A new analytical method to calibrate cylindrical phoswich and LaBr3(Ce) scintillation detectors

Nuclear Instruments and Methods in Physics Research A 621 (2010) 413–418

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

A new analytical method to calibrate cylindrical phoswich and LaBr3(Ce) scintillation detectors Mahmoud I. Abbas Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt

a r t i c l e in fo

abstract

Article history: Received 11 February 2010 Received in revised form 26 April 2010 Accepted 10 May 2010 Available online 24 May 2010

A new analytical method of efficiency calibration is proposed for cylindrical phoswich and lanthanum bromide (LaBr3:Ce) scintillation detectors. This method depends on the accurate analytical calculation of two important factors: the path length d, the photon traverses within the active volume of a gamma detector, and the geometrical solid angle O, subtended by the source to the detector at the point of entrance. In addition, the attenuation of photons by the detector housing materials is also treated by calculating the photon path length through these materials. The comparisons with the experimental and Monte Carlo method data reported in the literature indicate that the present method is useful in the efficiency calibration of the cylindrical phoswich and lanthanum bromide (LaBr3:Ce) scintillation detectors. & 2010 Elsevier B.V. All rights reserved.

Keywords: Cylindrical phoswich and LaBr3(Ce) scintillation detectors Geometrical efficiency Total efficiency Point and disk sources

1. Introduction Two different cylindrical scintillation detectors (phoswich and LaBr3:Ce) were used in this investigation. A phoswich detector consists of two or more scintillation detectors optically coupled as a phosphor sandwich, from which the scintillation light output is viewed by a single photomultiplier tube (PMT). This unique detector arrangement is designated as a PHOSWICH, which is the acronym for PHOSphor sandWICH [1]. Much current research is directed to the development of phoswich detectors as practical instruments for the simultaneous measurement and discrimination of alpha, beta, gamma or neutron radiation [2–16]. The cerium-doped lanthanum halide crystals have gained special interest due to their high density and atomic number, which results in excellent scintillation properties and higher detection efficiencies in comparison to NaI(Tl) [17–24]. The present work is mainly concerned with introducing a new straightforward theoretical approach to calibrate cylindrical phoswich and lanthanum bromide (LaBr3:Ce) scintillation detectors for isotropic radiating gamma-ray (point and plane) sources. This approach is based on the direct mathematical method reported by Selim and Abbas [25–32] and has been used successfully before to calibrate point, plane and volumetric sources with cylindrical, well-type, parallelepiped and 4p NaI(Tl) detectors. In addition, the present method is free of some major inconveniences of the conventional methods. Most importantly, it calculates the cylindrical phoswich

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and lanthanum bromide (LaBr3:Ce) scintillation detector’s efficiencies without the need for standard sources, as is the case for experimental methods, nor optimization of detector parameters as for simulation methods. The work described below involves the use of a new direct analytical expression to calculate the efficiencies of two different cylindrical scintillation detectors (phoswich and LaBr3:Ce). The arrangement of this paper is as follows. Section 2 presents direct mathematical formulae for the absolute efficiencies in the case of isotropic radiating non-axial point, and plane (circular disk) sources. The attenuation of photons by the CaF2(Eu) crystal, the quartz (SiO2) dead layer (in the case of phoswich detector) and the aluminum housing detector case (in the case of both, the phoswich and LaBr3(Ce) detectors) is also treated. Section 3 contains comparisons between the calculated efficiency using the formulae derived in this work with the published experimental and simulated values illustrating the validity of the present mathematical formulae. Conclusions are presented in Section 4.

2. Mathematical viewpoint 2.1. The case of a non-axial point source In the following, direct analytical expression for the absolute efficiency of a cylindrical detector is derived using an isotropic radiating non-axial point source. The location of the isotropic radiating point source P(r,h) is defined by the quantities (r,h) and the direction of the photon incidence by the polar (y) and the

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azimuthal (f) angles. For each photon emitted from the isotropic point source, there are two cases to be considered to find the photon path length d through the cylindrical detector medium, as shown in Fig. 1. The incident photon may enter the cylindrical detector upper surface and emerge from:

(a) the detector crystal base L cosy (b) the detector crystal side d1 ¼

d2 ¼

ð1Þ

MðfÞ h  siny cosy

ð2Þ

P(, h)



R

h

=0

=π 

2 d

2

The geometrical notations of R, L, r and h are as shown in Fig. 1. Consider the geometry illustrated in Fig. 2, where R is the radius of the cylindrical detector face, the lateral distance r is the distance from the center of the cylindrical detector face to the point source P(r,h) projection and M(f) is the distance from the projection of the point source P(r,h) to any point lying on the circumference of the circular face of the cylindrical detector. Thus the distance M(f), depending on the azimuthal angle (f) as shown in Fig. 2, is given as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ MðfÞ ¼ r cos f þ R2 r2 sin2 f For the special cases, when the azimuthal angle (f) takes the values 0, p/2 and p the distance M(f) takes the following values: Mð0Þ ¼ Rr

ð4Þ

p qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M ¼ R2 r2 2

ð5Þ

MðpÞ ¼ R þ r

ð6Þ

In addition, when the lateral distance r ¼0, the distance M(f) tends to R. The total efficiency of a cylindrical detector for a photon incident, with energy Eg, from an isotropic radiating nonaxial point source P(r,h) is derived as ! Z p Z y1 Z y2 1 ePoint ¼ f1 dy þ f2 dy df ð7Þ 2p 0 0 y1 where

L

y1 ¼ tan1

d 1

y2 ¼ tan1

 

MðfÞ h þL MðfÞ h

 ð8Þ  ð9Þ

fi ¼ fatt ð1emdi Þsin y,

1 0

Fig. 1. Schematic view of all the possible path lengths through the active volume of a cylindrical (2R  L) detector irradiated by photons of an isotropic radiating non-axial point source P(r, h). The source-to-detector distance is h.

R

i ¼ 1 and 2;

ð10Þ

where m is the attenuation coefficient of the detector crystal without the coherent part [33]. The attenuation factor fatt determining the photon attenuation by the CaF2(Eu) crystal, the quartz (SiO2) dead layer (in the case of phoswich detector) and the aluminum housing detector case (in the case of both the phoswich

R−



 =

 =0

 M () R

2

Fig. 2. Geometry to determine the distance, M(f), from the projection of the non-axial point source P(r, h) to any point lies on the circumference of the circular face of the cylindrical detector.

M.I. Abbas / Nuclear Instruments and Methods in Physics Research A 621 (2010) 413–418



P ( , h )

 R

415

S

D

R- D

h

t2

CaF2

t3

SiO2

L

t1

R

A

h

t2

CaF2

t3

SiO2

t1

A

NaI (T ) L

NaI (T )

Fig. 3. Three-dimensional view of the cylindrical phoswich scintillation detector.

Fig. 5. Schematic view of the disk source and cylindrical phoswich scintillation detector.

R t1

where epoint is the absolute efficiency of an off-axis radiating point source (as identified before in Eq. (7)).

A

3. Results L

LaBr3(Ce)

Fig. 4. Three-dimensional view of the cylindrical lanthanum bromide (LaBr3:Ce) scintillation detector.

and LaBr3(Ce) detectors), and is expressed as fatt ¼ eðm1 t1 þ m2 t2 þ m3 t3 Þ=cos y

ð11Þ

The geometrical notations of t1, t2 and t3 are as shown in Figs. 3 and 4. m1, m2 and m3 are the attenuation coefficients of the aluminum housing detector case (in the case of phoswich and LaBr3(Ce) detectors), the CaF2(Eu) crystal, and the quartz (SiO2) dead layer (in the case of phoswich detector) for a gamma-ray photon with energy Eg [33], respectively. 2.2. The case of a concentric coaxial plane (disk) source The derived analytical expression of the total efficiency of a concentric coaxial isotropically radiating circular disk source (with radius S, in which S oR, as shown in Fig. 5) is given by Z 2 S eDisk ¼ 2 ePoint r dr ð12Þ S 0

The absolute total efficiencies are calculated using the present work, and compared with those obtained by experimental measurement and Monte Carlo simulation for cylindrical phoswich and lanthanum bromide (LaBr3:Ce) scintillation detectors using point and circular disk sources. The phoswich detector consisted of a 0.00635 cm thick CaF2(Eu) crystal (decay constant 940 ns) and a 5.08  5.08 cm2 NaI(Tl) crystal (decay constant 230 ns) and was read out by a single PMT. The front face of the CaF2(Eu) crystal was coated with aluminum of a few hundred microns thick and the two scintillators have been separated by a 0.3175 cm thick dead quartz (SiO2) layer [16], see Fig. 3. The CaF2(Eu) crystal is used as the beta detector to absorb beta particles and conversion electrons and the NaI(Tl) acts as the gamma-ray detector to absorb gamma rays and X-rays [5]. However, the 2.54  2.54 cm2 LaBr3(Ce) crystal (decay constant 16 ns) is housed in 0.05 cm aluminum casing [23,24], see Fig. 4. In the case of a phoswich detector, the measured and simulated total efficiencies for axial point (i.e. the lateral distance, r ¼0) 57Co gamma (with energies 100 and 150 keV) and 137Cs gamma (with an energy 662 keV) sources [16] are summarized in Tables 1 and 2, respectively, together with the direct theoretical ones (present work). The simulated [16] and theoretical (present work) total efficiencies for an axial point source (i.e. the lateral distance, r ¼0) at different source to detector distances, h, are summarized in Table 3. In addition, the simulated [16] and theoretical (present work) total efficiencies for concentric coaxial disk sources of radii S¼1.17 and 2.51 cm at different source to detector distances, h, are summarized in Tables 4 and 5, respectively. In the case of a cylindrical lanthanum bromide (LaBr3:Ce) scintillation detector, Fig. 6 shows the absolute total efficiency (present work) of

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M.I. Abbas / Nuclear Instruments and Methods in Physics Research A 621 (2010) 413–418

2.54  2.54 cm2 LaBr3(Ce) scintillation detector plotted as a function of the gamma-ray energy in the energy range between 150 and 1332 keV. Table 6 shows the measured [23] in closegeometry using axial point (i.e. the lateral distance, r ¼ 0) 137Cs gamma (with an energy 662 keV) and 60Co gamma (with energies 1173.23 and 1332.50 keV) sources together with simulated [23] and theoretical (present work) total efficiencies. Anil Kumar et al. [23] claimed that, in the case of source–detector close geometry they have found that the emission spectrum from 137Cs is incorrect. It seems they encountered a serious problem with the study of the gamma energy line 662 keV spectrum, in the case of source–detector close geometry, in both measurement and simulation. Accordingly their absolute total efficiency value at this gamma line is not correct. Also Kumar’s efficiency values are inconsistent with each other, as shown in Table 6, because the efficiency value at the energy 662 keV should be greater than the efficiency value at 1173 keV as illustrated in Fig. 6. Finally in Fig. 7 we compare our theoretical total efficiency with the simulated values taken from Kumar et al. [24] for cylindrical LaBr3(Ce) scintillation detector of dimensions 2.54 cm diameter and

Table 1 Comparison between calculated (present work), experimental [16] and simulated [16] total efficiencies of cylindrical phoswich detector for a 57Co gamma (with energies 100 and 150 keV) source. The source-to-detector distance is h¼0.464 cm (the distance D ¼ 0.14 cm). Energy (MeV)

Expt. [16]

M.C. [16]

Present work

D1%

0.10 0.15

0.3030 0.3071

0.3061 0.3143

0.3036 0.3063

 0.99  2.28

D2%

[16]  0.20 0.26

Table 2 Comparison between calculated (present work), experimental [16] and simulated [16] total efficiencies of cylindrical phoswich detector for a 137Cs gamma (with an energy 662 keV) source. The source-to-detector distance is h¼ 0.345 cm (the distance D ¼ 0.021 cm).

2.54 cm length in the energy range from 662 keV to 5 MeV, for source to detector distance h¼10 cm. The cylindrical LaBr3(Ce) was considered to be encased in 0.02 cm thick Al with a gap of 0.03 cm between the Al casing and the crystal surfaces. Discrepancies from the reference data sets are calculated as

D1 % ¼

eexpt: eM:C: eexpt:

ð13Þ

D2 % ¼

eexpt: etheo: eexpt:

ð14Þ

D3 % ¼

eM:C: etheo: eM:C:

ð15Þ

where etheo, eM.C. and eexpt are the theoretical (present work), the simulated and the experimentally measured total efficiencies, respectively. In the case of a phoswich detector, the comparisons of the efficiency values in Tables 1–5 common features can be seen. In Tables 1 and 2, discrepancies between the present theoretical method with experimental results [16] (in the case of the point source, D2) are reduced to lower than 1.5%. In Tables 3–5, discrepancies between the present theoretical method with simulated results [16] (in the case of the point and disk sources, D3) are reduced to lower than 1%. In the case of a cylindrical lanthanum bromide (LaBr3:Ce) scintillation detector, in Table 6 the discrepancies (in the case of the point source, D2) between the measured [23] and the calculated (present theoretical method) efficiency values for the investigated geometry ranged between 0.6% and 2.5% (excluding the argument point for 137 Cs). Finally in Fig. 7 the discrepancies (in the case of the point source, 9D39) between the simulated [24] and the calculated (present theoretical method) efficiency values for the investigated geometry ranged between 0.04% and 2.8% (including the argument point for 137Cs), here Kumar et al. [24] succeeded in measuring spectrum from 137Cs because the source to detector distance is h¼10 cm, not in a source–detector close geometry like in the previous work [23].

4. Conclusions D1%

Energy (MeV)

Expt. [16]

M.C. [16]

Present work

[16]

0.662

0.1415

0.1504

0.1394

 5.92

D2%

+ 1.47

The present approach offers straightforward mathematical expressions to calibrate cylindrical phoswich and lanthanum bromide (LaBr3:Ce) scintillation detectors, over a large energy

Table 3 Comparison between calculated (present work), and simulated [16] total efficiencies of cylindrical phoswich detector for an isotropic radiating point source at different source to detector distances, h¼ D +0.324 cm. Energy (MeV)

0.050 0.060 0.080 0.100 0.150 0.200 0.300 0.400 0.500 0.600 0.662 0.800 1.000 1.500 2.000 3.000

D ¼0.43 cm

D ¼ 0.87 cm

D ¼ 1.05 cm

M.C. [16]

Present work

D3%

M.C. [16]

Present work

D3%

M.C. [16]

Present work

D3%

0.2217 0.2447 0.2647 0.2725 0.2677 0.2474 0.2037 0.1777 0.1610 0.1498 0.1443 0.1348 0.1247 0.1077 0.0993 0.0917

0.2214 0.2445 0.2648 0.2724 0.2680 0.2476 0.2041 0.1776 0.1611 0.1499 0.1443 0.1347 0.1241 0.1070 0.0984 0.0910

0.14 0.08  0.04 0.04  0.11  0.08  0.20 0.06  0.06  0.07 0.0 0.07 0.48 0.65 0.91 0.76

0.1892 0.2061 0.2199 0.2234 0.2140 0.1940 0.1578 0.1370 0.1241 0.1153 0.1110 0.1034 0.0957 0.0827 0.0761 0.0701

0.1893 0.2062 0.2199 0.2235 0.2140 0.1942 0.1580 0.1370 0.1241 0.1153 0.1109 0.1035 0.0952 0.0821 0.0754 0.0697

 0.05  0.05 0.0  0.04 0.0  0.10  0.13 0.0 0.0 0.0 0.09  0.10 0.52 0.73 0.92 0.57

0.1757 0.1908 0.2025 0.2049 0.1946 0.1760 0.1427 0.1239 0.1122 0.1042 0.1003 0.0936 0.0865 0.0747 0.0688 0.0633

0.1757 0.1906 0.2023 0.2049 0.1948 0.1760 0.1430 0.1239 0.1122 0.1042 0.1003 0.0935 0.0861 0.0742 0.0682 0.0630

0.0 0.11 0.10 0.0  0.10 0.0  0.21 0.0 0.0 0.0 0.0 0.11 0.46 0.67 0.87 0.47

M.I. Abbas / Nuclear Instruments and Methods in Physics Research A 621 (2010) 413–418

417

Table 4 Comparison between calculated (present work) and simulated [16] total efficiencies of cylindrical phoswich detector for an isotropic radiating concentric coaxial disk source with radius S¼ 1.17 cm at different source to detector distances, h¼ D +0.324 cm. Energy (MeV)

D ¼ 0.43 cm

0.050 0.060 0.080 0.100 0.150 0.200 0.300 0.400 0.500 0.600 0.662 0.800 1.000 1.500 2.000 3.000

D¼ 0.87 cm

D ¼1.05 cm

M.C. [16]

Present work

D3%

M.C. [16]

Present work

D3%

M.C. [16]

Present work

D3%

0.2158 0.2379 0.2569 0.2636 0.2569 0.2362 0.1944 0.1695 0.1539 0.1432 0.1380 0.1290 0.1194 0.1033 0.0952 0.0879

0.2157 0.2379 0.2569 0.2635 0.2570 0.2363 0.1946 0.1695 0.1539 0.1433 0.1380 0.1289 0.1188 0.1026 0.0944 0.0872

0.05 0.0 0.0 0.04  0.04  0.04  0.10 0.0 0.0  0.07 0.0 0.08 0.50 0.68 0.84 0.08

0.1813 0.1973 0.2101 0.2132 0.2035 0.1843 0.1504 0.1306 0.1186 0.1102 0.1064 0.0992 0.0917 0.0794 0.0730 0.0674

0.1814 0.1975 0.2102 0.2133 0.2033 0.1844 0.1505 0.1308 0.1186 0.1103 0.1061 0.0991 0.0913 0.0787 0.0724 0.0669

 0.06  0.10  0.05  0.05 0.10  0.05  0.07  0.15 0.0  0.09 0.28 0.10 0.44 0.88 0.83 0.74

0.1678 0.1818 0.1926 0.1949 0.1847 0.1670 0.1362 0.1184 0.1072 0.0997 0.0961 0.0897 0.0829 0.0717 0.0661 0.0609

0.1677 0.1818 0.1927 0.1949 0.1848 0.1671 0.1363 0.1183 0.1073 0.0998 0.0960 0.0897 0.0826 0.0712 0.0655 0.0605

0.06 0.0  0.05 0.0  0.05  0.06  0.07 0.08  0.09  0.10 0.10 0.0 0.36 0.70 0.91 0.66

Table 5 Comparison between calculated (present work) and simulated [16] total efficiencies of cylindrical phoswich detector for an isotropic radiating concentric coaxial disk source with radius S¼ 2.51 cm at different source to detector distances, h¼ D +0.324 cm. Energy (MeV)

D ¼0.43 cm

0.050 0.060 0.080 0.100 0.150 0.200 0.300 0.400 0.500 0.600 0.662 0.800 1.000 1.500 2.000 3.000

D ¼ 0.87 cm

M.C. [16]

Present work

D3%

M.C. [16]

Present work

D3%

M.C. [16]

Present work

D3%

0.1763 0.1938 0.2085 0.2124 0.2052 0.1892 0.1582 0.1391 0.1271 0.1187 0.1145 0.1074 0.0999 0.0868 0.0802 0.0743

0.1764 0.1940 0.2084 0.2125 0.2051 0.1891 0.1582 0.1391 0.1271 0.1187 0.1145 0.1074 0.0993 0.0861 0.0794 0.0736

 0.06  0.10 0.05  0.05 0.05 0.05 0.0 0.0 0.0 0.0 0.0 0.0 0.60 0.80 1.00 0.94

0.1447 0.1574 0.1675 0.1701 0.1625 0.1493 0.1244 .1091 0.0996 0.0930 0.0898 0.0840 0.0781 0.0678 0.0626 0.0580

0.1447 0.1575 0.1676 0.1700 0.1627 0.1492 0.1243 0.1092 0.0996 0.0930 0.0897 0.0840 0.0776 0.0673 0.0620 0.0575

0.0  0.06  0.06 0.06  0.12 0.07 0.08  0.09 0.0 0.0 0.11 0.0 0.64 0.74 0.96 0.86

0.1334 0.1450 0.1536 0.1557 0.1487 0.1360 0.1134 0.0996 0.0909 0.0849 0.0819 0.0766 0.0711 0.0618 0.0571 0.0527

0.1334 0.1449 0.1538 0.1557 0.1487 0.1363 0.1135 0.0996 0.0909 0.0849 0.0818 0.0766 0.0708 0.0614 0.0566 0.0524

0.0 0.07  0.13 0.0 0.0  0.22  0.09 0.0 0.0 0.0 0.12 0.0 0.42 0.65 0.87 0.57

0.5

Table 6 Comparison between calculated (present work), experimental [23] and simulated [23] total efficiencies of 2.54  2.54 cm2 cylindrical lanthanum bromide (LaBr3:Ce) detector for a 137Cs gamma (with an energy 662 keV) and a 57Co gamma (with energies 1.173 and 1.332 MeV) sources in close-geometry.

0.45 0.4 Absolute total efficiency

D ¼ 1.05 cm

0.35

Energy (MeV)

0.3 0.25

Expt. (%) [23]

M.C. (%) [23]

12.017 0.60 14.39 7 2.19 13.94 7 2.20

12.90 7 1.00 12.63 71.10 11.7571.14

662 keV

0.662 1.173 1.332

1173 keV

0.2 0.15 0.1

Present (%) work 18.3 14.3 13.6

D1% [23]

D2%

 7.41 12.23 15.71

 52.37 0.63 2.44

1332 keV

0.05 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Photon energy MeV Fig. 6. Plot of the absolute total efficiency versus gamma photon energy for 2.54  2.54 cm2 cylindrical lanthanum bromide (LaBr3:Ce) scintillation detector in close-geometry (i.e. h¼0).

range without the need for standard sources, as is the case for experimental methods, nor optimization of detector parameters as for other simulation methods. In addition, the attenuation of the photons by the detector housing material is also presented in a simple direct mathematical expression.

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M.I. Abbas / Nuclear Instruments and Methods in Physics Research A 621 (2010) 413–418

Absolute total efficiency %

0.25 0.2 0.15 0.1 0.05 0

0

1

2

3

4

5

6

Photon energy MeV Fig. 7. Plot of the absolute total efficiency versus gamma photon energy for 2.54  2.54 cm2 cylindrical lanthanum bromide (LaBr3:Ce) scintillation detector. Solid curve and symbols represent the present theoretical and simulated [24] total efficiency values, respectively. The source-to-detector distance is h¼10 cm.

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