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Determination of CR-39 detection efficiency for fast neutron registration and the absolute neutron dosimetry
Nuclear Instruments and Methods in Physics Research B 215 (2004) 443–448 www.elsevier.com/locate/nimb
Determination of CR-39 detection efficiency for fast neutron registration and the absolute neutron dosimetry A.R. El-Sersy *, N.E. Khaled, S.A. Eman Department of Ionizing Radiation, National Institute for Standards, P.O. Box 136, 12211 Cairo, Egypt Received 10 April 2003; received in revised form 7 August 2003
Abstract In this work, the efficiency g of CR-39 track detector for fast neutron registration was measured and compared with the calculated one. g was defined as the ratio of induced proton tracks in CR-39 detector to the incident neutron flux taken into account the neutron scattering cross-section of the reaction. In this study, a 5 Ci 241 Am–Be cylindrical shaped neutron source was used and different theoretical approaches for flux evaluation were considered. It was found that at small source-to-detector distances ( 6 90 cm) the cylindrical source configuration should only be considered in neutron flux calculations and absolute dosimetry evaluation. Also, a good agreement between the calculated and the measured values of g has been found. Moreover, calculated neutron doses have shown excellent agreement with those measured by track detectors and by a Secondary Standard Neutron Monitor. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Neutrons are indirectly ionizing radiation, they must react with another medium to produce a primary ionizing particle. Because of the strong dependence of neutron reaction rate on the crosssection for that particular reaction, different detection media should be used, depending on the energy of the neutrons that need to be measured, or the neutron energy distribution is modified in order to be compatible with the detector. Some of the basic neutron detection reactions used in health physics instrumentation are: 10 B (n; a) 7 Li,
*
Corresponding author. E-mail address: [email protected] (A.R. El-Sersy).
elastic scattering of high-energy neutrons by hydrogen atoms, nuclear fission and neutron activation. Among the personal neutron dosimeter used today, etched track detectors which have been considered as one of the most promising detectors since the introduction of CR-39 plastics [1]. The main advantage of using CR-39 in fast neutron dosimetry is its insensitivity to photon irradiation, and low neutron energy threshold. Also, the detector is not affected by the environmental conditions and is sensitive for wide range of neutron energy [2,3]. Registration efficiency is very important parameter for any dosimeter and should be obtained before its use. It depends not only upon dosimeter type or kind of radiation but also depends mainly
0168-583X/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2003.08.035
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A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
on the geometrical configuration between the source and detectors [4]. For charged particles the corresponding dose is obtained from the number of particles actually incident on the detector surface per unit time (flux). The simplest case of flux calculation is the point dimensionless source, the flux of neutrons is obtained per unit time from the relation uP ¼
AP ; 4pr2
ð1Þ
where AP is the source activity and r is the sourceto-detector distance. In case of cylindrical source configuration (see Fig. 1), the flux at the point P1 is given by [5] /cyl
Av R20 ½F ðh1 ; b1 Þ þ F ðh2 ; b2 Þ; ¼ 4ðr þ sÞ
ð2Þ
where Av is the volume activity i.e. activity per unit volume of the source, R0 is the radius of cylinder base, r is the source-to-detector distance, s is the depth corresponding to self-absorption of the source and b1 , b2 are factors describing attenuation coefficient of the source and the media, respectively. In case of line source the flux is given by (see Fig. 1) ul ¼
AL ½ðjh1 jÞ þ ðjh2 jÞ; 4pr
where AL is the line activity, i.e. activity per unit length of the source. Neglecting both the self-absorption of the source and attenuation coefficient of the media, Eq. (2) can be written as /cyl ¼
Av R20 ½F ðh1 Þ þ F ðh2 Þ; 4r
ð4Þ
where F ðh1 Þ equals to F ðh2 Þ and each of them is plotted against h (in degrees) and given in the appendix of [5]. F ðhÞ, as a function of h, is fitted with a correlation of 99% and given by F ðhÞ ¼ 0:016h þ 0:005:
ð5Þ
The main object of this work is to apply Eqs. (1), (3) and (4) to calculate the neutron flux from cylindrical shaped Am–Be source and to discuss their domains of interest in calculating registration efficiency, g. In this case, the calculated fluxes are used to determine the registration efficiency ðgÞ of CR-39, where g is defined as the ratio of the induced track density to the individually calculated incident neutron flux. Consequently using neutron flux–dose conversion factor, the neutron doses are calculated and compared with those measured by CR-39 detector and Secondary Standard Neutron Monitor.
ð3Þ 2. Experimental work θ1
θ2
Ro
h
P2
S
P1
θ1 θ2
r Fig. 1. Schematic diagram of neutrons emitted from cylindrical source to flat detector.
Sheets of 250 lm CR-39 track detectors (TASTRAK supplied by Bristol, UK) were irradiated using a 5 Ci Am–Be neutron source of cylindrical shape with 3 cm base diameter and 7 cm height at the National Institute for Standards (NIS) of Egypt. Irradiation was carried out at different distances directly in air and for various durations. The irradiated samples were etched at optimum etching conditions (6.25 N NaOH at 70 °C for 10 h) [6–8]. Background tracks originated in an unexposed detectors etched under the same etching conditions were first measured and then subtracted from those measured in exposed detectors before real track density evaluation. Track counting was performed using a fully automatic image analyzer (ELBEK SAMAICA, Germany) using the interactive mode which gives the ability
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
to the user to accept the selected tracks in each field. Track counting was carried out on the detector surface facing the neutron source. Doses from the neutron source were measured using a neutron monitor (Nuclear Enterprise, UK NM2). 3. Results and discussion 3.1. Flux calculations Calculations of neutron fluxes ðuÞ were carried out considering different source configurations namely, point (1), line (2) and cylindrical (4) at different source-to-detector distances and represented in Fig. 2. The deviation between the cylindrical and line source shape is the smallest. The line source is coincident with the cylindrical source starting at 90 cm, i.e. about 13 times the height of the source. From inspection of Fig. 2, line source configuration should only be considered at distances P 90 cm while the cylindrical shape can be considered along the entire studied distances. From Eq. (4), the value of u depends only on the spherical components r; h ¼ f ðx; y; zÞ. Then one can represent the function u in three-dimensional form along x and y coordinates for fixed paffiffiffiffiffiffiffiffiffiffiffiffiffiffi value of z and for different values of r ¼ x2 þ y 2 (see Fig. 3(a)).
445
The flux calculations of Am–Be source using cylindrical approximation (Eq. (4)) were represented in three-dimensional curve ðx; y; uÞ and contour map (Fig. 3) assuming that the origin point is at mid-plane of the source. Fig. 3(b) represents a group of iso-flux curves where values of u can be read through x,y plane, where ðxÞ is the longitudinal source-to-detector distance and ðyÞ is the lateral distance for a given value of z. This figure can be used to obtain the neutron flux precisely at any point of coordinate system ðX ; Y Þ in the specified volume with certain value of z (h=2 6 z 6 h=2, h is the source height). 3.2. Neutron-dose value determination using CR-39 The calculated fluxes have been used in the determination of the fast neutron registration efficiency ðgÞ of CR-39. g was determined from the ratio of the measured induced track density to the incident neutron flux. Moreover, g was calculated by the ratio of the expected track density to the incident neutron flux. Track density ðqÞ is given by q ¼ gu:
ð6Þ
The efficiency factor g depends on two factors, e and s as [9] g ¼ es;
ð7Þ
where e is the probability of proton induced due to the elastic scattering of fast neutron by the Hatoms in CR-39 detector (latent efficiency) and given by [10] Neutron flux ( cm.-2 sec-1)
e ¼ 1 expðN rs dÞ;
Source-to-detector distance (cm)
Fig. 2. Neutron flux as a function of source-to-detector distance for cylindrical, line and point sources.
ð8Þ
where N is the number density of H in CR-39 (number of H atoms in 1 cm3 of CR-39), rs is scattering cross-section of fast neutron by H atoms in the detector material and d is the removal layer thickness in cm. s is the etching efficiency of the induced protons in CR-39 (the ratio of the etched proton tracks to the number of induced protons by the neutron interaction with CR-39). s for the internal source (proton is formed inside the detector) is equal to cos2 hc , where hc is the critical angle of etching ½hc ¼ sin1 ð1=V Þ and V is the ratio of track etch rate VT to the bulk etch rate VB of the detector material [9,11].
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A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
(a)
(b)
Lateral distance (cm)
20
10
0
-10
-20 10
20
30
40
50
60
70
80
90
100
Source-to-detector distance (cm)
Fig. 3. Neutron flux as a function of distances in ðx; yÞ coordinate (a) and iso-dose chart (b) for a fixed value of z.
Fig. 4 represents the numerical values of calculated e and g as a function of the thickness of removal layers by etching using hc ¼ 40° on average value. hc was calculated from an average determined value of V that equals to 1.55. Fig. 5 illustrates a comparison between the measured and the calculated track densities (Eq. (6)) with the incident neutron fluences using CR-39 samples irradiated in air and etched for 10 h. This figure reflects a good agreement between calculated and measured track densities.
The calculated flux is used to calculate the neutron dose equivalent ðH Þ from the relation [12] H ¼ hu u;
ð9Þ
where hu is the mean neutron fluence to dose equivalent conversion factor for the Am–Be source; hu ¼ 3:8 1014 Sv m2 and u is the neutron fluence (m2 ). The calculated dose (see Eq. (9)) is compared with that measured using the NM2 neutron monitor.
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
447
0.0004 Latent effici
Detection efficiency
Total effici
0.0003
0.0002
0.0001
0.0000 0
5
10
15
20
25
30
35
40
45
Removal layer (µm) Fig. 4. Variation of the calculated detection efficiency with the removal thickness layer.
Fig. 6. Neutron equivalent dose versus source-to-detector distance.
From the inspection of Fig. 6 there is an excellent agreement between the measured and calculated dose values using cylindrical source geometry.
120000
measured
Track density (T/cm 2 )
Calculated
80000
4. Conclusion
40000
0 0.00E+0
1.00E+9
2.00E+9
3.00E+9
4.00E+9
Neutron fleunce (N/cm2 ) Fig. 5. Calculated and measured track density as a function of neutron fluence.
Fig. 6 represents a comparison between calculated and measured neutron-dose values. The measured dose values were determined using the neutron monitor and those obtained from CR-39 using track density–flux relationship (Eq. (6)) and flux–dose relationship (Eq. (9)).
The flux of the Am–Be neutron source was calculated using different theoretical approaches (point, line and cylindrical configurations). It was concluded that for an accurate flux calculation, the source should be considered as cylindrical shape at small source-to-detector distance. On the other hand for large source-to-detector distances (>90 cm), line source geometry can sufficiently be considered for simplicity with excellent approximation. Measured and calculated registration efficiencies of CR-39 detector were found to be in good agreement. Moreover, calculated neutron dose values were in an excellent agreement with those measured by CR-39 and NM2 neutron monitor. This would lead to the fact that CR-39 track detectors have shown essential and important roles in the field of fast neutron measurements specially for neutron-dose determination.
448
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
Acknowledgements The authors would like to express their deep thanks and appreciation to Prof. Dr. A. Hussein, Professor of Radiation Physics, El Menofia University for his valuable advice and fruitful discussion.
References [1] B. D€ orschel, R. Bretschneider, D. Hermsdorf, K. Kadner, H. K€ uhne, Radiat. Meas. 31 (1999) 103. [2] J. Charvat, Radiat. Prot. Dosim. 23 (1/4) (1988) 171. [3] E. Pitt, A. Scharmann, R. Simmer, Nucl. Tracks Radiat. Meas. 19 (1991) 517.
[4] H. El-Samman, M. Mansy, A. Hussein, M. El-Hawary, A. El-Sersy, Nucl. Instr. and Meth. B 155 (1999) 426. [5] K.R. Kase, W.R. Nelson, Concepts of Radiation Dosimetry, Pergamon Press, 1978. [6] M. Bruno, M. DÕAgostino, M.L. Fiandri, Nucl. Instr. and Meth. A 234 (1985) 468. [7] I. Lengar, J. Skvae, R. Iliccß, Nucl. Instr. and Meth. B 192 (2002) 440. [8] P. Meyer, M. Fromm, A. Chambaudet, J. Laugier, L. Makovicka, Radiat. Meas. 25 (1–4) (1995) 449. [9] R.F. Khan, N. Ahmed, Aslam, Matiullah, Radiat Meas. 33 (2001) 129. [10] G.F. Knoll, Radiation Detection and Measurement, second ed., Wiley, Chichester, USA, 1989. [11] S. Durrani, R. Bull, Solid State Nuclear Track Detection, Pergamon Press, Oxford, UK, 1987. [12] G. Burger, R.B. Schwaster, TRS, 285, IAEA, Vienna, 1988.
Determination of CR-39 detection efficiency for fast neutron registration and the absolute neutron dosimetry A.R. El-Sersy *, N.E. Khaled, S.A. Eman Department of Ionizing Radiation, National Institute for Standards, P.O. Box 136, 12211 Cairo, Egypt Received 10 April 2003; received in revised form 7 August 2003
Abstract In this work, the efficiency g of CR-39 track detector for fast neutron registration was measured and compared with the calculated one. g was defined as the ratio of induced proton tracks in CR-39 detector to the incident neutron flux taken into account the neutron scattering cross-section of the reaction. In this study, a 5 Ci 241 Am–Be cylindrical shaped neutron source was used and different theoretical approaches for flux evaluation were considered. It was found that at small source-to-detector distances ( 6 90 cm) the cylindrical source configuration should only be considered in neutron flux calculations and absolute dosimetry evaluation. Also, a good agreement between the calculated and the measured values of g has been found. Moreover, calculated neutron doses have shown excellent agreement with those measured by track detectors and by a Secondary Standard Neutron Monitor. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction Neutrons are indirectly ionizing radiation, they must react with another medium to produce a primary ionizing particle. Because of the strong dependence of neutron reaction rate on the crosssection for that particular reaction, different detection media should be used, depending on the energy of the neutrons that need to be measured, or the neutron energy distribution is modified in order to be compatible with the detector. Some of the basic neutron detection reactions used in health physics instrumentation are: 10 B (n; a) 7 Li,
*
Corresponding author. E-mail address: [email protected] (A.R. El-Sersy).
elastic scattering of high-energy neutrons by hydrogen atoms, nuclear fission and neutron activation. Among the personal neutron dosimeter used today, etched track detectors which have been considered as one of the most promising detectors since the introduction of CR-39 plastics [1]. The main advantage of using CR-39 in fast neutron dosimetry is its insensitivity to photon irradiation, and low neutron energy threshold. Also, the detector is not affected by the environmental conditions and is sensitive for wide range of neutron energy [2,3]. Registration efficiency is very important parameter for any dosimeter and should be obtained before its use. It depends not only upon dosimeter type or kind of radiation but also depends mainly
0168-583X/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2003.08.035
444
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
on the geometrical configuration between the source and detectors [4]. For charged particles the corresponding dose is obtained from the number of particles actually incident on the detector surface per unit time (flux). The simplest case of flux calculation is the point dimensionless source, the flux of neutrons is obtained per unit time from the relation uP ¼
AP ; 4pr2
ð1Þ
where AP is the source activity and r is the sourceto-detector distance. In case of cylindrical source configuration (see Fig. 1), the flux at the point P1 is given by [5] /cyl
Av R20 ½F ðh1 ; b1 Þ þ F ðh2 ; b2 Þ; ¼ 4ðr þ sÞ
ð2Þ
where Av is the volume activity i.e. activity per unit volume of the source, R0 is the radius of cylinder base, r is the source-to-detector distance, s is the depth corresponding to self-absorption of the source and b1 , b2 are factors describing attenuation coefficient of the source and the media, respectively. In case of line source the flux is given by (see Fig. 1) ul ¼
AL ½ðjh1 jÞ þ ðjh2 jÞ; 4pr
where AL is the line activity, i.e. activity per unit length of the source. Neglecting both the self-absorption of the source and attenuation coefficient of the media, Eq. (2) can be written as /cyl ¼
Av R20 ½F ðh1 Þ þ F ðh2 Þ; 4r
ð4Þ
where F ðh1 Þ equals to F ðh2 Þ and each of them is plotted against h (in degrees) and given in the appendix of [5]. F ðhÞ, as a function of h, is fitted with a correlation of 99% and given by F ðhÞ ¼ 0:016h þ 0:005:
ð5Þ
The main object of this work is to apply Eqs. (1), (3) and (4) to calculate the neutron flux from cylindrical shaped Am–Be source and to discuss their domains of interest in calculating registration efficiency, g. In this case, the calculated fluxes are used to determine the registration efficiency ðgÞ of CR-39, where g is defined as the ratio of the induced track density to the individually calculated incident neutron flux. Consequently using neutron flux–dose conversion factor, the neutron doses are calculated and compared with those measured by CR-39 detector and Secondary Standard Neutron Monitor.
ð3Þ 2. Experimental work θ1
θ2
Ro
h
P2
S
P1
θ1 θ2
r Fig. 1. Schematic diagram of neutrons emitted from cylindrical source to flat detector.
Sheets of 250 lm CR-39 track detectors (TASTRAK supplied by Bristol, UK) were irradiated using a 5 Ci Am–Be neutron source of cylindrical shape with 3 cm base diameter and 7 cm height at the National Institute for Standards (NIS) of Egypt. Irradiation was carried out at different distances directly in air and for various durations. The irradiated samples were etched at optimum etching conditions (6.25 N NaOH at 70 °C for 10 h) [6–8]. Background tracks originated in an unexposed detectors etched under the same etching conditions were first measured and then subtracted from those measured in exposed detectors before real track density evaluation. Track counting was performed using a fully automatic image analyzer (ELBEK SAMAICA, Germany) using the interactive mode which gives the ability
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
to the user to accept the selected tracks in each field. Track counting was carried out on the detector surface facing the neutron source. Doses from the neutron source were measured using a neutron monitor (Nuclear Enterprise, UK NM2). 3. Results and discussion 3.1. Flux calculations Calculations of neutron fluxes ðuÞ were carried out considering different source configurations namely, point (1), line (2) and cylindrical (4) at different source-to-detector distances and represented in Fig. 2. The deviation between the cylindrical and line source shape is the smallest. The line source is coincident with the cylindrical source starting at 90 cm, i.e. about 13 times the height of the source. From inspection of Fig. 2, line source configuration should only be considered at distances P 90 cm while the cylindrical shape can be considered along the entire studied distances. From Eq. (4), the value of u depends only on the spherical components r; h ¼ f ðx; y; zÞ. Then one can represent the function u in three-dimensional form along x and y coordinates for fixed paffiffiffiffiffiffiffiffiffiffiffiffiffiffi value of z and for different values of r ¼ x2 þ y 2 (see Fig. 3(a)).
445
The flux calculations of Am–Be source using cylindrical approximation (Eq. (4)) were represented in three-dimensional curve ðx; y; uÞ and contour map (Fig. 3) assuming that the origin point is at mid-plane of the source. Fig. 3(b) represents a group of iso-flux curves where values of u can be read through x,y plane, where ðxÞ is the longitudinal source-to-detector distance and ðyÞ is the lateral distance for a given value of z. This figure can be used to obtain the neutron flux precisely at any point of coordinate system ðX ; Y Þ in the specified volume with certain value of z (h=2 6 z 6 h=2, h is the source height). 3.2. Neutron-dose value determination using CR-39 The calculated fluxes have been used in the determination of the fast neutron registration efficiency ðgÞ of CR-39. g was determined from the ratio of the measured induced track density to the incident neutron flux. Moreover, g was calculated by the ratio of the expected track density to the incident neutron flux. Track density ðqÞ is given by q ¼ gu:
ð6Þ
The efficiency factor g depends on two factors, e and s as [9] g ¼ es;
ð7Þ
where e is the probability of proton induced due to the elastic scattering of fast neutron by the Hatoms in CR-39 detector (latent efficiency) and given by [10] Neutron flux ( cm.-2 sec-1)
e ¼ 1 expðN rs dÞ;
Source-to-detector distance (cm)
Fig. 2. Neutron flux as a function of source-to-detector distance for cylindrical, line and point sources.
ð8Þ
where N is the number density of H in CR-39 (number of H atoms in 1 cm3 of CR-39), rs is scattering cross-section of fast neutron by H atoms in the detector material and d is the removal layer thickness in cm. s is the etching efficiency of the induced protons in CR-39 (the ratio of the etched proton tracks to the number of induced protons by the neutron interaction with CR-39). s for the internal source (proton is formed inside the detector) is equal to cos2 hc , where hc is the critical angle of etching ½hc ¼ sin1 ð1=V Þ and V is the ratio of track etch rate VT to the bulk etch rate VB of the detector material [9,11].
446
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
(a)
(b)
Lateral distance (cm)
20
10
0
-10
-20 10
20
30
40
50
60
70
80
90
100
Source-to-detector distance (cm)
Fig. 3. Neutron flux as a function of distances in ðx; yÞ coordinate (a) and iso-dose chart (b) for a fixed value of z.
Fig. 4 represents the numerical values of calculated e and g as a function of the thickness of removal layers by etching using hc ¼ 40° on average value. hc was calculated from an average determined value of V that equals to 1.55. Fig. 5 illustrates a comparison between the measured and the calculated track densities (Eq. (6)) with the incident neutron fluences using CR-39 samples irradiated in air and etched for 10 h. This figure reflects a good agreement between calculated and measured track densities.
The calculated flux is used to calculate the neutron dose equivalent ðH Þ from the relation [12] H ¼ hu u;
ð9Þ
where hu is the mean neutron fluence to dose equivalent conversion factor for the Am–Be source; hu ¼ 3:8 1014 Sv m2 and u is the neutron fluence (m2 ). The calculated dose (see Eq. (9)) is compared with that measured using the NM2 neutron monitor.
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
447
0.0004 Latent effici
Detection efficiency
Total effici
0.0003
0.0002
0.0001
0.0000 0
5
10
15
20
25
30
35
40
45
Removal layer (µm) Fig. 4. Variation of the calculated detection efficiency with the removal thickness layer.
Fig. 6. Neutron equivalent dose versus source-to-detector distance.
From the inspection of Fig. 6 there is an excellent agreement between the measured and calculated dose values using cylindrical source geometry.
120000
measured
Track density (T/cm 2 )
Calculated
80000
4. Conclusion
40000
0 0.00E+0
1.00E+9
2.00E+9
3.00E+9
4.00E+9
Neutron fleunce (N/cm2 ) Fig. 5. Calculated and measured track density as a function of neutron fluence.
Fig. 6 represents a comparison between calculated and measured neutron-dose values. The measured dose values were determined using the neutron monitor and those obtained from CR-39 using track density–flux relationship (Eq. (6)) and flux–dose relationship (Eq. (9)).
The flux of the Am–Be neutron source was calculated using different theoretical approaches (point, line and cylindrical configurations). It was concluded that for an accurate flux calculation, the source should be considered as cylindrical shape at small source-to-detector distance. On the other hand for large source-to-detector distances (>90 cm), line source geometry can sufficiently be considered for simplicity with excellent approximation. Measured and calculated registration efficiencies of CR-39 detector were found to be in good agreement. Moreover, calculated neutron dose values were in an excellent agreement with those measured by CR-39 and NM2 neutron monitor. This would lead to the fact that CR-39 track detectors have shown essential and important roles in the field of fast neutron measurements specially for neutron-dose determination.
448
A.R. El-Sersy et al. / Nucl. Instr. and Meth. in Phys. Res. B 215 (2004) 443–448
Acknowledgements The authors would like to express their deep thanks and appreciation to Prof. Dr. A. Hussein, Professor of Radiation Physics, El Menofia University for his valuable advice and fruitful discussion.
References [1] B. D€ orschel, R. Bretschneider, D. Hermsdorf, K. Kadner, H. K€ uhne, Radiat. Meas. 31 (1999) 103. [2] J. Charvat, Radiat. Prot. Dosim. 23 (1/4) (1988) 171. [3] E. Pitt, A. Scharmann, R. Simmer, Nucl. Tracks Radiat. Meas. 19 (1991) 517.
[4] H. El-Samman, M. Mansy, A. Hussein, M. El-Hawary, A. El-Sersy, Nucl. Instr. and Meth. B 155 (1999) 426. [5] K.R. Kase, W.R. Nelson, Concepts of Radiation Dosimetry, Pergamon Press, 1978. [6] M. Bruno, M. DÕAgostino, M.L. Fiandri, Nucl. Instr. and Meth. A 234 (1985) 468. [7] I. Lengar, J. Skvae, R. Iliccß, Nucl. Instr. and Meth. B 192 (2002) 440. [8] P. Meyer, M. Fromm, A. Chambaudet, J. Laugier, L. Makovicka, Radiat. Meas. 25 (1–4) (1995) 449. [9] R.F. Khan, N. Ahmed, Aslam, Matiullah, Radiat Meas. 33 (2001) 129. [10] G.F. Knoll, Radiation Detection and Measurement, second ed., Wiley, Chichester, USA, 1989. [11] S. Durrani, R. Bull, Solid State Nuclear Track Detection, Pergamon Press, Oxford, UK, 1987. [12] G. Burger, R.B. Schwaster, TRS, 285, IAEA, Vienna, 1988.