/halo model. Voltz et al . [6] discuss an equation for the specific luminescence of the form dx
-A
x 1 +fnl dx {( 1 - fh) exp[ - Bs(1 - fh) d
This formulation has also been discussed in Ahlen et al . [7]. We will refer to this as Model 1. Another form of this was given by Tarlé et al. [8]: _ dL _ A(1 -fh )dE/dx _ dE dx 1 + BS(1 - fh )dE/dx +Afh dx .
This will be referred to as Model 2. Salamon and Ahlen [9] also evaluated both these models in connection with accelerator data and found Model 2 to be favored. It is easily seen that the second form (eq. (3)) represents the first two terms after an expansion of the exponential in eq. (2). Thus mathematically it may be regarded as an approximation of eq. (2). Physically, however, we shall see that eq. (3) seems to reflect more accurately the physical processes involved.
Fig. 5. (a) Comparison of balloon flight data and curve fitted from Model 1 (eq. (2)) for one particular energy interval . The unsaturated response (straight line) is also shown. (b) Same as (a) for Model 2 (eq. (3)).
R. Dwyer, D. Zhou / Scintillator response to relativistic nuclei
Z2 , i.e . no saturation, derived from our lower Z data. When looking at the fits for all energy bins, both models are clearly within the error bars of all the data . However, there is some indication that the curvature of the Model 2 fit seems to provide a slightly better match to the trend of the data . The values of chi square are very low in both cases representing fluctuations among the velocity intervals considered . Table 2 gives the best fit parameters for each model with all energies observed in this experiment considered in one bin. There is a small variation with energy of these fit parameters . In particular, the values for fn found in both models increase slightly with energy. This is expected however since the spatial distribution of energy deposited is changing as the maximum transferable energy to a delta ray increases . Thus the contribution from the halo should be increasing with energy. It should also be noted that this core/halo distinction should not be expected to apply to low velocities of the primary particle . These models are specifically intended for relativistic energies . Shown in figs. 6a and 6b are the separate contribu1200 1000
175
Table 2 Parameters for best fit of models to data for all energies 0.7-10 GeV/n Bs !n Model 1 .22)X10-3 .35±0 (eq. (2)) 0.638±0 .005 0.527±0.005 (5 Model 2 (7 .30)X10-3 (eq. (3)) 0.729±0 .005 0.392±0.004 .71±0
tions from the core and halo to the total light signal. Here one notes the physical consequences of the mathematical difference between the two versions. In the expression with the full exponential, eq . (2), the core contribution increases, reaches a maximum and then decreases asymptotically to zero. This is not the case if one only takes the approximate expression, eq . (3). Here the core contribution increases to a maximum and gradually saturates. Physically, as the specific energy loss increases, the light from the core is apt to follow the behavior given by the approximate expression. It would never be expected to fall back towards zero. In this sense we might expect eq. (3) to be a better representation if extended to higher specific energy losses, e.g. to account for higher Z relativistic particles.
800
5. Conclusion
600
We have measured the response of plastic scintillator Pilot Y to relativistic nuclei of charge less than or equal to 28 (nickel) for six velocity intervals from 0.7 to 10 GeV/n . These measurements have then been fitted to two versions of a simple model of scintillator saturation . Both produce excellent fits over this charge and energy range although one is slightly favored due to its more realistic physical interpretation .
400 200 0
1200 1000 800 6 400 200 0 Fig. 6. (a) The individual contributions from the core and halo are shown for the fit to the data using Model 1 (eq. (2)) for one energy interval . (b) Same as (a) for Model 2 of eq . (3).
Acknowledgments The authors would like to thank Prof . P. Meyer for many helpful discussions and careful reading of the manuscript. The staff of the Laboratory for Astrophysics and Space Research at the University of Chicago, and in particular W. Johnson, G. Kelderhouse, W. Hollis, L. Glennie are thanked for instrument development. The staff of the National Scientific Balloon Facility in Palestine, Texas ably carried out balloon launch and recovery . References [11 Nuclear Enterprises, Inc., San Carlo, CA, USA . [21 R. Dwyer, S. Jordan and P. Meyer, Nucl . Instr. and Meth . 224 (1984) 247.
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[3] R. Dwyer and P. Meyer, Astrophys . 1294 (1985) 441 . [4] J .B . Birks, The Theory and Practice of Scintillation Counting (Pergamon, New York, 1964) . [5] A. Meyer and R.B. Murray, Phys. Rev. 128 (1962) 98 . [6] R. Voltz, J. Lopes da Silva, G. Lanstriat and A. Coche, J. Chem. Phys . 45 (1966) 3306 . [7] S.P. Ahlen, B .G. Cartwright and G . Tarlé, Nucl. Instr. and Meth. 147 (1977) 321 .
[8] G. Tarlé, S.P . Ahlen and B.G . Cartwright, Astrophys . J. 230 (1979) 607 . [9] M.H. Salomon and S .P . Ahlen, Nucl. Instr. and Meth . 195 (1982) 557 . [10] P.R. Bevington, Data Reduction and Error Analysis for the Physcial Sciences (McGraw-Hill, New York, 1969) ch. 11 .