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Effect of sample thickness on the measured mass attenuation coefficients of some compounds and elements for 59.54, 661.6 and 1332.5 keV γ-rays
Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
E!ect of sample thickness on the measured mass attenuation coe$cients of some compounds and elements for 59.54, 661.6 and 1332.5 keV c-rays夽 M.A. Abdel-Rahman*, E.A. Badawi, Y.L. Abdel-Hady, N. Kamel Department of Physics, Faculty of Science, El-Minia University, El-Minia, Egypt Received 3 August 1999; received in revised form 27 September 1999; accepted 10 November 1999
Abstract Measurements have been made to determine c-rays attenuation coe$cients very accurately by using an extremely narrow-collimated-beam transmission method. The e!ect of the sample thickness on the measured values of the mass attenuation coe$cients (k/o) cm/g of perspex, bakelite, para$n, Al, Cu, Pb and Hg have been investigated at three di!erent c-ray energies (59.54, 661.6 and 1332.5 keV). It is seen that for these chosen materials (k/o) remains constant in good agreement with the theoretical values up to 3 mean free paths and after that (k/o) values for Cu, Pb and Hg decrease with further increase in the absorber thickness. This result may be attributed to the increase in the number of coherent small-angle scattering photons which reach the detector. 2000 Elsevier Science B.V. All rights reserved. Keywords: Attenuation coe$cients; c-Rays
1. Introduction The most important quantity characterizing the penetration and di!usion of c rays in extended media is the mass attenuation coe$cient (k/o). Accurate values of (k/o) of c rays in several materials are of interest for industrial, biological, agricultural, and medical studies. They are also needed in solving various problems in radiation physics and radiation dosimetry. Recently, a signi"cant number
夽
See also Nucl. Instr. and Meth. A 446 (2000) 498}504. * Corresponding author. Fax: 020-863-42601. E-mail address: [email protected] (M.A. Abdel-Rahman).
of photon attenuation coe$cient measurements, calculations, and compilations have been published [1}12]. Appreciable discrepancies between some of the experimental and theoretical values indicate the need for additional accurate and consistent measurements of total mass attenuation coe$cients. Conner et al. [13], Goswami et al. [14,15], Gopal et al. [16], and Makhan et al. [17] investigated the e!ect of sample thickness on the measured (k/o) of some elements and compounds. The conclusions in Refs. [16,17] reported an increase in the (k/o) with increasing the absorber thickness after 1 mean free path. These conclusions deviate from the result obtained in Refs. [13}15], where the experimental values of the mass attenuation coe$cient remain constant between 1 and 3 mean free
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 2 5 7 - 7
M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
path. Keeping the above points in view, an attempt was made to investigate the e!ect of absorber thickness on (k/o) of perspex, para$n, bakelite, Cu, Pb and Hg at three energies (59.54, 661.6, and 1332.5 keV).
2. Experiment Fig. 1 represents a schematic diagram of the experimental arrangement and a c-ray spectrometer. The c-ray source is located in a collimated lead
433
source holder, 17 cm in diameter with a collimating hole 3 mm in diameter and 24.5 mm in length. The radiation leaving this collimator was allowed to fall on the sample A. The transmitted radiation was allowed to pass through another four collimators of a total thickness of 24 cm of lead with axial holes 0.5, 1, 1.05 and 2 cm in diameter, respectively. The collimator shields prevent photons scattered in the air, nearby objects, and the shield materials from reaching the detector. The radiation leaving this collimator was allowed to fall on a 3 in.;3 in. NaI(Tl) scintillation crystal (adequately shielded
Fig. 1. (a) Schematic diagram of the experimental arrangement. (b) Block diagram for c-ray spectrometer.
434
M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
from external radiation) coupled to a conventional system of photomultiplier tube, pre-ampli"er (type `ORTECa model `276a), ampli"er (type `ORTECa model `575a), high-voltage unit (type `ORTECa model `487a) and a multichannel analyzer (type `ORTECa model `7150a). The source, the collimators and the detector shields (having the same dimension 17 cm in diameter) were mounted on two iron bars of 2 m length, "xed on a rigid bench in the middle of an air-conditioned room. The position of the collimators can easily be changed, so that measurements at two or more geometries could be carried out after minor changes of the collimator separation or aperatures. The symmetry axis of the arrangement is a horizontal line adjusted by a laser beam. The radiation beam cross-sectional area at the absorber position must be less than that of the absorber area to avoid contribution from direct photons in the transmitted intensity. The collimator holes lie on the same source detector solid angle, to prevent contribution from terminated photons. In measurements carried out with sample at 35 cm from the source, the collimation solid angle subtended by the detector at the attenuator was 9.1;10\ sr and the maximum scattering angle was h &0.53. In the measurements per formed using the Co source, the exit aperture was 0.5 cm in diameter, the source detector solid angle was 4.06;10\ sr, the collimation solid angle was &10\ sr and the maximum scattering angle was h "2.33.
channels under the (FWHM) for measurements performed with Co source to avoid the contribution from the low-energy component. The attenuated beam intensities were measured with the sample placed in a movable holder, which positioned the sample normal to the incident beam. The sample could be moved with respect to the beam so that any part of the sample surface could be exposed to the c rays. For liquid samples the incident beam intensity was taken with an empty container, similar to that contained the sample, and placed in the attenuator position. The backgrounds were taken as the channel contents of the photopeak under consideration after placing a 15 cm lead block in the beam path. For each sample, counts were taken in the sequence of Conner et al. [13].
4. Results and discussion The measured values of mass attenuation coe$cients k/o cm/g of perspex, bakelite, Cu, and Pb, for 59.54 keV c-rays, against the absorber thickness [(k/o);t] (number of mean free paths), are shown in Figs. 2}4. It is seen that for these chosen materials k/o remains constant in good agreement with
3. Experimental procedure Measurements were carried out under steady conditions of the detector system. No drift of the photopeak was detected for at least 12 h. In addition to sample thickness, three quantities were measured to calculate the mass attenuation coe$cients, namely the incident beam intensity, the attenuated beam intensity and the background for the same time period (1000 s in the present work) and the same condition. These intensities were taken as the total counts in channels under the whole photopeak for measurements performed with Am and Cs sources and taken as the total counts in the
Fig. 2. Experimental and theoretical values of (k/o), of perspex and bakelite, for 59.54 keV c rays, as a function of [(k/o);t].
M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
Fig. 3. Experimental and theoretical values of (k/o), of copper, for 59.54 keV c-rays, as a function of [(k/o);t] at two solid angle .
Fig. 4. Experimental and theoretical values of (k/o), of Pb, for 59.54 keV c-rays, as a function of [(k/o);t].
the theoretical values up to 3 mean free paths and after that k/o values for Cu Figs. 3 and 4 decrease with the further increase in the absorber thickness. This result may be attributed to the increase in the
435
Fig. 5. Experimental and theoretical values of (k/o), of Al, perspex para$n, Al, Hg and Pb, for 661.6 keV c-rays, as a function of [(k/o);t].
number of small-angle scattering and multiple scattering photons that reach the detector. This e!ect of the contribution from the scattered photons for large thickness samples can be reduced by decreasing the collimation solid angle as illustrated in Fig. 3. The values of k/o for perspex, para$n, Al, Pb and Hg, for 661.6 keV c-rays, as a function of the absorber thickness [(k/o);t], are shown in Fig. 5. It is clear that for perspex, para$n, Al and Pb k/o remains constant in good agreement with the theoretical values up to three mean free path sample thicknesses. But for Hg the value of k/o decreases as the sample thickness increases beyond 3 mean free paths. This result may be also attributed to the increase in the number of scattered photons reaching the detector. Fig. 6 shows the values of k/o of perspex, Cu, Pb and Hg, for 1332.5 keV c-rays, as a function of the absorber thickness (k/o);t. It is obvious that k/o remains constant in good agreement with the theoretical values up to 3 mean free path sample thickness. It is also observed that for small sample thickness less than 1 mean free path, the statistical error becomes large. These results agree with the conclusions reported in Refs. [13}15], but do not agree with the results reported in Refs. [16,17].
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M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
Fig. 6. Experimental and theoretical values of (k/o) of perspex, Cu, Pb and Hg, for 1332.5 keV c-rays, as a function of [(k/o);t].
References [1] J.H. Hubbell, Int. J. Appl. Radiat. Isot. 33 (1982) 1269.
[2] D.F. Jackson, D.J. Hawkes, Phys. Rep. 70 (1981) 169. [3] G.S. Mudahar, M. Singh, G. Singh, Appl. Radiat. Isot. 42 (1991) 509. [4] G.S. Bhandal, K. Singh, Appl. Radiat. Isot. 43 (1992) 517. [5] M.J. Berger, J.H. Hubbell, (XCOM) Photon cross section on a personal computer, NBSIR 87-3597 (1987). [6] A.H. El-kateb, A.S. Abdul-Hamid, Appl. Radiat. Isot. 42 (1991) 303. [7] G.S. Bhandal, I. Ahmed, K. Singh, Appl. Radiat. Isot. 43 (1992) 1185. [8] A. Perumallu, A.S. Nageswara Rao, K. Rao, Can. J. Phys. 62 (1984) 454. [9] S. Lingam, K. Suresh Babu, D.V. Reddy, Indian J. Phys. 58A (1984) 285. [10] D.A. Bradley, C.S. Chong, A.M. Ghose, Appl. Radiat. Isot. 37 (1986) 1195. [11] V. Lakshminarayana, A.T.L. Tan, I.S. Giles, A. Rajartnam, Nuovo Cimento 91A (1986) 331. [12] A.T.L. Tan, V. Lakshminarayana, I.S. Giles, A. Rajartnam, Nuovo Cimento 99A (1988) 587. [13] A.L. Conner, H.F. Atwater, E.H. Plassmann, J.H. McCrary, Phys. Rev. 1A (1970) 539. [14] B. Goswami, N. Chowdhuri, Phys. Rev. 7A (1973) 1912. [15] B. Goswami, N. Chowdhuri, Nucl. Instr. and Meth. 92 (1971) 433. [16] S. Gopal, B. Sanjeevaiah, Nucl. Instr. and Meth. 107 (1973) 221. [17] M. Singh, G. Mudahar, Indian J. Phys. 67A (1993) 79.
E!ect of sample thickness on the measured mass attenuation coe$cients of some compounds and elements for 59.54, 661.6 and 1332.5 keV c-rays夽 M.A. Abdel-Rahman*, E.A. Badawi, Y.L. Abdel-Hady, N. Kamel Department of Physics, Faculty of Science, El-Minia University, El-Minia, Egypt Received 3 August 1999; received in revised form 27 September 1999; accepted 10 November 1999
Abstract Measurements have been made to determine c-rays attenuation coe$cients very accurately by using an extremely narrow-collimated-beam transmission method. The e!ect of the sample thickness on the measured values of the mass attenuation coe$cients (k/o) cm/g of perspex, bakelite, para$n, Al, Cu, Pb and Hg have been investigated at three di!erent c-ray energies (59.54, 661.6 and 1332.5 keV). It is seen that for these chosen materials (k/o) remains constant in good agreement with the theoretical values up to 3 mean free paths and after that (k/o) values for Cu, Pb and Hg decrease with further increase in the absorber thickness. This result may be attributed to the increase in the number of coherent small-angle scattering photons which reach the detector. 2000 Elsevier Science B.V. All rights reserved. Keywords: Attenuation coe$cients; c-Rays
1. Introduction The most important quantity characterizing the penetration and di!usion of c rays in extended media is the mass attenuation coe$cient (k/o). Accurate values of (k/o) of c rays in several materials are of interest for industrial, biological, agricultural, and medical studies. They are also needed in solving various problems in radiation physics and radiation dosimetry. Recently, a signi"cant number
夽
See also Nucl. Instr. and Meth. A 446 (2000) 498}504. * Corresponding author. Fax: 020-863-42601. E-mail address: [email protected] (M.A. Abdel-Rahman).
of photon attenuation coe$cient measurements, calculations, and compilations have been published [1}12]. Appreciable discrepancies between some of the experimental and theoretical values indicate the need for additional accurate and consistent measurements of total mass attenuation coe$cients. Conner et al. [13], Goswami et al. [14,15], Gopal et al. [16], and Makhan et al. [17] investigated the e!ect of sample thickness on the measured (k/o) of some elements and compounds. The conclusions in Refs. [16,17] reported an increase in the (k/o) with increasing the absorber thickness after 1 mean free path. These conclusions deviate from the result obtained in Refs. [13}15], where the experimental values of the mass attenuation coe$cient remain constant between 1 and 3 mean free
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 2 5 7 - 7
M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
path. Keeping the above points in view, an attempt was made to investigate the e!ect of absorber thickness on (k/o) of perspex, para$n, bakelite, Cu, Pb and Hg at three energies (59.54, 661.6, and 1332.5 keV).
2. Experiment Fig. 1 represents a schematic diagram of the experimental arrangement and a c-ray spectrometer. The c-ray source is located in a collimated lead
433
source holder, 17 cm in diameter with a collimating hole 3 mm in diameter and 24.5 mm in length. The radiation leaving this collimator was allowed to fall on the sample A. The transmitted radiation was allowed to pass through another four collimators of a total thickness of 24 cm of lead with axial holes 0.5, 1, 1.05 and 2 cm in diameter, respectively. The collimator shields prevent photons scattered in the air, nearby objects, and the shield materials from reaching the detector. The radiation leaving this collimator was allowed to fall on a 3 in.;3 in. NaI(Tl) scintillation crystal (adequately shielded
Fig. 1. (a) Schematic diagram of the experimental arrangement. (b) Block diagram for c-ray spectrometer.
434
M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
from external radiation) coupled to a conventional system of photomultiplier tube, pre-ampli"er (type `ORTECa model `276a), ampli"er (type `ORTECa model `575a), high-voltage unit (type `ORTECa model `487a) and a multichannel analyzer (type `ORTECa model `7150a). The source, the collimators and the detector shields (having the same dimension 17 cm in diameter) were mounted on two iron bars of 2 m length, "xed on a rigid bench in the middle of an air-conditioned room. The position of the collimators can easily be changed, so that measurements at two or more geometries could be carried out after minor changes of the collimator separation or aperatures. The symmetry axis of the arrangement is a horizontal line adjusted by a laser beam. The radiation beam cross-sectional area at the absorber position must be less than that of the absorber area to avoid contribution from direct photons in the transmitted intensity. The collimator holes lie on the same source detector solid angle, to prevent contribution from terminated photons. In measurements carried out with sample at 35 cm from the source, the collimation solid angle subtended by the detector at the attenuator was 9.1;10\ sr and the maximum scattering angle was h &0.53. In the measurements per formed using the Co source, the exit aperture was 0.5 cm in diameter, the source detector solid angle was 4.06;10\ sr, the collimation solid angle was &10\ sr and the maximum scattering angle was h "2.33.
channels under the (FWHM) for measurements performed with Co source to avoid the contribution from the low-energy component. The attenuated beam intensities were measured with the sample placed in a movable holder, which positioned the sample normal to the incident beam. The sample could be moved with respect to the beam so that any part of the sample surface could be exposed to the c rays. For liquid samples the incident beam intensity was taken with an empty container, similar to that contained the sample, and placed in the attenuator position. The backgrounds were taken as the channel contents of the photopeak under consideration after placing a 15 cm lead block in the beam path. For each sample, counts were taken in the sequence of Conner et al. [13].
4. Results and discussion The measured values of mass attenuation coe$cients k/o cm/g of perspex, bakelite, Cu, and Pb, for 59.54 keV c-rays, against the absorber thickness [(k/o);t] (number of mean free paths), are shown in Figs. 2}4. It is seen that for these chosen materials k/o remains constant in good agreement with
3. Experimental procedure Measurements were carried out under steady conditions of the detector system. No drift of the photopeak was detected for at least 12 h. In addition to sample thickness, three quantities were measured to calculate the mass attenuation coe$cients, namely the incident beam intensity, the attenuated beam intensity and the background for the same time period (1000 s in the present work) and the same condition. These intensities were taken as the total counts in channels under the whole photopeak for measurements performed with Am and Cs sources and taken as the total counts in the
Fig. 2. Experimental and theoretical values of (k/o), of perspex and bakelite, for 59.54 keV c rays, as a function of [(k/o);t].
M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
Fig. 3. Experimental and theoretical values of (k/o), of copper, for 59.54 keV c-rays, as a function of [(k/o);t] at two solid angle .
Fig. 4. Experimental and theoretical values of (k/o), of Pb, for 59.54 keV c-rays, as a function of [(k/o);t].
the theoretical values up to 3 mean free paths and after that k/o values for Cu Figs. 3 and 4 decrease with the further increase in the absorber thickness. This result may be attributed to the increase in the
435
Fig. 5. Experimental and theoretical values of (k/o), of Al, perspex para$n, Al, Hg and Pb, for 661.6 keV c-rays, as a function of [(k/o);t].
number of small-angle scattering and multiple scattering photons that reach the detector. This e!ect of the contribution from the scattered photons for large thickness samples can be reduced by decreasing the collimation solid angle as illustrated in Fig. 3. The values of k/o for perspex, para$n, Al, Pb and Hg, for 661.6 keV c-rays, as a function of the absorber thickness [(k/o);t], are shown in Fig. 5. It is clear that for perspex, para$n, Al and Pb k/o remains constant in good agreement with the theoretical values up to three mean free path sample thicknesses. But for Hg the value of k/o decreases as the sample thickness increases beyond 3 mean free paths. This result may be also attributed to the increase in the number of scattered photons reaching the detector. Fig. 6 shows the values of k/o of perspex, Cu, Pb and Hg, for 1332.5 keV c-rays, as a function of the absorber thickness (k/o);t. It is obvious that k/o remains constant in good agreement with the theoretical values up to 3 mean free path sample thickness. It is also observed that for small sample thickness less than 1 mean free path, the statistical error becomes large. These results agree with the conclusions reported in Refs. [13}15], but do not agree with the results reported in Refs. [16,17].
436
M.A. Abdel-Rahman et al. / Nuclear Instruments and Methods in Physics Research A 447 (2000) 432}436
Fig. 6. Experimental and theoretical values of (k/o) of perspex, Cu, Pb and Hg, for 1332.5 keV c-rays, as a function of [(k/o);t].
References [1] J.H. Hubbell, Int. J. Appl. Radiat. Isot. 33 (1982) 1269.
[2] D.F. Jackson, D.J. Hawkes, Phys. Rep. 70 (1981) 169. [3] G.S. Mudahar, M. Singh, G. Singh, Appl. Radiat. Isot. 42 (1991) 509. [4] G.S. Bhandal, K. Singh, Appl. Radiat. Isot. 43 (1992) 517. [5] M.J. Berger, J.H. Hubbell, (XCOM) Photon cross section on a personal computer, NBSIR 87-3597 (1987). [6] A.H. El-kateb, A.S. Abdul-Hamid, Appl. Radiat. Isot. 42 (1991) 303. [7] G.S. Bhandal, I. Ahmed, K. Singh, Appl. Radiat. Isot. 43 (1992) 1185. [8] A. Perumallu, A.S. Nageswara Rao, K. Rao, Can. J. Phys. 62 (1984) 454. [9] S. Lingam, K. Suresh Babu, D.V. Reddy, Indian J. Phys. 58A (1984) 285. [10] D.A. Bradley, C.S. Chong, A.M. Ghose, Appl. Radiat. Isot. 37 (1986) 1195. [11] V. Lakshminarayana, A.T.L. Tan, I.S. Giles, A. Rajartnam, Nuovo Cimento 91A (1986) 331. [12] A.T.L. Tan, V. Lakshminarayana, I.S. Giles, A. Rajartnam, Nuovo Cimento 99A (1988) 587. [13] A.L. Conner, H.F. Atwater, E.H. Plassmann, J.H. McCrary, Phys. Rev. 1A (1970) 539. [14] B. Goswami, N. Chowdhuri, Phys. Rev. 7A (1973) 1912. [15] B. Goswami, N. Chowdhuri, Nucl. Instr. and Meth. 92 (1971) 433. [16] S. Gopal, B. Sanjeevaiah, Nucl. Instr. and Meth. 107 (1973) 221. [17] M. Singh, G. Mudahar, Indian J. Phys. 67A (1993) 79.