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Angular properties of 6.13 MeV gamma rays penetrating lead, steel and concrete shields
165
Nuclear Instruments and Methods in Physics Research A255 (1987) 165-168 North-Holland, Amsterdam
ANGULAR PROPERTIES OF 6.13 MeV GAMMA RAYS PENETRATING LEAD, STEEL AND CONCRETE SHIELDS G.B . BISHOP
Department of Mechanical Engineering, The University of Liverpool, PO Box 147, Liverpool, L69 3BX, UK
Experimentally determined angular flux spectra for 6.13 MeV source photons from disc geometry penetrating shielding slabs of lead, steel and concrete are analysed . For all three shield materials, the proportion of photons scattered in a forward direction increases with increasing penetration thickness. At any given polar angle, the scattered photon properties decrease exponentially with increasing shield thickness. An angular exposure dose buildup factor is defined and angular contributions to the scalar buildup factor are presented. 1. Introduction In any radiation field, the angular flux at a specified position and angle is the most basic characteristic of the scattered radiation. Integration of the angular flux over all directions gives the scalar flux from which integrated properties such as exposure rate and buildup factor can be evaluated. Benchmark angular flux spectra for 6.13 MeV source photons emitted from disc geometry penetrating shielding slabs of lead, steel and concrete have been obtained by experimental measurement and reported by Banai [1] and Bishop and Banai [2]. The source photons were emitted from the decay of nitrogen-16 produced in the URR reactor cooling water flowing between the fuel plates in regions of high fast neutron flux . The activated water was pumped to a shielded cell containing the disc radiator at one end. The source-shield-detector geometry is shown in fig. 1. Measurements were taken with a lead collimated sodium iodide detector at polar angles (B) of 0° (source axis), 15°, 30°, 40°, 50° and 60° . The detector spectrometer pulse height distributions were unfolded using the code RADAK [3]. The angular spectra O(fLx, E;, 0) were presented as photon fluxes per cm2 s sr MeV for 32 energy bins covering the energy range 110 keV up to source energies . The term a x represents the shield thickness in mean free paths. The first 29 bins represent the energy distribution of the scattered photons above 110 keV, which was the lowest practical level of measurement, and the values given are for the flux at the mid-bin energy E;. The MeV-1 in the flux unit relates to the energy width of the bin AE; . Bin number 30 represented the value for the uncollided flux of 6.13 MeV photons. Two additional bins take account of the 7% of the source photons emitted in the decay of nitrogen-16 at 7.12 MeV. Since the reaction cross sections for 7.12 0168-9002/87/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
MeV photons differ only slightly from those for the 6.13 MeV photons, it was assumed that 7% of the scattered photons in all the bins 1-29 originated from the higher energy source photons . All the flux values given were related to a source strength of 6.13 MeV photons of 6.816 X 10 5 photons s-1 cm2 where cm2 refers to unit area of the uniform disc source . Analysis of the angular flux spectra has been carried out. The variation of the total energy of the scattered photons with polar angle, and penetration depth has been established for each shield material . Spectral changes have been analysed and the concept of angular buildup factor discussed and characteristics established .
i
I
I
I
i
(50cm. rad) for different angular position
Shield supporting trame(zero shield position)
Fig. 1. Schematic plan view of the experimental setup. II . RADIATION TRANSPORT
166
GB . Bishop / Angular properties of 6.13 Me V gamma rays
2. Experimental determination of angular flux spectra The nitrogen-16 radiation facility, installed on the Universities Research Reactor at Risley, near Warrington, provides a uniform disc source of 6.13 MeV photons at one end of a shielded cell . Nitrogen-16 is produced by the 16O(n, P) 16 N reaction as the reactor cooling water flows over the fuel element plates. Nitrogen-16 decays with a 7.3 s half-life emitting 6.13 and 7.12 MeV gamma-rays with relative contributions of 93% and 7% respectively. A detailed description of the facility has been reported [4]. Due to the short half-life of the nitrogen-16 and the finite time of the activated water to flow through the disc radiator, the water cross section through the disc must be adjusted to maintain uniform photon emission per unit surface area over the entire disc surface. The development of the disc radiator design has been described by Bishop and Cleaver [5]. Angular flux measurements were taken with a lead collimated 7.54 cm diameter x 7.54 cm NaI(T1) scintillation detector coupled to an amplifier and pulse height analyser. The detector has been calibrated with a number of monoenergetic gamma-ray emitting radioisotopes over the desired energy range. An established method of generating a collimated detector response matrix, incorporating the response function linear interpolation method of Marker and Muckenthaler [6] and the determination of the integrated effective aperture of the collimator by the linear model of Dahlstrom and Thompson [7], has been described by Bishop and Abookazemi (1979) . In establishing a 32 x 64 response matrix, the method of Dahlstrom and Thompson was modified to an exponential model following analysis of the observations of Watts and Pena [8]. To obtain angular flux spectra, the measured pulse height distributions were unfolded using the code RADAK. This code was chosen on the basis of the conclusions drawn by Marafie and Bishop [9,10] in their
105 Es(8) 10 MeV
comparison of unfolding codes. RADAK provides the facility to unfold up to 10 consistent sets of input data ; allows for errors in the response matrix elements and input data ; incorporates the theory of maximum likelihood to the solution ; and applies a Monte Carlo sampling procedure to estimate standard deviations for each element of the unfolded flux spectra. It was considered as ideal for the "benchmark" criteria. The accuracy of the unfolded spectra depends directly on the accuracy of the response matrix elements in representing the detector performance. Tests of the response matrix were made by unfolding pulse height distributions obtained from characteristic gamma-ray emission from selected radioisotopes. Results showed the excellent resolving power of the method used. 3. Angular distribution of the scattered photon energy The energies of the scattered photons ES (MeV) at the measured polar angles 0 have been calculated for all three shield materials and thicknesses using the expression : 29
E,(0)
= Y_ E,B(gx, Ei , B)JE, . i=1
Fig. 2 shows how ES(B) varies with 0 and 1Ax for lead, steel and concrete (density 2.33 g cm -3 ). In all three materials, the forward scattering becomes more pronounced with increasing shield penetration, particularly so with the lowest atomic number material concrete . To obtain a relationship for the energy attenuation of the scattered photons penetrating each shield material, Es(B) was plotted against penetration thickness for each polar angle (fig . 3) . The curves show that the scattered energy at each polar angle was attenuated exponentially with the exponential coefficient increasing with increas-
Lead m.f.p . 126
103
Fig. 2. Variation of total scattered energy with polar angle and penetration depth for lead, steel and concrete shields.
167
G. B. Bishop / Angular properties of 6.13 Me V gamma rays 105 ES (9) Me 104
2
6 4 ~,x m1p .
0
2
4 6 (l.x m .f.p.
Fig. 3 . Scattered energy attenuation, through lead, steel and concrete shields .
ing polar angle . Assuming that this property applied at deeper penetrations, then the scattered energy at any polar angle and shield thickness could be predicted . 4. Spectral variations with shield penetration Comparisons were made of the scattered energy spectra over the range of shield penetration thicknesses. Fig. 4 compares the scattered energy spectrum leaving similar shield thicknesses (- 3 .7 m.f .p .) of lead, steel and concrete . The effect of the increasing pair-production cross section and photoelectric cross section with increasing atomic number is shown in the relative removal of high and low energy photons respectively . This removal is partially offset by the bremsstrahlung photon
production which increases with increasing Z. The bremsstrahlung contribution to the lead spectrum can be seen up to an energy level of about 2 .5 MeV and up to about 1 MeV in the steel spectrum . The overall integrated results leads to a similar value for E,(0°) for steel and concrete and a lower value for lead. For concrete shields, with low equivalent atomic number and predominantly Compton scattering reactions, the spectra hardened with penetration depth . Fig. 5 shows how the concrete spectrum changes with penetration depth. The curves for concrete were normalised to the total scattered energy E,(0°) for 1 .23 m.f .p . penetration. The situation can be compared to neutron scattering within the reflector region of the reaction . There is a higher probability of the low energy multiply scattered photons returning towards the source .
104 ,~ Concrete 3-70mtp. i
3-65m .f.p .
i
i
Lead
E S (0°) M eV
Concrete
3-70m .tp . 2-47m .t p 1- 23nf.p .
377m .f.p . 103
10 Fig. 4 . Comparison of the scattered energy spectra at 0° polar angle for similar penetration depths in lead, steel and concrete shields .
Fig. 5 . Comparison of the scattered energy spectra at 0° polar angle for 1 .23, 2 .47, 3 .70 m .f .p . concrete shields with values normalized to 1 .23 m .f.p . II . RADIATION TRANSPORT
168
G. B. Bishop /Angularproperties of 6.13 McVgamma rays
60°
50°
40°
30°
MIp
Bo
1-22 2.43 3-65 4-86
1390 1616 1917 2167
Fig. 6. Variation of angular exposure dose-rate buildup factor with polar angle in steel shields . 5. Angular exposure dose buildup factor The angular exposure dose buildup factor BD(B) has been calculated using the expression : 29
BD(e)
__
Y, k(Ei )O(gx, E,, 9)Ei áE,
i_1
k(EO)O(ttx, E,)EoaEo
+1,
where k(Ei) converts the energy flux from MeV cm -2 s-1 sr -1 to Sv h-1 sr -1 ; the suffix 0 refers to the source energy 6.13 MeV represented by energy bin number 30 ; and O(px, Eo ) is the uncollided scalar flux leaving the shield after a penetration thickness px . Fig. 6 illustrates the variation of BD(B) with polar angle and m.f.p . penetration for steel shields. Similar distributions were obtained for lead and concrete . Fig. 6 clearly shows the buildup of forward scattered photons with increasing penetration . Also given in fig. 6 are the scalar exposure dose buildup factors for each steel shield thickness. At higher penetrations the forward-scattered photons make the dominant contribution to the scalar buildup factor.
with its higher ratio of Compton scatterings . At any given polar angle, the scattered photon flux, total energy and exposure dose-rate decrease exponentially with increasing shield thickness. The variation of the angular buildup factor with polar angle illustrated the buildup of forward-scattered photons with penetration depth. Acknowledgements The author wishes to thank Dr . J. Banai for his work in establishing the benchmark angular spectra from which the angular properties have been derived. References [1] [2] [3] [4] [5]
6. Conclusions
[6]
Experimental results for the angular penetration of 6.13 MeV photons through lead, steel and concrete have been analysed . For all three materials, the photon distribution leaving the outer shield surface was increasing in the forward direction as the penetration thickness increased. This was more marked for the concrete shield
[7] [8] [91 [10]
J. Banai Ph .D . Thesis, University of Liverpool (1984) . G.B . Bishop and J. Banai, Ann. Nucl . En . 12 (1985) 593. M.J . Grimstone Report AEEW-M-1455 (1976). G.B . Bishop and I. Birchhall, Ann. Nucl. En . 2 (1975) 467. G.B . Bishop and J.W . Cleaver, J. Brit, Nucl . En. Soc. 11 (1972) 113 . R.E. Maerker and F.J . Muckenthaler, Report ORNL-4382 (1967) . T.S. Dahlstrom and W.E. Thompson, Report USN-RDLTR-558 (1962) . R.S . Watts and H.G. Pena, J. Nucl. Biol . Med. 16 (1972) 51 . A.M. Marafie and G.B. Bishop, Ann. Nucl . En . 5 (1978) 197. A.M . Marafie and G.B . Bishop, Nucl . En . 18 (1979) 409.
Nuclear Instruments and Methods in Physics Research A255 (1987) 165-168 North-Holland, Amsterdam
ANGULAR PROPERTIES OF 6.13 MeV GAMMA RAYS PENETRATING LEAD, STEEL AND CONCRETE SHIELDS G.B . BISHOP
Department of Mechanical Engineering, The University of Liverpool, PO Box 147, Liverpool, L69 3BX, UK
Experimentally determined angular flux spectra for 6.13 MeV source photons from disc geometry penetrating shielding slabs of lead, steel and concrete are analysed . For all three shield materials, the proportion of photons scattered in a forward direction increases with increasing penetration thickness. At any given polar angle, the scattered photon properties decrease exponentially with increasing shield thickness. An angular exposure dose buildup factor is defined and angular contributions to the scalar buildup factor are presented. 1. Introduction In any radiation field, the angular flux at a specified position and angle is the most basic characteristic of the scattered radiation. Integration of the angular flux over all directions gives the scalar flux from which integrated properties such as exposure rate and buildup factor can be evaluated. Benchmark angular flux spectra for 6.13 MeV source photons emitted from disc geometry penetrating shielding slabs of lead, steel and concrete have been obtained by experimental measurement and reported by Banai [1] and Bishop and Banai [2]. The source photons were emitted from the decay of nitrogen-16 produced in the URR reactor cooling water flowing between the fuel plates in regions of high fast neutron flux . The activated water was pumped to a shielded cell containing the disc radiator at one end. The source-shield-detector geometry is shown in fig. 1. Measurements were taken with a lead collimated sodium iodide detector at polar angles (B) of 0° (source axis), 15°, 30°, 40°, 50° and 60° . The detector spectrometer pulse height distributions were unfolded using the code RADAK [3]. The angular spectra O(fLx, E;, 0) were presented as photon fluxes per cm2 s sr MeV for 32 energy bins covering the energy range 110 keV up to source energies . The term a x represents the shield thickness in mean free paths. The first 29 bins represent the energy distribution of the scattered photons above 110 keV, which was the lowest practical level of measurement, and the values given are for the flux at the mid-bin energy E;. The MeV-1 in the flux unit relates to the energy width of the bin AE; . Bin number 30 represented the value for the uncollided flux of 6.13 MeV photons. Two additional bins take account of the 7% of the source photons emitted in the decay of nitrogen-16 at 7.12 MeV. Since the reaction cross sections for 7.12 0168-9002/87/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
MeV photons differ only slightly from those for the 6.13 MeV photons, it was assumed that 7% of the scattered photons in all the bins 1-29 originated from the higher energy source photons . All the flux values given were related to a source strength of 6.13 MeV photons of 6.816 X 10 5 photons s-1 cm2 where cm2 refers to unit area of the uniform disc source . Analysis of the angular flux spectra has been carried out. The variation of the total energy of the scattered photons with polar angle, and penetration depth has been established for each shield material . Spectral changes have been analysed and the concept of angular buildup factor discussed and characteristics established .
i
I
I
I
i
(50cm. rad) for different angular position
Shield supporting trame(zero shield position)
Fig. 1. Schematic plan view of the experimental setup. II . RADIATION TRANSPORT
166
GB . Bishop / Angular properties of 6.13 Me V gamma rays
2. Experimental determination of angular flux spectra The nitrogen-16 radiation facility, installed on the Universities Research Reactor at Risley, near Warrington, provides a uniform disc source of 6.13 MeV photons at one end of a shielded cell . Nitrogen-16 is produced by the 16O(n, P) 16 N reaction as the reactor cooling water flows over the fuel element plates. Nitrogen-16 decays with a 7.3 s half-life emitting 6.13 and 7.12 MeV gamma-rays with relative contributions of 93% and 7% respectively. A detailed description of the facility has been reported [4]. Due to the short half-life of the nitrogen-16 and the finite time of the activated water to flow through the disc radiator, the water cross section through the disc must be adjusted to maintain uniform photon emission per unit surface area over the entire disc surface. The development of the disc radiator design has been described by Bishop and Cleaver [5]. Angular flux measurements were taken with a lead collimated 7.54 cm diameter x 7.54 cm NaI(T1) scintillation detector coupled to an amplifier and pulse height analyser. The detector has been calibrated with a number of monoenergetic gamma-ray emitting radioisotopes over the desired energy range. An established method of generating a collimated detector response matrix, incorporating the response function linear interpolation method of Marker and Muckenthaler [6] and the determination of the integrated effective aperture of the collimator by the linear model of Dahlstrom and Thompson [7], has been described by Bishop and Abookazemi (1979) . In establishing a 32 x 64 response matrix, the method of Dahlstrom and Thompson was modified to an exponential model following analysis of the observations of Watts and Pena [8]. To obtain angular flux spectra, the measured pulse height distributions were unfolded using the code RADAK. This code was chosen on the basis of the conclusions drawn by Marafie and Bishop [9,10] in their
105 Es(8) 10 MeV
comparison of unfolding codes. RADAK provides the facility to unfold up to 10 consistent sets of input data ; allows for errors in the response matrix elements and input data ; incorporates the theory of maximum likelihood to the solution ; and applies a Monte Carlo sampling procedure to estimate standard deviations for each element of the unfolded flux spectra. It was considered as ideal for the "benchmark" criteria. The accuracy of the unfolded spectra depends directly on the accuracy of the response matrix elements in representing the detector performance. Tests of the response matrix were made by unfolding pulse height distributions obtained from characteristic gamma-ray emission from selected radioisotopes. Results showed the excellent resolving power of the method used. 3. Angular distribution of the scattered photon energy The energies of the scattered photons ES (MeV) at the measured polar angles 0 have been calculated for all three shield materials and thicknesses using the expression : 29
E,(0)
= Y_ E,B(gx, Ei , B)JE, . i=1
Fig. 2 shows how ES(B) varies with 0 and 1Ax for lead, steel and concrete (density 2.33 g cm -3 ). In all three materials, the forward scattering becomes more pronounced with increasing shield penetration, particularly so with the lowest atomic number material concrete . To obtain a relationship for the energy attenuation of the scattered photons penetrating each shield material, Es(B) was plotted against penetration thickness for each polar angle (fig . 3) . The curves show that the scattered energy at each polar angle was attenuated exponentially with the exponential coefficient increasing with increas-
Lead m.f.p . 126
103
Fig. 2. Variation of total scattered energy with polar angle and penetration depth for lead, steel and concrete shields.
167
G. B. Bishop / Angular properties of 6.13 Me V gamma rays 105 ES (9) Me 104
2
6 4 ~,x m1p .
0
2
4 6 (l.x m .f.p.
Fig. 3 . Scattered energy attenuation, through lead, steel and concrete shields .
ing polar angle . Assuming that this property applied at deeper penetrations, then the scattered energy at any polar angle and shield thickness could be predicted . 4. Spectral variations with shield penetration Comparisons were made of the scattered energy spectra over the range of shield penetration thicknesses. Fig. 4 compares the scattered energy spectrum leaving similar shield thicknesses (- 3 .7 m.f .p .) of lead, steel and concrete . The effect of the increasing pair-production cross section and photoelectric cross section with increasing atomic number is shown in the relative removal of high and low energy photons respectively . This removal is partially offset by the bremsstrahlung photon
production which increases with increasing Z. The bremsstrahlung contribution to the lead spectrum can be seen up to an energy level of about 2 .5 MeV and up to about 1 MeV in the steel spectrum . The overall integrated results leads to a similar value for E,(0°) for steel and concrete and a lower value for lead. For concrete shields, with low equivalent atomic number and predominantly Compton scattering reactions, the spectra hardened with penetration depth . Fig. 5 shows how the concrete spectrum changes with penetration depth. The curves for concrete were normalised to the total scattered energy E,(0°) for 1 .23 m.f .p . penetration. The situation can be compared to neutron scattering within the reflector region of the reaction . There is a higher probability of the low energy multiply scattered photons returning towards the source .
104 ,~ Concrete 3-70mtp. i
3-65m .f.p .
i
i
Lead
E S (0°) M eV
Concrete
3-70m .tp . 2-47m .t p 1- 23nf.p .
377m .f.p . 103
10 Fig. 4 . Comparison of the scattered energy spectra at 0° polar angle for similar penetration depths in lead, steel and concrete shields .
Fig. 5 . Comparison of the scattered energy spectra at 0° polar angle for 1 .23, 2 .47, 3 .70 m .f .p . concrete shields with values normalized to 1 .23 m .f.p . II . RADIATION TRANSPORT
168
G. B. Bishop /Angularproperties of 6.13 McVgamma rays
60°
50°
40°
30°
MIp
Bo
1-22 2.43 3-65 4-86
1390 1616 1917 2167
Fig. 6. Variation of angular exposure dose-rate buildup factor with polar angle in steel shields . 5. Angular exposure dose buildup factor The angular exposure dose buildup factor BD(B) has been calculated using the expression : 29
BD(e)
__
Y, k(Ei )O(gx, E,, 9)Ei áE,
i_1
k(EO)O(ttx, E,)EoaEo
+1,
where k(Ei) converts the energy flux from MeV cm -2 s-1 sr -1 to Sv h-1 sr -1 ; the suffix 0 refers to the source energy 6.13 MeV represented by energy bin number 30 ; and O(px, Eo ) is the uncollided scalar flux leaving the shield after a penetration thickness px . Fig. 6 illustrates the variation of BD(B) with polar angle and m.f.p . penetration for steel shields. Similar distributions were obtained for lead and concrete . Fig. 6 clearly shows the buildup of forward scattered photons with increasing penetration . Also given in fig. 6 are the scalar exposure dose buildup factors for each steel shield thickness. At higher penetrations the forward-scattered photons make the dominant contribution to the scalar buildup factor.
with its higher ratio of Compton scatterings . At any given polar angle, the scattered photon flux, total energy and exposure dose-rate decrease exponentially with increasing shield thickness. The variation of the angular buildup factor with polar angle illustrated the buildup of forward-scattered photons with penetration depth. Acknowledgements The author wishes to thank Dr . J. Banai for his work in establishing the benchmark angular spectra from which the angular properties have been derived. References [1] [2] [3] [4] [5]
6. Conclusions
[6]
Experimental results for the angular penetration of 6.13 MeV photons through lead, steel and concrete have been analysed . For all three materials, the photon distribution leaving the outer shield surface was increasing in the forward direction as the penetration thickness increased. This was more marked for the concrete shield
[7] [8] [91 [10]
J. Banai Ph .D . Thesis, University of Liverpool (1984) . G.B . Bishop and J. Banai, Ann. Nucl . En . 12 (1985) 593. M.J . Grimstone Report AEEW-M-1455 (1976). G.B . Bishop and I. Birchhall, Ann. Nucl. En . 2 (1975) 467. G.B . Bishop and J.W . Cleaver, J. Brit, Nucl . En. Soc. 11 (1972) 113 . R.E. Maerker and F.J . Muckenthaler, Report ORNL-4382 (1967) . T.S. Dahlstrom and W.E. Thompson, Report USN-RDLTR-558 (1962) . R.S . Watts and H.G. Pena, J. Nucl. Biol . Med. 16 (1972) 51 . A.M. Marafie and G.B. Bishop, Ann. Nucl . En . 5 (1978) 197. A.M . Marafie and G.B . Bishop, Nucl . En . 18 (1979) 409.