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Scintillation response of organic and inorganic scintillators
NUCLEAR INSTRUMENTS 8 METHODS IN PHYSICS RESEARCH
__ 55 l!ld ELSEYIER
Sectm
Nuclear Instruments and Methods in Physics Research A 434 (1999) 337-344
A
wwu.eisevier.nl/locatelnima
Scintillation
response of organic and inorganic scintillators L. Papadopoulos*
Imtitute
of Microelectronics, NCSR-Demokritos,
PO Box 60228, 15310 A&
Pnmskeci
.4ttikis. Atkens. Greece
Received 12 August 1998: received in revised form 4 March 1999; accepted 3 April 1999
Abstract A method to evaluate the scintillation response of organic and inorganic scintillators to different heavy ionizing particles is suggested. A function describing the rate of the energy consumed as fluorescence emission is derived, i.e., the differential response with respect to time. This function is then integrated for each ion and scintillator (anthracene. stilbene and CsI(T1)) to determine scintillation response. The resulting scintillation responses are compared to the previously reported measured responses. Agreement to within 3.5% is observed when these data are normalized to each other. In addition, conclusions regarding the quenching parameter kB dependence on the type of the particle and the computed values of kB for certain ions are included. SC; 1999 Elsevier Science B.V. All rights reserved.
with
1. Introduction The rate of energy dissipated as excitation and ionization when a particle passes through a scintillator has been determined to be [l]
i” =
2Tce4z’M
n
(41
m0
4m0
dE _= dt
_
(1)
A fraction of this energy is emitted as fluorescence. Using the Birks relation that describes the quenching effect, it is found that [l] dL
(2)
dt where C = i ln(jtE)
*Corresponding 651 1723.
(3)
author: Tel.: 30-l-6503236: fax: + 30-1-
E-mail address: [email protected]
(L. Papadopoulos)
j1= MI
(51
where mo, e are the mass and charge of an electron, respectively, Z, M are the atomic number and the mass of the incident particle, respectively, I, H are the mean excitation and ionization potential and the electrons per unit volume of the absorber, respectively, and S is the absolute scintillation efficiency. During the stopping process. dL/dt increases to a maximum value at E = E,. This value is determined by differentiating Eq. (2) with respect to E and then setting the result equal to zero. We find kB/lln (,&,) EV = 1 - 2/ln (@,)
0168-9002/99/$-see front matter CC;1999 Elsevier Science B.V. All rights reserved. PII:SO168-9002(99)00489- 1
(6)
338
L. Papudopoulos
Table 1 The values of E, for anthracene. Scintillator
Anthracene Stilbene CsI(T1)
/ Nuclear 1nsttwnerzt.s md A4ethods in Plq~sics Reseurch A 334 (I 999) 337-344
stilbene.
CsI(T1) scintillators
and different
ions as they are computed
from Eq. (6)
E, WV) P
D
He
C
N
0
Mg
Si
3.909 8.963 1.953
8.355 17.84
51.10 85.07 10.52
153.3
218.5
390.6
733.6
950.8
where liB is the quenching parameter. The solution of Eq. (6) gives the value of E, for any case of scintillator and ion. In Table 1 the values of E, for different particles and scintillators are summarized. Note, the values of liB used in these calculations are determined in Section 3. The quenching effect in organic and inorganic crystals is mainly due to two reasons:
25000
I
20000
AfltbXCST? -
Stilbene
(1) Conversion
of some of their electronic excitation energy into vibration energy and heat. with other excited molecules or (11)Interaction ions. A particle passing through a scintillator produces excited and ionized molecules along its track. The excited molecules decay by emitting a photon or quenching. An ionized molecule, by recombination with an electron forms an excited molecule which decays as previously described. For an excited molecule, the probability of decay by emission of a photon rather than by quenching, depends, for a certain molecule, on its environment [2]. When the ionization density increases in the environment of the track, the probability of photon emission decreases. The quenching by process (II) is accentuated and hence the light output is reduced for a more heavily ionizing particle. The energy E, corresponds to the maximum of dL/dt. In the stopping process when the particle energy is E > E, the photon emission increases and when the particle energy becomes E < E, the photon emission decreases, as is shown in Figs. 1 and 2. We may then assume that the energy E, is related to the quenching effect and that
04
I
0
50
100
150
200
250
300
E[MeV]
Fig. 1. The variation of dLjdt as a function of the energy for the ions p. D. He, and for anthracene and stilbene scintillators. 1200000
T
I
Csl(Tl)
SI
1000000 -~
8”O”“O
Mg
--
8
2 $
600000 --
2
0 N C
400000 --
200000 --
o.0
50
100
150
200
250
300
Wevl
Fig. 2 The variation of dL/dr as a function of the energy for the ions p, He. C, N. 0. Mg. Si. and for CsI(T1) scintillator.
electron excitation is the main stopping mechanism for E > E, and that the ionization process dominates for E -c E,.
2. Fluorescence The general dL Tt=(
$ln
emission rate form of Eq. (2) may be written
as
(pE) (7)
E + kBi ln(/tE)
Table 2 The values of the coefficients i, p. 5, as a function of the incident particle atomic number (z) and mass number IA). for antracene. stilbene, and CsI(TI). scmtillators. The coefficient of < is computed so as dL/dr is given in eV!ps. when the energy E of the incident particle is in MeV i (MeV’/cm)
< (MeV3
where
(8)
Anthracene
95.11.4:’
40.51/A
5000,/~;2--’
Stilbene
89.13.4:’
41.86/,4
393oJi--’
3x1/,4
11150,~~~’
268.7.4s’
CsIITI)
with M rz Am,. where A is the mass number of the particle and no, = 1.673 x 10mz4 g is the mass of a proton. From relations (4), (5), (8), and by substituting the values of the different physical constants. the general forms of the coefficients A. 1-1,i, are obtained:
30000
T
Anthracene Stilbene
25000 c
-
1. = 239.22 x 1o-z5 AZ’?? ,~l= 21.785 x 10P’$
(9)
and 4 = 330.89 x lo- l5 ~Sfi?
01 0
where II and r are determined by Eqs. (5) and (6). respectively, of Ref. [l]. We have found for anthracene, stilbene, and CsI, respectively: ilAnth. = 3.98 x 1013 e/cm”. ns,i,. = 3.71 x 1013 e/cm3, tzcs, = 11.2 x 10z3 e/cm”, and IAnth, = 53.8 eV, is,i,, = 50.8 eV. Icsr = 572 eV. The values, of the absolute scintillation efficiencies, of the respective scintillators are [3]: Santh, = 0.038, Sstil, = 0.032. Scsl = 0.03. The coefficients i., ,K <, as functions of A and 2 of the incident particle for anthracene, stilbene, and CsI(T1) are shown in Table 2. Using these values in Eq. (7), dL/dt is found in each case. Figs. 1 and 2 show the variations of dL/dt as a function of E for different particles being stopped by anthracene, stilbene, and CsI(T1) scintillators. Eq. (2) may be expressed as a function of time using the transformation
1
when E, is the incident
particle
IS””
2000
4 2500
3000
Fig. 3. The variation of dL/dt as a function of the time for the ions p. D, He, and for anthracene and stilbene scintillators.
This equation is the result of integration of Eq. (1) by the assumption that C is a constant since the logarithmic term varies slowly with the energy. Figs. 3 and 4 show the variation of dL/dt as a function of time in anthracene, stilbene. and CsI(Tl), respectively. The area under any curve is a graphical representation of the scintillation response.
3. The scintillation Based on
(10) energy.
I”“0
tips1
2:3
=
I
‘I 500
dL
dLdE
dt-
dE dt
response
340
L. Papadopoulos
‘ooo: : 200
0
400
/Nuclear
800
600
Instntment.~ and Methods in Physics Reseclrch A 434 (I 999) 337-314
IOCIO
1200
The product kBi_ in the denominator of Eq. (11) is the factor which defines mainly the behavior of the scintillator. From Eq. (11) we see that the coefficient I;Bi. and consequently the quenching effect. does not have the same weight in all scintillation response cases. In the case of inorganic scintillators like CsI(T1). this coefficient is very small for protons. Consequently. quenching becomes negligible, and the response L is approximately a linear function of energy. The CsI(T1) response to He is close to linear as well. For the heavier ions the coefficient kBi is increased by the factor ,4? and the logarithmic term has the main contribution in the scintillation response. For higher energies this logarithmic term tends to be constant, and consequently the scintillation response becomes linear. The factor )., which includes the A? term, defines the response dependence on the mass number and the atomic number of the particle. The quenching parameter kB characterizes the scintillator and has been defined experimentally by many researchers for different scintillators [3]. The value of kB appears to have a dependence on the type of ion, being greater for protons than for heavier ions. Comparison of Eqs. (8) and (2) in Refs. Cl.41 respectively, gives
1400
UPSI
Csl(ll)-b
TSI
10
5
0
15
20
tips1
Fig. 4. The variation of dL/dt as a function of the time for the ions p, He. (a) and C, N. 0, Mg. Si, (b) and for CsI(T1) scintillator.
C = CA?. Eq. (12) combined kB = a2Az’/C.
dL
dE can be determined
dL=
using Eqs. (1) and (2):
E
-S
E + kBA ln@E)
dE.
(11)
Integrating Eq. (11) between the values E. and E, the value of L is found as a function of Eo. E, is defined from the initial condition where dEJdt becomes negative, or ,uE > 1. In the case of anthracene, stilbene, and CsI the values of E, as a function of the mass number are E,(anthracene) EJstilbene) E,(CsI)
> A/40.51 MeV > A/42.86 MeV
> A/3.81 MeV.
(12) with Eq. (5) in Ref. [4] gives (13)
Horn et al. [4] determined that for protons u2 = 0.326 MeV. The value of C is computed from Eq. (3) at the same energy az is evaluated (i.e., at 4 MeV), whereas 1 and ~1 are computed from Eqs. (4) and (5) respectively. For protons being stopped by CsI(T1) one finds (&I),,,,, = 0.445 x 10e3 cm/MeV. The respective (kBJ&cs, = 0.12 MeV. Integrating Eq. (11) using this value of kBi, and response different values of E,,, the theoretical curve for protons stopped by CsI(T1) was determined and plotted as in Fig. 5. To find the values of kl3 for any ion, the product liBi is initially evaluated using a single point on the experimental L versus E curves and Eq. (1 l), and then the kB value is computed since the value of i, is known. Subsequently, Eq. (11) is integrated using this kB2 value and a range of E, values to
L. Papadopoulos
/ Nuclear Instruments
urld Metimds in Plysirs
determine the theoretical response L as a function of the incident particle energy. To compute (kBE.)s for He and N, experimental response data of Quinton et al. for H+, HeS, Cl’, N1”, Oi6, as given in Fig. 1 in Ref. [S], in arbitrary response units. are used. Normalizing the experimental curve of H+ and the theoretical proton response curve at 22.5 MeV, the normalization scaling constant equal to 1870 eV/a.u is found. To find kBi. for He”, we select, on the respective experimental curve in Fig. 1, Ref. [S], a value of E. in MeV and the respective L normalized in eV and integrating Eq. (11) for these values, kBi and thus kB is determined. Preferably E,, is selected to have the same response L as the proton response at
Fig. 5. The response of CsI(T1) as a function of the incident particle energy for p. He, C, N. 0. The experimental data of Quinton et al. [5] and the respective theoretical response curve, as solid lines. are shown.
341
Research A 434 (1999) 337-344
22.5 MeV. Integration of Eq. (11) for different values of E. gives the theoretical response curve for He4 stopped by CsI(T1). The IiBE. of N’;’ stopped by CsI(T1) is computed, following the same procedure as for He’. Using the experimental response data of Colona et al. as given in Fig. 2 in Ref. [6], and the previously computed value of kBi, for He”, the (kBh)s for ions C”, 016, MgZ4. and Sizs, stopped by CsI(T1) are determined. Normalizing the experimental and theoretical response curves at 102 MeV of the He4 curve the normalization scale constant equal to 12 100 eV/a.u. is found. A parallel to energy axis from the normalization point, the energies E0 for equal response for all ions are defined. Then, by the same procedure as above, (kBi,)s of C”, 0i6, Mgz4, and SiZ8 are determined. Since it is difficult to have a closed-form solution for integral of Eq. (1 l), an iterative process is used. In any case, since the experimental response L and the respective energy E, at the normalization point are known, the value of kBi for the given E. is varied such that the value of kBi. for which the integral gives the known response L is found. In the case of organic scintillators, anthracene and stilbene, we base the evaluation of (kBi)s for deuterons, molecular hydrogen and alphas, on the experimental data of Taylor et al. as given in Figs. 3,4 and 7 in Ref. [8]. kBi for protons stopped by anthracene and stilbene have been experimentally determined since the decade of 1950s [9] (Table 3) with the corresponding values: (kB)p.Anth,= 6.3 cm air equivalent/MeV and (kB),.,,i,, = 13.7 cm
Table 3 The values of kB for anthracene, stilbene, and CsI(TI) scintillators and certain ions as they are estimated using the iterative process and the numerical integration of Eq. (1I ) to define the product kBi. Bold-faced numbers represent values for both protons given by Fowler and Roos [9] and deuterons computed on the basis of Hz(p) data curves. The regular numbers are the values computed from the experimental data Scintillator
kB (cm/MeV) P
Anthracene 4.91x10-2 Stilbene
15.93 x 1O-3 11.25x10-”
CsI(TI)
4.45 x 1o-J
D
He
5.26 x 1O-3 5.23x lo-’
3.94 x 10m3
16.04 x 10m3 11.21x10-’
8.84 x 1O-3
1.39 x 10-4
C
N
0
Mg
Si
1.64 X lo-”
1.48 x lo-“
1.31 X 1o-4
0.95 X 10-4
0.78 x 1o-4
342
L. Papadopotdos
J Nuclear Imtmments
and Methods in Phwics Re.wwch
air equivalent/MeV, or fitting the Bragg-Kleemann rule (kB)p.Anth.= 11.2 x 10m3 cm/MeV and (kB),,stii. = 4.91 x lo- 3 cm/MeV. Integrating Eq. (11) for different values of EO, based on these values of (kB),, theoretical response curves for protons stopped by anthracene and stilbene are determined, as shown in Fig. 8. Fig. 7 in Ref. [S] shows the experimental proton response curve. in arbitrary units, stopped by anthracene. Normalizing the two curves, theoretical and experimental, of anthracene, at 8 MeV, the normalization scaling constant equal to 638 eV/a.u. is found. This scaling constant is also valid for the curves of Figs. 3 and 4, Ref. [S]. Based on the known values of (kBi.), for anthracene and stilbene, and the experimental data as given in Figs. 3 and 4 in Ref. [S], respectively. following the same procedure as in the case of CsI(T1). the kB3. values for deuterons and alphas, are found. To begin this process we select equal response data points on the curves (i.e. at 8 MeV for Hf and D and 16 MeV for He’ in the case of anthracene, and 8 and 15.1 MeV for stilbene. respectively). For molecular hydrogen we may compute the response data independently of experimental data, based on the well-known process that the molecular hydrogen ions are dissociated when they pass through the first layers of the crystal. So the response of molecular ions is equivalent to the response of two protons with half of the molecular hydrogen energy. i.e. L,,(&J
= 2L,(-W2).
4. Comparison with the experimental
A 434 (1999) 337-344
on the H’ response experimental curve. the relative response data in eV. of CsI(T1). versus incident particle energy in MeV, and the respective theoretical response curves, as solid lines. for these ions. are shown in Fig. 5. The scintillation response of CsI(T1) to intermediate-energy heavy ions reactions has been studied, by Colona et al. [6]. as well. The experimental response data normalized in eV. for He”. Cl’. 016. Mg”‘, Si18, and other ions. as a function of the incident particle energy in MeV, and the respective theoretical curves as solid lines. are shown in Fig. 6. At 102 MeV experimental and theoretical response curves of He are normalized. The anthracene and stilbene energy response, normalized in eV, as a function of the incident particle energy in MeV. measured experimentally by Taylor et al. [7.8] for deuterons, molecular hydrogen ions, and alphas. are shown in Figs. 7-9. Fig. 8 shows a respective curve for protons stopped by anthracene. In the same figures the respective theoretical response curves. are shown as solid lines. versus the same incident particle energy in MeV. The values of E0 and L from the respective published experimental response curves were determined by the visual inspection of the published graphs. This process can potentially introduce significant inaccuracies in the given data. Nonetheless, the quantity AL:‘L. where AL is the difference between the responses of the experimental and
(14)
results
Theoretical response curves have been produced for certain heavy ions being stopped by CsI(T1) and anthracene and stilbene scintillators. The mathematical procedure was carried out by fitting the numerical integration using the “Mathematics @” computer program [lo]. Quinton et al. [S] have determined the light output from thallium- activated cesium iodide crystals using the heavy ions Cl’. N’“, 016. with energies up to 10 MeV per nucleon and compared it with those produced by protons and r-particles of known energies. Normalizing the scale at 22.5 MeV
Fig. 6. particle Colona as solid
The response of CsUTI) as a function of the mcldent energy for He. C. 0. Mg. Si. The experimental data of et al. [6] and the respective theoretical response curve. lines. are shown.
343
,/
L. Papadopoulos / Nuclear Instruments and Methods in Phwics Research A 434 (I 999) 337-344 140000
j
HzD 12O”O”
100000
0
5
10
15
20
25
I
Stllbene
0
kWV1
I
200000
Anthracene
1
w :/ exp.po1nts
100000
0
0 protons
0
5
10
15
20
25
Fig. 9. particle Taylor as solid
Hz D
;
5
15
10
5
Fig. 7. The response of anthracene as a function of the incident particle energy for D. Hz. and He. The experimental data of Taylor et al. [S] and the respective theoretical response curves. as solid lines, are shown.
600000
HZ(P)
20
25
WV1
The response of stilbene as a function of the incident energy for D. H,. and He. The experimental data of et al. [8]. and the respective theoretical response curve, lines. are shown.
curves of H3 and D are shown after normalization of the respective experimental curves, evaluating the respective (kBA)s and then integrating Eq. (11) for different values of E,,, and the curve produced by fitting relation (14), based on the known proton data. These curves, in the case of anthracene, are in good conformity. with a deviation between them better than 2.7%. In the case of stilbene the respective deviation is within 27%.
5. Discussion
kWv1
Fig. 8. The response of anthracene as a function of the incident particle energy for protons. The experimental data of Taylor et al. [S] and the respective theoretical response curve, as sohd line. are shown.
theoretical data and L the experimental data, for different points on the curves are measured. Theoretical response data. appears to be in satisfactory agreement with the experimental data, with an average deviation better than 2.5%, in all cases. Theoretical response data for H, ions stopped by anthracene and stilbene, have been computed by two different ways. In Figs. 7 and 9 the two theoretical response curves are shown. The common
To theoretically predict the experimental curves in Figs. 5-9, changing the Y-axis units, a normalization point. and consequently. a normalization constant. is used. To use the same normalization constant, to reproduce curves drawn by the same scale, a necessary presupposition is considered. Under this condition there is not a good fitting of experimental results to the theoretical response curves. This means that to use the same normalization scale constant is a necessary condition, but not sufficient. Michaelian et al. [11,12], have used different normalization constants for each individual ion, to obtain a best fit of the model generated curves to the data. In this work it is supposed that the unconformity between the curves is due to the kB dependence on the type of ion.
344
L. Papadopoulos
Nuclear Instruments
Methods VI
Consequently, the product evaluated and kB was computed for every ion and scintillator. To check the conformity of theoretical and experimental data in the case of Hz ions stopped by anthracene and stilbene, the two theoretical curves HZ, D and H?(p) are compared. The credibility of this checking is absolute because the curve Hz(p) is drawn independently of the given experimental data, and depends only on the value of (kB), of protons stopped by anthracene and stilbene, respectively, determined by other experiments [3,9]. Figs. 7 and 9 show these two curves, respectively. The deviation of 2.7%. in the case of anthracene, shows a good conformity of the two curves produced by different ways and validates the method suggested. The large deviation of the respective curves in the case of stilbene, perhaps due to energy uncertainties which are ascertained in the energy response curves for deuterons on stilbene [S]. kB for protons stopped by stilbene may be computed using the experimental data as shown, in common response curve for molecular hydrogen ions and deuterons, in Fig. 4, Ref. [S]. Normalizing this curve in eV. and computing the common kBi for H2 and D, we may produce theoretical response data for these ions. by integrating Eq. (11) for various values of E,. Dividing by two these data and the respective values of E,,, the proton data, according to Eq. (14) are produced. Integrating Eq. (11) at E,, = 8 MeV, (kB3.),.stil. = 1.42 MeV is found, and (kB),,stil, = 15.93 cm/MeV in stilbene or (liB)p,stil, = 19.4 cm air equivalent/MeV. This value is not in good agreement with the respective value found
Research A
(I 999)
experimentally by Fowler and Roos [9], which is (kB),.s,ii, = 13.7 cm air equivalent/MeV. The difference perhaps is due to the same reasons as described above.
Acknowledgements The author wishes to thank Dr. N. Glezos for his fruitful contribution to carry out this work. Thanks are due, as well, to Dr. J. Raptis for his computing aid. and Dr. E. Kossionides for the useful discussion on the subject.
References [I] L. Papadopoulos,
Nucl. Instr. and Meth. A 401 (1997) 32. [2] F.D. Brooks, Nucl. Instr. and Meth. 4 (1959) 151, [3] J.B. Birks. The Theory and Practice of Scintillation Counting, Pergamon Press. New York, 1964. pp. 189-191. [4] D. Horn, G.C. Ball. A. Galindo-Uribarri, E. Hagberg, R.B. Walker. Nucl. Instr. and Meth. A 320 (1992) 273. [5] A.R. Quinton, C.E. Anderson, W.J. Knox, Phys. Rev. 115 (4) (1959) 886. [6] N. Colona. G.J. Wozniak, A. Veeck. W. Skulski. G.W. Goth, L. Manduci. P.M. Milazzo, P.F. Mastinu. Nucl. Instr. and Meth. A 321 (1993) 529. [7] C.J. Taylor, M.E. Remley, W.K. Jentschke. P.G. Kruger. Phys. Rev. 83 (1951) 169. [S] C.J. Taylor. W.K. Jentschke, M.E. Remley. F.S. Eby. P.G. Kruger. Phys. Rev. 54 (5) (1951) 1034. [9] J.M. Fowler. C.E. Roos. Phys. Rev. 98 (4) (1995) 996. [lo] Copyright ‘(:I 1988, 1991. 1996. by Wolfram Research, Inc. [11] K. Michaelian. A. Menchaca-Rocha. Phys. Rev. 49 (13) (1994) 15 550. [l?] K. Michaelian, A. Menchaca-Rocha, E. Belmont-Moreno, Nucl. Instr. and Meth. A 356 (1995) 297.
__ 55 l!ld ELSEYIER
Sectm
Nuclear Instruments and Methods in Physics Research A 434 (1999) 337-344
A
wwu.eisevier.nl/locatelnima
Scintillation
response of organic and inorganic scintillators L. Papadopoulos*
Imtitute
of Microelectronics, NCSR-Demokritos,
PO Box 60228, 15310 A&
Pnmskeci
.4ttikis. Atkens. Greece
Received 12 August 1998: received in revised form 4 March 1999; accepted 3 April 1999
Abstract A method to evaluate the scintillation response of organic and inorganic scintillators to different heavy ionizing particles is suggested. A function describing the rate of the energy consumed as fluorescence emission is derived, i.e., the differential response with respect to time. This function is then integrated for each ion and scintillator (anthracene. stilbene and CsI(T1)) to determine scintillation response. The resulting scintillation responses are compared to the previously reported measured responses. Agreement to within 3.5% is observed when these data are normalized to each other. In addition, conclusions regarding the quenching parameter kB dependence on the type of the particle and the computed values of kB for certain ions are included. SC; 1999 Elsevier Science B.V. All rights reserved.
with
1. Introduction The rate of energy dissipated as excitation and ionization when a particle passes through a scintillator has been determined to be [l]
i” =
2Tce4z’M
n
(41
m0
4m0
dE _= dt
_
(1)
A fraction of this energy is emitted as fluorescence. Using the Birks relation that describes the quenching effect, it is found that [l] dL
(2)
dt where C = i ln(jtE)
*Corresponding 651 1723.
(3)
author: Tel.: 30-l-6503236: fax: + 30-1-
E-mail address: [email protected]
(L. Papadopoulos)
j1= MI
(51
where mo, e are the mass and charge of an electron, respectively, Z, M are the atomic number and the mass of the incident particle, respectively, I, H are the mean excitation and ionization potential and the electrons per unit volume of the absorber, respectively, and S is the absolute scintillation efficiency. During the stopping process. dL/dt increases to a maximum value at E = E,. This value is determined by differentiating Eq. (2) with respect to E and then setting the result equal to zero. We find kB/lln (,&,) EV = 1 - 2/ln (@,)
0168-9002/99/$-see front matter CC;1999 Elsevier Science B.V. All rights reserved. PII:SO168-9002(99)00489- 1
(6)
338
L. Papudopoulos
Table 1 The values of E, for anthracene. Scintillator
Anthracene Stilbene CsI(T1)
/ Nuclear 1nsttwnerzt.s md A4ethods in Plq~sics Reseurch A 334 (I 999) 337-344
stilbene.
CsI(T1) scintillators
and different
ions as they are computed
from Eq. (6)
E, WV) P
D
He
C
N
0
Mg
Si
3.909 8.963 1.953
8.355 17.84
51.10 85.07 10.52
153.3
218.5
390.6
733.6
950.8
where liB is the quenching parameter. The solution of Eq. (6) gives the value of E, for any case of scintillator and ion. In Table 1 the values of E, for different particles and scintillators are summarized. Note, the values of liB used in these calculations are determined in Section 3. The quenching effect in organic and inorganic crystals is mainly due to two reasons:
25000
I
20000
AfltbXCST? -
Stilbene
(1) Conversion
of some of their electronic excitation energy into vibration energy and heat. with other excited molecules or (11)Interaction ions. A particle passing through a scintillator produces excited and ionized molecules along its track. The excited molecules decay by emitting a photon or quenching. An ionized molecule, by recombination with an electron forms an excited molecule which decays as previously described. For an excited molecule, the probability of decay by emission of a photon rather than by quenching, depends, for a certain molecule, on its environment [2]. When the ionization density increases in the environment of the track, the probability of photon emission decreases. The quenching by process (II) is accentuated and hence the light output is reduced for a more heavily ionizing particle. The energy E, corresponds to the maximum of dL/dt. In the stopping process when the particle energy is E > E, the photon emission increases and when the particle energy becomes E < E, the photon emission decreases, as is shown in Figs. 1 and 2. We may then assume that the energy E, is related to the quenching effect and that
04
I
0
50
100
150
200
250
300
E[MeV]
Fig. 1. The variation of dLjdt as a function of the energy for the ions p. D. He, and for anthracene and stilbene scintillators. 1200000
T
I
Csl(Tl)
SI
1000000 -~
8”O”“O
Mg
--
8
2 $
600000 --
2
0 N C
400000 --
200000 --
o.0
50
100
150
200
250
300
Wevl
Fig. 2 The variation of dL/dr as a function of the energy for the ions p, He. C, N. 0. Mg. Si. and for CsI(T1) scintillator.
electron excitation is the main stopping mechanism for E > E, and that the ionization process dominates for E -c E,.
2. Fluorescence The general dL Tt=(
$ln
emission rate form of Eq. (2) may be written
as
(pE) (7)
E + kBi ln(/tE)
Table 2 The values of the coefficients i, p. 5, as a function of the incident particle atomic number (z) and mass number IA). for antracene. stilbene, and CsI(TI). scmtillators. The coefficient of < is computed so as dL/dr is given in eV!ps. when the energy E of the incident particle is in MeV i (MeV’/cm)
< (MeV3
where
(8)
Anthracene
95.11.4:’
40.51/A
5000,/~;2--’
Stilbene
89.13.4:’
41.86/,4
393oJi--’
3x1/,4
11150,~~~’
268.7.4s’
CsIITI)
with M rz Am,. where A is the mass number of the particle and no, = 1.673 x 10mz4 g is the mass of a proton. From relations (4), (5), (8), and by substituting the values of the different physical constants. the general forms of the coefficients A. 1-1,i, are obtained:
30000
T
Anthracene Stilbene
25000 c
-
1. = 239.22 x 1o-z5 AZ’?? ,~l= 21.785 x 10P’$
(9)
and 4 = 330.89 x lo- l5 ~Sfi?
01 0
where II and r are determined by Eqs. (5) and (6). respectively, of Ref. [l]. We have found for anthracene, stilbene, and CsI, respectively: ilAnth. = 3.98 x 1013 e/cm”. ns,i,. = 3.71 x 1013 e/cm3, tzcs, = 11.2 x 10z3 e/cm”, and IAnth, = 53.8 eV, is,i,, = 50.8 eV. Icsr = 572 eV. The values, of the absolute scintillation efficiencies, of the respective scintillators are [3]: Santh, = 0.038, Sstil, = 0.032. Scsl = 0.03. The coefficients i., ,K <, as functions of A and 2 of the incident particle for anthracene, stilbene, and CsI(T1) are shown in Table 2. Using these values in Eq. (7), dL/dt is found in each case. Figs. 1 and 2 show the variations of dL/dt as a function of E for different particles being stopped by anthracene, stilbene, and CsI(T1) scintillators. Eq. (2) may be expressed as a function of time using the transformation
1
when E, is the incident
particle
IS””
2000
4 2500
3000
Fig. 3. The variation of dL/dt as a function of the time for the ions p. D, He, and for anthracene and stilbene scintillators.
This equation is the result of integration of Eq. (1) by the assumption that C is a constant since the logarithmic term varies slowly with the energy. Figs. 3 and 4 show the variation of dL/dt as a function of time in anthracene, stilbene. and CsI(Tl), respectively. The area under any curve is a graphical representation of the scintillation response.
3. The scintillation Based on
(10) energy.
I”“0
tips1
2:3
=
I
‘I 500
dL
dLdE
dt-
dE dt
response
340
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0
400
/Nuclear
800
600
Instntment.~ and Methods in Physics Reseclrch A 434 (I 999) 337-314
IOCIO
1200
The product kBi_ in the denominator of Eq. (11) is the factor which defines mainly the behavior of the scintillator. From Eq. (11) we see that the coefficient I;Bi. and consequently the quenching effect. does not have the same weight in all scintillation response cases. In the case of inorganic scintillators like CsI(T1). this coefficient is very small for protons. Consequently. quenching becomes negligible, and the response L is approximately a linear function of energy. The CsI(T1) response to He is close to linear as well. For the heavier ions the coefficient kBi is increased by the factor ,4? and the logarithmic term has the main contribution in the scintillation response. For higher energies this logarithmic term tends to be constant, and consequently the scintillation response becomes linear. The factor )., which includes the A? term, defines the response dependence on the mass number and the atomic number of the particle. The quenching parameter kB characterizes the scintillator and has been defined experimentally by many researchers for different scintillators [3]. The value of kB appears to have a dependence on the type of ion, being greater for protons than for heavier ions. Comparison of Eqs. (8) and (2) in Refs. Cl.41 respectively, gives
1400
UPSI
Csl(ll)-b
TSI
10
5
0
15
20
tips1
Fig. 4. The variation of dL/dt as a function of the time for the ions p, He. (a) and C, N. 0, Mg. Si, (b) and for CsI(T1) scintillator.
C = CA?. Eq. (12) combined kB = a2Az’/C.
dL
dE can be determined
dL=
using Eqs. (1) and (2):
E
-S
E + kBA ln@E)
dE.
(11)
Integrating Eq. (11) between the values E. and E, the value of L is found as a function of Eo. E, is defined from the initial condition where dEJdt becomes negative, or ,uE > 1. In the case of anthracene, stilbene, and CsI the values of E, as a function of the mass number are E,(anthracene) EJstilbene) E,(CsI)
> A/40.51 MeV > A/42.86 MeV
> A/3.81 MeV.
(12) with Eq. (5) in Ref. [4] gives (13)
Horn et al. [4] determined that for protons u2 = 0.326 MeV. The value of C is computed from Eq. (3) at the same energy az is evaluated (i.e., at 4 MeV), whereas 1 and ~1 are computed from Eqs. (4) and (5) respectively. For protons being stopped by CsI(T1) one finds (&I),,,,, = 0.445 x 10e3 cm/MeV. The respective (kBJ&cs, = 0.12 MeV. Integrating Eq. (11) using this value of kBi, and response different values of E,,, the theoretical curve for protons stopped by CsI(T1) was determined and plotted as in Fig. 5. To find the values of kl3 for any ion, the product liBi is initially evaluated using a single point on the experimental L versus E curves and Eq. (1 l), and then the kB value is computed since the value of i, is known. Subsequently, Eq. (11) is integrated using this kB2 value and a range of E, values to
L. Papadopoulos
/ Nuclear Instruments
urld Metimds in Plysirs
determine the theoretical response L as a function of the incident particle energy. To compute (kBE.)s for He and N, experimental response data of Quinton et al. for H+, HeS, Cl’, N1”, Oi6, as given in Fig. 1 in Ref. [S], in arbitrary response units. are used. Normalizing the experimental curve of H+ and the theoretical proton response curve at 22.5 MeV, the normalization scaling constant equal to 1870 eV/a.u is found. To find kBi. for He”, we select, on the respective experimental curve in Fig. 1, Ref. [S], a value of E. in MeV and the respective L normalized in eV and integrating Eq. (11) for these values, kBi and thus kB is determined. Preferably E,, is selected to have the same response L as the proton response at
Fig. 5. The response of CsI(T1) as a function of the incident particle energy for p. He, C, N. 0. The experimental data of Quinton et al. [5] and the respective theoretical response curve, as solid lines. are shown.
341
Research A 434 (1999) 337-344
22.5 MeV. Integration of Eq. (11) for different values of E. gives the theoretical response curve for He4 stopped by CsI(T1). The IiBE. of N’;’ stopped by CsI(T1) is computed, following the same procedure as for He’. Using the experimental response data of Colona et al. as given in Fig. 2 in Ref. [6], and the previously computed value of kBi, for He”, the (kBh)s for ions C”, 016, MgZ4. and Sizs, stopped by CsI(T1) are determined. Normalizing the experimental and theoretical response curves at 102 MeV of the He4 curve the normalization scale constant equal to 12 100 eV/a.u. is found. A parallel to energy axis from the normalization point, the energies E0 for equal response for all ions are defined. Then, by the same procedure as above, (kBi,)s of C”, 0i6, Mgz4, and SiZ8 are determined. Since it is difficult to have a closed-form solution for integral of Eq. (1 l), an iterative process is used. In any case, since the experimental response L and the respective energy E, at the normalization point are known, the value of kBi for the given E. is varied such that the value of kBi. for which the integral gives the known response L is found. In the case of organic scintillators, anthracene and stilbene, we base the evaluation of (kBi)s for deuterons, molecular hydrogen and alphas, on the experimental data of Taylor et al. as given in Figs. 3,4 and 7 in Ref. [8]. kBi for protons stopped by anthracene and stilbene have been experimentally determined since the decade of 1950s [9] (Table 3) with the corresponding values: (kB)p.Anth,= 6.3 cm air equivalent/MeV and (kB),.,,i,, = 13.7 cm
Table 3 The values of kB for anthracene, stilbene, and CsI(TI) scintillators and certain ions as they are estimated using the iterative process and the numerical integration of Eq. (1I ) to define the product kBi. Bold-faced numbers represent values for both protons given by Fowler and Roos [9] and deuterons computed on the basis of Hz(p) data curves. The regular numbers are the values computed from the experimental data Scintillator
kB (cm/MeV) P
Anthracene 4.91x10-2 Stilbene
15.93 x 1O-3 11.25x10-”
CsI(TI)
4.45 x 1o-J
D
He
5.26 x 1O-3 5.23x lo-’
3.94 x 10m3
16.04 x 10m3 11.21x10-’
8.84 x 1O-3
1.39 x 10-4
C
N
0
Mg
Si
1.64 X lo-”
1.48 x lo-“
1.31 X 1o-4
0.95 X 10-4
0.78 x 1o-4
342
L. Papadopotdos
J Nuclear Imtmments
and Methods in Phwics Re.wwch
air equivalent/MeV, or fitting the Bragg-Kleemann rule (kB)p.Anth.= 11.2 x 10m3 cm/MeV and (kB),,stii. = 4.91 x lo- 3 cm/MeV. Integrating Eq. (11) for different values of EO, based on these values of (kB),, theoretical response curves for protons stopped by anthracene and stilbene are determined, as shown in Fig. 8. Fig. 7 in Ref. [S] shows the experimental proton response curve. in arbitrary units, stopped by anthracene. Normalizing the two curves, theoretical and experimental, of anthracene, at 8 MeV, the normalization scaling constant equal to 638 eV/a.u. is found. This scaling constant is also valid for the curves of Figs. 3 and 4, Ref. [S]. Based on the known values of (kBi.), for anthracene and stilbene, and the experimental data as given in Figs. 3 and 4 in Ref. [S], respectively. following the same procedure as in the case of CsI(T1). the kB3. values for deuterons and alphas, are found. To begin this process we select equal response data points on the curves (i.e. at 8 MeV for Hf and D and 16 MeV for He’ in the case of anthracene, and 8 and 15.1 MeV for stilbene. respectively). For molecular hydrogen we may compute the response data independently of experimental data, based on the well-known process that the molecular hydrogen ions are dissociated when they pass through the first layers of the crystal. So the response of molecular ions is equivalent to the response of two protons with half of the molecular hydrogen energy. i.e. L,,(&J
= 2L,(-W2).
4. Comparison with the experimental
A 434 (1999) 337-344
on the H’ response experimental curve. the relative response data in eV. of CsI(T1). versus incident particle energy in MeV, and the respective theoretical response curves, as solid lines. for these ions. are shown in Fig. 5. The scintillation response of CsI(T1) to intermediate-energy heavy ions reactions has been studied, by Colona et al. [6]. as well. The experimental response data normalized in eV. for He”. Cl’. 016. Mg”‘, Si18, and other ions. as a function of the incident particle energy in MeV, and the respective theoretical curves as solid lines. are shown in Fig. 6. At 102 MeV experimental and theoretical response curves of He are normalized. The anthracene and stilbene energy response, normalized in eV, as a function of the incident particle energy in MeV. measured experimentally by Taylor et al. [7.8] for deuterons, molecular hydrogen ions, and alphas. are shown in Figs. 7-9. Fig. 8 shows a respective curve for protons stopped by anthracene. In the same figures the respective theoretical response curves. are shown as solid lines. versus the same incident particle energy in MeV. The values of E0 and L from the respective published experimental response curves were determined by the visual inspection of the published graphs. This process can potentially introduce significant inaccuracies in the given data. Nonetheless, the quantity AL:‘L. where AL is the difference between the responses of the experimental and
(14)
results
Theoretical response curves have been produced for certain heavy ions being stopped by CsI(T1) and anthracene and stilbene scintillators. The mathematical procedure was carried out by fitting the numerical integration using the “Mathematics @” computer program [lo]. Quinton et al. [S] have determined the light output from thallium- activated cesium iodide crystals using the heavy ions Cl’. N’“, 016. with energies up to 10 MeV per nucleon and compared it with those produced by protons and r-particles of known energies. Normalizing the scale at 22.5 MeV
Fig. 6. particle Colona as solid
The response of CsUTI) as a function of the mcldent energy for He. C. 0. Mg. Si. The experimental data of et al. [6] and the respective theoretical response curve. lines. are shown.
343
,/
L. Papadopoulos / Nuclear Instruments and Methods in Phwics Research A 434 (I 999) 337-344 140000
j
HzD 12O”O”
100000
0
5
10
15
20
25
I
Stllbene
0
kWV1
I
200000
Anthracene
1
w :/ exp.po1nts
100000
0
0 protons
0
5
10
15
20
25
Fig. 9. particle Taylor as solid
Hz D
;
5
15
10
5
Fig. 7. The response of anthracene as a function of the incident particle energy for D. Hz. and He. The experimental data of Taylor et al. [S] and the respective theoretical response curves. as solid lines, are shown.
600000
HZ(P)
20
25
WV1
The response of stilbene as a function of the incident energy for D. H,. and He. The experimental data of et al. [8]. and the respective theoretical response curve, lines. are shown.
curves of H3 and D are shown after normalization of the respective experimental curves, evaluating the respective (kBA)s and then integrating Eq. (11) for different values of E,,, and the curve produced by fitting relation (14), based on the known proton data. These curves, in the case of anthracene, are in good conformity. with a deviation between them better than 2.7%. In the case of stilbene the respective deviation is within 27%.
5. Discussion
kWv1
Fig. 8. The response of anthracene as a function of the incident particle energy for protons. The experimental data of Taylor et al. [S] and the respective theoretical response curve, as sohd line. are shown.
theoretical data and L the experimental data, for different points on the curves are measured. Theoretical response data. appears to be in satisfactory agreement with the experimental data, with an average deviation better than 2.5%, in all cases. Theoretical response data for H, ions stopped by anthracene and stilbene, have been computed by two different ways. In Figs. 7 and 9 the two theoretical response curves are shown. The common
To theoretically predict the experimental curves in Figs. 5-9, changing the Y-axis units, a normalization point. and consequently. a normalization constant. is used. To use the same normalization constant, to reproduce curves drawn by the same scale, a necessary presupposition is considered. Under this condition there is not a good fitting of experimental results to the theoretical response curves. This means that to use the same normalization scale constant is a necessary condition, but not sufficient. Michaelian et al. [11,12], have used different normalization constants for each individual ion, to obtain a best fit of the model generated curves to the data. In this work it is supposed that the unconformity between the curves is due to the kB dependence on the type of ion.
344
L. Papadopoulos
Nuclear Instruments
Methods VI
Consequently, the product evaluated and kB was computed for every ion and scintillator. To check the conformity of theoretical and experimental data in the case of Hz ions stopped by anthracene and stilbene, the two theoretical curves HZ, D and H?(p) are compared. The credibility of this checking is absolute because the curve Hz(p) is drawn independently of the given experimental data, and depends only on the value of (kB), of protons stopped by anthracene and stilbene, respectively, determined by other experiments [3,9]. Figs. 7 and 9 show these two curves, respectively. The deviation of 2.7%. in the case of anthracene, shows a good conformity of the two curves produced by different ways and validates the method suggested. The large deviation of the respective curves in the case of stilbene, perhaps due to energy uncertainties which are ascertained in the energy response curves for deuterons on stilbene [S]. kB for protons stopped by stilbene may be computed using the experimental data as shown, in common response curve for molecular hydrogen ions and deuterons, in Fig. 4, Ref. [S]. Normalizing this curve in eV. and computing the common kBi for H2 and D, we may produce theoretical response data for these ions. by integrating Eq. (11) for various values of E,. Dividing by two these data and the respective values of E,,, the proton data, according to Eq. (14) are produced. Integrating Eq. (11) at E,, = 8 MeV, (kB3.),.stil. = 1.42 MeV is found, and (kB),,stil, = 15.93 cm/MeV in stilbene or (liB)p,stil, = 19.4 cm air equivalent/MeV. This value is not in good agreement with the respective value found
Research A
(I 999)
experimentally by Fowler and Roos [9], which is (kB),.s,ii, = 13.7 cm air equivalent/MeV. The difference perhaps is due to the same reasons as described above.
Acknowledgements The author wishes to thank Dr. N. Glezos for his fruitful contribution to carry out this work. Thanks are due, as well, to Dr. J. Raptis for his computing aid. and Dr. E. Kossionides for the useful discussion on the subject.
References [I] L. Papadopoulos,
Nucl. Instr. and Meth. A 401 (1997) 32. [2] F.D. Brooks, Nucl. Instr. and Meth. 4 (1959) 151, [3] J.B. Birks. The Theory and Practice of Scintillation Counting, Pergamon Press. New York, 1964. pp. 189-191. [4] D. Horn, G.C. Ball. A. Galindo-Uribarri, E. Hagberg, R.B. Walker. Nucl. Instr. and Meth. A 320 (1992) 273. [5] A.R. Quinton, C.E. Anderson, W.J. Knox, Phys. Rev. 115 (4) (1959) 886. [6] N. Colona. G.J. Wozniak, A. Veeck. W. Skulski. G.W. Goth, L. Manduci. P.M. Milazzo, P.F. Mastinu. Nucl. Instr. and Meth. A 321 (1993) 529. [7] C.J. Taylor, M.E. Remley, W.K. Jentschke. P.G. Kruger. Phys. Rev. 83 (1951) 169. [S] C.J. Taylor. W.K. Jentschke, M.E. Remley. F.S. Eby. P.G. Kruger. Phys. Rev. 54 (5) (1951) 1034. [9] J.M. Fowler. C.E. Roos. Phys. Rev. 98 (4) (1995) 996. [lo] Copyright ‘(:I 1988, 1991. 1996. by Wolfram Research, Inc. [11] K. Michaelian. A. Menchaca-Rocha. Phys. Rev. 49 (13) (1994) 15 550. [l?] K. Michaelian, A. Menchaca-Rocha, E. Belmont-Moreno, Nucl. Instr. and Meth. A 356 (1995) 297.