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Penetration of 2.75 MeV γ-rays through shielding slabs of graphite, aluminium, steel and lead
Ann. nucl. Energy, Vol. 13, No. 10, pp. 559-573, 1986 Printed in Great Britain. All rights reserved
0306-4549/86 $3.00+0.00 Copyright © 1986 PergamonJournals Ltd
TECHNICAL
NOTES
PENETRATION OF 2.75 MeV ?-RAYS THROUGH SHIELDING SLABS OF GRAPHITE, ALUMINIUM, STEEL AND LEAD I. KAPPOS, t G. B. BISHOP2 and N. F. TSAGASt ~Department of Electrical Engineering, Democritos University of Thrace, 67100 Xanthi, Greece 2Department of Mechanical Engineering, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, England (Received I0 April 1986) Abstract--Experimentally determined angular and scalar flux spectra are presented for 2.75 MeV source photons of disc geometry penetrating shielding slabs of graphite, aluminium, steel and lead. The scalar flux spectra are compared with calculated values using the SAM-FMonte Carlo code. The data presented can be used in the assessment of calculational methods.
INTRODUCTION Carefully derived data for y-ray penetration through shielding materials is required for the assessment of calculational methods. Angular and scalar flux are particularly useful for this purpose to test fine structure analysis, and integrated values can readily be determined from the spectra. Recent publications of benchmark angular and scalar flux spectra are available for y-ray source energies of 662 keV (Banai, 1983), 1.43 MeV (Kappos et aL, 1986) and 6.13 MeV (Bishop and Banai, 1985). To extend the source energy range, angular and scalar flux spectra are presented for 2.75 MeV ?-rays penetrating single material shielding slabs of graphite, aluminium, steel and lead. No monoenergetic y-ray-emitting radioisotope is available at 2.75 MeV but the decay of 24Na produces two y-rays at energies 2.75 and 1.37 MeV. The activated Na2CO3 solution used for the measurements therefore provided a uniform disc source of y-rays at both energies. Activated NHnVO3 solution emitting 1.43 MeV y-rays was also available. The emerging angular spectra for the Na2CO 3 and NH4VO 3 solutions were compared and spectra for 2.75 MeV source photons were derived by subtraction. Scalar flux spectra have also been evaluated by suitable integration of the angular flux spectra.
diated for a period of 7 h in a region of thermal-neutron flux 1.4" 10~2 neutron/cm:" s. After overnight decay the sample was fired into the rabbit-tube terminal within the leadshielded hot cell. The NazCO~ powder was then transferred by remote handling equipment into 5 1. of distilled water in a storage tank, stirred and dissolved. The radioactive solution was then pumped by means of a remotely operated electrical pump to the disc radiator in the shielded cell via a shielded small-bore pipe running in ducting underground. The volume of the disc radiator was 3.32 1. and pumping continued until the radiator was completely filled and excess solution collected in a lead-shielded overflow tank. This ensured that the disc radiator was completely full of the active solution. The initial source strength within the radiator was 9.583" 109 Bq and angular flux measurements were made for periods of up to three half-lives of 24Na (45 h) with suitable corrections for decay. At the end of each set of measurements, the solution was forced back to the storage tank within the hot cell by means of a simple foot pump. The solution was then stored until the activity level had reduced to discharge values. A cross-section of the 24Na facility is shown in Fig. 1.
DESCRIPTION OF THE EXPERIMENTAL FACILITY DETERMINATION OF ANGULAR FLUX SPECTRA AT 2.75 MeV The 24Na facility installed at the Universities Research Reactor Centre (Risley, Warrington, Ches.) provides a uniAngular flux measurements were taken with a leadform disc source, 0.86 m active diameter, of mixed 2.75 and collimated 5.08 cm dia × 5.08 cm NaI(T1) scintillation detec1.37 MeV y-rays at one end of a concrete shielded cell. The tor coupled to an amplifier and multichannel pulse-height 24Na is produced by irradiating Na in the form of Na2CO3 analyser. A schematic plan view of the source-shield~letecpowder in the core of the reactor using the rabbit-tube tor arrangement is shown in Fig. 2. Measurements were facility. 24Na is produced by the 23Na(n,y)24Na reaction taken at polar angles of 0 °, 15°, 30°, 45 ° and 60 ° for shielding which has an activation cross-section of 0.40 barn. It decays slabs of aluminium (5, 10 and 15 cm), steel (2.5 and 5 cm), graphite (15 cm) and lead (2.5 cm). with a half-life of 15 h emitting 2.75 and 1.37 MeV y-rays Before the output pulse-height distributions can be with equal intensity. For these experiments, 7 g of Na:CO3 powder was irra- unfolded using the code RADAK (Grimstone, 1976) a col559
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Technical Notes
561
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limated detector response matrix must be established. The detector spectrometer was carefully calibrated using eleven monoenergetic 7-ray-emitting radioisotopes covering the entire energy range up to the higher source energy 2.75 MeV. Suitable calibration isotopes are given by Bishop and Marafie (1978). A method of generating a collimated detector response matrix from the calibration response functions has been described by Bishop and Banai (1985). The matrix must be normalized to the detector intrinsic efficiency and collimator integrated effective aperture. In the latter case, the method of Dahlstrom and Thompson (1962) has been modified to an exponential model following analysis of the observations of Watts and Pena (1972). The energy group structure and normalization factors used in constructing a 21 x 33 response matrix are given in Table 1. Table 2 gives the values of the response matrix elements. The standard deviation on each element was typically of the order of 1% due to the statistics of emission of the source photons. The unfolded pulse-height distributions produced angular flux spectra for the mixture of 1.37 and 2.75 MeV source photons. To obtain the spectra for a monoenergetic source
energy of 2.75 MeV the contribution from the 1.37 MeV source photons must be subtracted. To do this, the angular flux spectra obtained for the penetration of 1.43 MeV source photons, from the decay of 52V, through similar sourceshield~letector configurations was used. First, the 1.43 MeV spectra were normalized to the same source strength as the 1.37 MeV photons. Then, the spectra were adjusted so that the energy structure coincided with the 1.37 MeV spectra. The modified 1.43 MeV spectra were then subtracted from the combined 2.75 and 1.37 MeV spectra, leaving an angular flux distribution representing 2.75 MeV photon penetration. The 1.43 MeV spectra was chosen since this energy level was very close to the lower source energy from 24Na. Since the reaction cross-sections at 1.43 and 1.37 MeV are very close, only a small error is introduced by this subtraction procedure. Due to the physical dimensions of the detector lead collimator, it was not possible to take measurements at polar angles greater than 60° . Values of the angular flux spectra above this angle have been calculated using the method given by Kappos et al. (1986). The angular flux spectra for 2.75 MeV source photons are presented in Tables 3~5 for selected
562
Technical Notes Table 1. Energy group structure of the response matrix
Bin No.
Mid-bin energy, E, (MeV)
l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.15957 0.24282 0.32607 0.40932 0.49257 0.57582 0.65907 0.74232 0.82557 0.92963 1.07532 1.24182 1.40832 1.57482 1.74132 1.90782 2.07432 2.24082 2.40732 2.57382 2.75410
Upper and lower boundaries (MeV) 0.201195 0.284445 0.367695 0.450945 0.534195 0.617445 0.700695 0.783945 0.867195 0.992070 1.158570 1.325070 1.491570 •.658070 1.824570 1.991070 2.157570 2.324070 2.490570 2.657070 2.851130
0.117945 0.201195 0.284445 0.367695 0.450945 0.534195 0.617445 0,700695 0.783945 0.867195 0.992070 1.158570 1.325070 1.481570 1.658070 1.824570 1.991070 2.157570 2.324070 2.490570 2.657070
shield thicknesses of aluminium, steel, graphite and lead, respectively. The data include derived values for polar angles of 70 ~' and 80 °. Complete values for all the shields used can be obtained from the authors. Figures 3 and 4 show graphically the angular spectral distributions emerging from 1.52 m.f.p, aluminium and 0.75 m.f.p, steel shields, respectively. DETERMINATION OF SCALAR FLUX SPECTRA Because of the two 7-ray energies emitted in the 24Na decay, it was not possible to measure the scalar flux spectra emerging from the shielding slabs due to the 2.75 MeV photons. The scalar flux spectra were therefore obtained by integration of the angular flux spectra for polar angles of 0°-90 ° . The relationship between scalar flux ~(x, E), where x is the shield thickness and E the photon energy, and the angular flux O(x, E, 0), where 0 is the polar angle, is given by
• (x, E) = ~ ~(x, E, f~) d~, which for semi-infinite geometry becomes q~(x, E) = 2re
q)(x, E, 0)" sin 0" d0.
Bin width, AE, (MeV) 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.124875 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.19406
Intrinsic efficiency of the detector 1.0000 0.9965 0.9825 0.9575 0.9350 0.9100 0.8862 0.8613 0.8400 0.8175 0.7888 0.7625 0.7400 0.7213 0.7050 0.6920 0.6772 0.6700 0.6610 0.6525 0.6470
Aperture normalization coefficient, A~, (cmz" sr) 0.03855 0.03916 0.03983 0.04099 0.04215 0.04308 0.04458 0.04469 0.04568 0.04670 0.04814 0.04943 0.05069 0.05200 0.05280 0.05361 0.05427 0.05475 0.05515 0.05546 0.05578
was taken as 180. The values for the derived scalar flux spectra obtained by this method are included in Tables 3-6 for the selected shields and further values are available. For direct comparison, calculations have been made using the Monte Carlo code SAM-F (Lichtenstein et al., 1979), of the scalar flux spectra emerging from each shield. For each shield thickness, 106 case histories were considered, which gave typically 5 15% SD on the calculated values for elements of the angular flux spectra. Comparisons were made with the experimentally derived values. Table 7 gives values for shields of 1.01 m.f.p, aluminium, 1.49 m.f.p, steel, 0.97 m.f.p, graphite and 1.21 m.f.p, lead. The calculated values have been normalized to a c o m m o n source strength. Figures 5-8 compare the derived experimental values with SAM-F calculated values for each shield of aluminium, steel, graphite and lead, respectively. CONCLUDING COMMENTS The stripping away of the modified 1.43 MeV source photon energy angular flux spectra from the spectra obtained using the mixed source energy from 24Na, resulted in spectra representing 2.75 MeV source photon energy. Continuous angular flux spectra were obtained and by suitable integration, scalar flux spectra were derived. These spectra
were compared directly with calculated values using the In order to compute the scalar flux, it was necessary to estimate the angular fluxes between the measured angles and between 60 ° and 90 °. The method of Kappos et al. (1986) was used. After the evaluation of q~(x, E, 0) for all 0 the integration was done arithmetically using the formula
~(x,E) = 2~ ~ q~(x,E, Oi)'sin 0i'A0,, i-I
where n, the number of integration steps between 0 and rr/2
s~a~-F code and reasonable agreement was achieved, except for the lead shield. The main discrepancies at the lower end of the spectra were due to unfolding errors aggravated by the stripping process. For lead shields, the presence o f annihilation and bremsstrahlung photons plus the dominance of photoelectric reactions at lower photon energies, results in a severe test on both the calculated and derived methods giving much larger values for the standard deviation on the scattered components of the spectrum.
1
3.86E--02 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Energy group No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
8.32E 3.07E 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 03 02
6.76E--03 3.33E-03 2.89E - 02 I.~E-~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3 6.26E--03 3.86E-03 1.47E - 03 2.~E-02 I. ~ E - 03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4 5.28E-03 5.22E-03 3.07E - 03 2.07E-03 2. M E - 02 3. ~ E - ~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
5 4.51E--03 4.51E-03 4.53E - 03 2.55E-03 2.03 E - 03 2 . ~ E - 02 5.26E-~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
6
Response function N o .
4.02E--03 4 . 0 2 E - 03 4.02E - 03 4.08E-03 2.16E - 03 1. M E -- 03 1.85E-02 9.02E- ~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
7 3.57E--03 3.57E-03 3.59E - 03 3.68E-03 3.70E - 03 1.91E - 03 1.62E-03 l . ~ E - 02 8.75E- ~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
8
3.28E-03 3.28E-03 3.28 E - 03 3.33E-03 3. ~ E - 03 3 . ~ E - 03 1.74E-03 1 . ~ E - - 03 1.39E - ~ 1.1 I E - 0 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
9
Table 2.21 x 33 response m a t r i x at 2.75 M e V , normalized to unity, detector intrinsic efficiency, collimator integrated effective aperture a n d energy g r o u p width
contm~doverleaf
2.96E-- 03 2 . ~ E - 03 2.96E - 03 2.97E--03 3 . ~ E -- 03 3.19E - 03 3.27E-03 1.91 E - - 03 1.21E 1.25E-02 1.23E-03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
10
LO
Z O
t%
11
2.62E-03 2.62E-03 2.62E-03 2.62E-03 2.62E-03 2.64E-03 2.73E-03 2.91E-03 2.73E--03 1.38E--03 1.40E-03 1.00E- 02 1.08E-03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Energy group No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
2.31E-03 2.31E-03 2.31E-03 2.33E-03 2.29E-03 2.29E-03 2.24E-03 2.33E-03 2.44E-03 2.64E-03 2.39E-03 1.19E 03 1.23E-03 8.30E 03 1.10E-03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
12 2.08E-03 2.09E-03 2.11E-03 2.15E-03 2.18E--03 2.18E--03 2.13E--03 2.11E--03 2.12E-03 2.20E--03 2.24E--03 2.38E--03 2.05E--03 1.19E-03 1.24E-03 6.07E--03 1.01E--03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
13 1.94E-03 1.94E--03 1.95E-03 1.97E-03 2.05E-03 2.02E--03 1.97E--03 1.95E-03 1.94E 03 1.92E 03 1.93E 03 2.05E-03 2.03E-03 2.11E-03 1.79E-03 1.05E-03 1.13E-03 4.89E--03 8.91E--04 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
14 1.80E-03 1.81E-03 1.81E-03 1.84E--03 1.91E--03 1.86E--03 1.88E-03 1.89E-03 1.80E-03 1.74E-03 1.74E-03 1.72E--03 1,71E--03 1.89E--03 1.SlE-03 1.84E- 03 1.54E-03 8.81E-04 9.95E-04 4.16E-03 5.91E-04 0.0 0.0 0,0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
15 1.60E-03 1.60E--03 1.60E--03 1.61E-03 1.75E-03 1.65E-03 1.63E-03 1.63E-03 1.70E 03 1.77E 03 1.63E 03 1.58E-03 1.57E-03 1.56E-03 1.54E-03 1.80E--03 1.70E-03 1.69E-03 1.39E-03 7.74E--04 9.28E-- 04 3.53E--03 8 . 6 6 E - 04 0,0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
16
17 1.41E-03 1.41E--03 1.41E-03 1.42E-03 1.57E--03 1.44E-03 1.42E- 03 1.43E-03 1.43E-03 1.44E-03 1.52E-03 1.66E--03 1.48E-03 1.45E-03 1.45E-03 1.43E-03 1.42E-03 1.76E-03 1.63E 03 1.59E-03 1.28E 03 6.79E-04 8.93E 04 3.27E-03 8 . 5 2 E - 04 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Response function No.
Table 2--continued
1.25E-03 1.26E-03 1.26E-03 1.27E--03 1.43E--03 1.29E-03 1.26E- 03 1.26E-03 1.27E 03 1.27E 03 1.28E-03 1.28E-03 1.39E--03 1.59E-03 1.38E-03 1.36E--03 1.36E--03 1.33E--03 1.33E-03 1.75E-03 1.60E-03 1.53E--03 1.21E-03 6 . 4 0 E - 04 8 . 7 9 E - 04 3.11E--03 8.57E--04 0.0 0.0 0.0 0.0 0.0 0.0
18 1.09E-03 1.11E-03 1.12E--03 1.13E--03 1.32E--03 1.17E-03 1.12E-03 1.12E--03 1.13E--03 1.13E--03 1.13E--03 1.14E-03 |.14E-03 1.15E-03 1.27E-03 1.54E 03 1.29E-03 1.29E-03 1.28E-03 1.25E--03 1.26E--03 1.77E--03 1.58E-03 1.48E--03 1.16E--03 5.90E--04 8 . 7 6 E - 04 2.97E-03 8.72E--04 0.0 0.0 0.0 0.0
19
9.35E-04 9.51E--04 9.66E 04 9.91E-04 1.22E-03 1.04E-03 1.00E--03 1.00E--03 1.00E-03 1.01E-03 1.01E-03 1.01E--03 1.01E--03 1.02E--03 1.02E-03 1.02E- 03 1.17E--03 1.51E--03 1.22E- 03 1.23E-03 1.23E-03 1.20E--03 1.20E--03 1.81E-03 1.60E 03 1.47E--~)3 1.12E 03 5.50E-04 8.86E-04 2.88E--03 9.01E-04 0.0 0.0
20
7.71E-04 7.90E-04 8.09E--04 8.40E-04 l,llE-03 9.15E-04 8.87E 04 8.90E--04 8.93E 04 8.95E--04 8.98E-04 9.00E-04 9.03E-04 9.06E-04 9.08E--04 9.11E-04 9.13E-04 9.16E-04 1.09E--03 1.53E--03 1.17E-03 1.21E-03 1.21E--03 1.17E--03 1.18E-03 1.91E-03 1.66E-03 1.49E--03 1.12E-03 5.20E-04 9.26E-04 2.87E--03 9.86E - 04
21
Z o
W
,H
Energy (MeV)
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
Bin No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
Width (MeV)
8.42E+ 05 7.99E + 05 5.98E + 05 4.30E + 05 3.24E+05 2.83E+05 2.11E+05 1.90E + 05 1.83E+05 1.01E+05 7.28E+04 8.94E+04 7.55E + 04 7.55E+04 8.11E+04 6.83E+ 04 7.77E + 04 7.68E+04 7.47E+04 6.12E+04 8.96E+05
Scalar flux 2.31E+05 2.12E + 05 1.51E + 05 1.09E + 05 9.36E+04 8.84E+04 7.17E+04 6.16E + 04 6.20E+04 3.31E+04 2.49E+04 2.63E+04 1,97E + 04 1.97E+04 1.98E+04 1.44E + 0 4 1.77E + 04 1.88E+04 1.42E+04 1.13E+04 2.61E+05
0.0
2.22E+05 2.07E + 05 1.44E + 05 1.0BE + 05 8.91E+04 8.08E+04 6.38E+04 5.76E + 04 5.53E+04 2.96E+04 2.22E+04 2.51E+04 1.84E + 04 1.84E+04 1.81E+04 1.63E+ 04 1.89E + 04 1.71E+0,:I 1.46E+04 1.03E+04 2.61E+05
15.0
1.87E+ 05 1.76E + 05 1.26E + 05 9.29E + 04 7.51E+04 6.60E+04 4.88E+04 4.43E + 04 4.42E+04 2.36E+04 1.84E+04 2.01E+04 1.78E + 04 1.78E+04 1.90E+04 1.32E+04 1.53E + 04 1.47E+04 1.34E+04 1.06E+04 2.15E+05
30.0
1.95E+05 1.85 E + 05 1.38E + 05 1.00E + 05 7.42E+04 6.63E+04 4.82E+04 4.35E + 04 4.19E+04 2.29E+04 1.54E+04 2.31E+04 1.79E + 04 1.79E+04 2.07E+04 1.65E+ 04 1.87E + 04 1.61E+04 1.87E+04 1.47E+04 2.20E+05
45.0
1.65E+05 1.58 E + 05 1.22E + 05 8,59E + 04 6.24E+04 5.31E+04 4.00E+04 3.56E + 04 3.39E+04 1.92E+04 1.39E+04 1.59E+04 1.44E + 04 1.44E+04 1.49E+04 1.39E+04 1.58E + 04 1.79E+04 1.57E+04 1.37E+04 1.59E+05
60.0
Angular fluxes (photon/MeV • cm 2" s" st)
Table 3. Angular flux spectra emerging from a 1.01 m.f.p, aluminium shield
1.12E+05 1.08E + 05 8.37E + 04 5.94E + 04 4.16E+04 3.51E+04 2.52E+04 2.29E + 04 2.17E+04 1.22E+04 8.56E+03 1.13E+04 1.02E + 04 1.02E+04 1.14E+04 1.01E + 0 4 1.12E + 04 1.12E+04 1.19E+04 1.02E+04 1.12E+05
70.0
3.83E+ 04 3.72E + 04 2.94E + 04 2.07E + 04 1.41E+04 1.17E+IM 8.27E+03 7.56E + 03 7.13E+03 4.05E+03 2.80E+03 3.82E+03 3.55E + 03 3.55E+03 4.00E+03 3.65E+03 4.00E + 03 4.02E+03 4.45E+03 3.86E+03 3.75E+04
80.0
L,h
O
--]
Energy (MeV)
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
Bin No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
Width (MeV)
8.08E + 04 3.55E + 05 3.32E+05 2.62E+05 2.25E + 05 1.91E+05 1.39E+05 1.26E + 05 1.18E+05 6.62E+04 4.59E + 04 4.96E + 04 5.31E+04 5.31E+04 5.64E + 04 5.14E+04 5.66E+04 6.06E+04 4.66E+ 04 3.91E + 04 4.32E + 05
Scalar flux 2.60E + 04 1.01E + 05 9.08E+04 7.10E+04 6.61E + 04 6.17E+04 4.85E+04 4.49E + 04 4.34E+04 2.38E+04 1.72E + 04 1.80E+04 1.52E+04 1.52E+04 1.56E + 04 1.18E+04 1.40E+04 1.44E+04 1.22E+04 9.67E + 03 1.52E + 05
0.0 2.16E + 04 9.67E + 04 8.62E+04 6.77E+04 6.32E + 04 5.78E+04 4.31E+04 4.06E + 04 3.81E+04 2.10E+04 1.39E + 04 1.49E+04 1.48E+04 1.48E+04 1.61E + 04 1.30E+04 1.48E+04 1.57E+04 1.31E+04 8.82E + 03 1.48E + 05
15.0 2.09E + 04 9.25E + 04 8.36E+04 6.65E+04 6.03E + 04 5.18E+04 3.87E+04 3.56E + 04 3.41E+04 1.83E+04 1.32E + 04 1.49E+04 1.47E+04 1.47E+04 1.54E + 04 1.37E+04 1.59E+04 1.51E+04 1.12E+04 9.63E + 03 1.40E + 05
30.0 1.77E + 04 8.20E + 04 7.69E+04 6.17E+04 5.16E + 04 4.42E+04 3.17E+04 2.87E + 04 2.64E + 04 1.48E+04 1.05E + 04 1.17E+04 1.32E+04 1.32E+04 1.40E + 04 1.24E+04 1.30E+04 1.42E+04 1.18E+04 9.69E + 03 1.08E + 05
45.0 1.75 E + 04 7.36E + 04 7.10E+04 5.52E+04 4.59E + 04 3.75E+04 2.65E+04 2.39E + 04 2.22E+04 1.29E+04 8.65E 4- 03 8.98E+03 1.00E+04 1.00E + 04 1.07E + 04 1.04E+04 1.15E+04 1.29E+04 9.32E+03 8.29E + 03 6.88E + 04
60.0
Angular fluxes (photon/MeV • em:" s" sr)
Table 4. Angular flux spectra emerging from a 1.49 m.f.p, steel shield
8.37E + 03 3.81E + 04 3.68E+04 2.91E+04 2.36E + 04 1.89E+04 1.31E+04 1.17E + 04 1.07E+04 6.t8E+03 4.23E + 03 4.58E+03 5.54E+03 5.54E+03 5.95 E 4- 03 5.99E+03 6.36E+03 7.04E+03 5.13E+03 4.62E + 03 3.79 E + 04
70.0
1.39E + 03 6.43E + 03 6.29E+03 4.97E+03 3.95 E + 03 3.09E+03 2.11E+03 1.88 E + 03 1.71E+03 9.91E+02 6.74E + 02 7.31E+02 9.25E+02 9.25E+02 9.98E + 02 1.05E+03 1.09E+03 1.23E+03 8.74E+02 8.11E + 02 5.95E 4- 03
80.0
Z Q
o~
9 10 11 12 13 14 15 16 17 18 19 20 21
8
5 6 7
4
2 3
1
Bin No.
Scalar flux
8.73E + 05 7.ME + 05 5.48E + 05 3.81E+05 2.78 E + 05 2.36E+05 1.79E+05 1.66E + 05 1.62E + 05 9.47E+04 6.72E + 04 4.80E+04 6.30E+ 04 6.30E+04 6.31E+04 4.52E+04 6.52E + 04 8.71E+04 6.85E+04 5.32E+04 9.44E+05
Width (MeV)
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
Energy (MeV)
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
2.36E + 05 1.98E + 05 1.39E + 05 1.02E+05 7.99E + 04 7.62E+04 5.95E+04 5.75E + 04 5.35E + 04 3.45E+04 2.00E + 04 1.45E+04 1.80E+04 1.80E+04 1.68E+04 1.10E+04 1.47E + 04 1.65E+04 1.49E+04 1.11E+04 2.75E+05
0.0 2.27E + 05 1.89E + 05 1.34E + 05 9.66E+ 04 7.60E + 04 6.90E+04 5.43E+04 5.02E + 04 4.94E + 04 2.68E+04 1.96E + 04 1.04E+04 1.64E+ 04 1.64E+04 1.50E+04 1.06E+04 1.48E + 04 1.99E+04 1.55E+04 1.06E+04 2.72E+05
15.0 2.19E + 05 1.84E + 05 1.31E + 05 9.36E+04 7.27E + 04 6.23E+04 4.82E+04 4.30E + 04 4.42E + 04 2.51E+04 1.74E + 04 9.97E +03 1.70E+04 1.70E+04 1.73E+04 1.16E+04 1.67E + 04 1.75E+04 1.46E+04 1.16E+04 2.61E+05
30.0 1.97E + 05 1.66E + 05 1.24E + 05 8.69E + 04 6.24E + 04 5.46E+04 4.04E+04 3.79E + 04 3.65E + 04 2.18E+04 1.59E + 04 1.05E+04 1..50E+ 04 1.50E+04 1.53E+04 1.16E+04 1.60E + 04 1.74E+04 1.67E+04 1.11E+04 2.29E+05
45.0 1.71E + 05 1.44E + 05 1.12E + 05 7.58E+04 5.30E + 04 4.34E+04 3.29E+IM 3.09E + 04 2.96E + 04 1.75E+04 1.23E + 04 1.1 I E + 0 4 1.15E+04 1.15E+04 1.15E+04 8.16E+03 1.22E + 04 2.08E+04 1.40E+04 1.23E+04 1.64E+05
60.0
Angular fluxes (photon/MeV • cm 2"s" sr)
Table 5. Angular flux spectra emerging from a 0.97 m.f.p, graphite shield
1.12E + 05 9.46E + 04 7.34E + 04 4.96E+04 3.43 E + 04 2.75E+04 2.05E+04 1.89E + 04 1.85E + 04 1.07E+04 8.07E + 03 6.43E+03 7.82E+03 7.82E+03 8.16E+03 6.07E+03 9.04E + 03 1.32E+04 9.86E+03 8.00E+03 1.13E+05
70.0
3.48E + 04 2.95E + 04 2.32E + 04 1.55E+04 1.05E + 04 8.24E+03 6.09E+03 5.60E + 03 5.50E + 03 3.15E+03 2.44E + 03 2.03E+03 2.40E+ 03 2.40E+03 2.54E+03 1.92E+03 2.90E + 03 4.43E+03 3.22E+03 2.67E+03 3.42E+04
80.0
o
Z
g.
o
,-q
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Width (MeV)
Energy (MeV)
Bin No.
1.11E+03 2.62E + 04 3.06E + 04 4.20E + 04 1.19E + 05 1.25E + 05 6.59E + 04 7.79E + 04 8.69E+04 4.53E+04 4.24E + 04 4.12E+04 5.72E+04 5.72E+04 6.04E+ 04 4.79E + 04 5.67E+04 7.01E+04 5.20E+04 3.78E + 04 6.95 E + 05
Scalar flux 3.42E+03 1. I 1E + 04 5.49 E + 03 6.97E + 03 2.92E + 04 3.70E + 04 2.45E + 04 2.75E + 04 3.10E+ 04 1.69E+04 1.33 E + 04 1.21E+04 1.33E+04 1.33E+04 1.22E+04 8.27E + 03 1.15E+04 1.41E+04 9.44E+03 6.81E + 03 2.01E + 05
0.0 1.77E+03 9.57E + 03 4.56E + 03 5.79E + 03 2.78E + 04 3.39E + 04 2.04E + 04 2.46E + 04 2.69E+ 04 1.33E+04 1.23E + 04 9.83E+03 1.36E+04 1.36E+04 1.29E+04 7.93E + 03 1.15E+04 1.29E+04 9.84E+03 6.56E + 03 1.99E + 05
15.0 1.82E+03 1.07E + 04 5.65E + 03 7.50E + 03 2.75E + 04 2.92E + 04 1.68E + 04 2.09E + 04 2.34E+04 1.27E+04 1.24E + 04 1.06E+04 1.28E+04 1.28E+04 1.42E+04 9.59E + 03 1.16E+04 1.72E+04 1.17E+04 8.09 E + 03 1.88 E + 05
30.0 1.08E+01 6.18 E + 03 6.67E + 03 8.61E + 03 2.49E + 04 2.63E + 04 1.34E + 04 1.62E + 04 1.83E+ 04 9.31E+03 9.12E + 03 8.46E+03 1.31E+04 1.31E+04 1.35E+04 1.09E + 04 1.23E+04 1.52E+04 1.15E+04 7.78 E + 03 1.61E + 05
45.0 6.03E--01 3.38 E + 03 7.36E + 03 1.07E + 04 2.57E + 04 2.61E + 04 1.30E + 04 1.47E + 04 1.63E+ 04 8.62E+03 7.64E + 03 8.58E+03 1.16E+04 1.16E+04 1.23E+04 1.06E + 04 1.27E+04 1.47E+04 1.10E+04 8.69E + 03 1.24E + 05
60.0
Angular fluxes (photon/MeV- cm 2. s" sr)
Table 6. Angular flux spectra emerging from a 1.21 m.f.p, lead shield
2.58E--01 2.41E + 03 5.18 E + 03 7.39 E + 03 1.67E + 04 1.60E + 04 7.45E + 03 8.84E + 03 9.85E+03 5.10E+03 5.03 E + 03 5.35E+03 8.07E+03 8.07E+03 9.01E+03 7.95 E + 03 8.72E+03 1.07E+04 8.22E+03 6.13 E + 03 8.56E + 04
70.0
2.02E 02 6.96E + 02 1.92E + 03 2.80E + 03 5.66E + 03 5.22E + 03 2.32E + 03 2.75E + 03 3.07E+03 1.59E+03 1.59E + 03 1.76E+03 2.75E+03 2.75E+03 3.15E+03 2.92E + 03 3.09E+03 3.80E+03 2.95E+03 2.23E + 03 2.75E + 04
80.0
o
7~
-]
oo
Technical Notes
"C
106
c~
E 10 5
10 4
3
10:3
3 < IO
2
O0
0.5
1.0 Energy,
1..5
2.0
2.5
3.0
E (MeV)
Fig. 3. Angular flux variation through 1.52 m.f.p. (15 cm) of aluminium, for photons emitted at 2.75 MeV, measured using the disc radiator.
569
570
Technical Notes
~0 6
"2 ca'
~o~
=o ~4
~0 D
0
<
2 10 OO
05
10
1.5
20
2.5
3.0
Energy, E ( M e V )
Fig. 4. Angular flux variation through 0.75 m.f.p. (2.5 cm) of steel, for photons emitted at 2.75 MeV, measured using the disc radiator.
571
Technical Notes
Table 7. Comparison of scalar flux spectra for selected shields 1.01 m.f.p. Aluminium Integrated experimental angular flux 8.42E+05 7.99E+05 5.98E+05 4.30E+05 3.24E+05 2.83E+05 2.11E+05 1.90E+05 1.83E+05 1.01E+05 7.28E+04 8.94E+04 7.55E+04 7.55E+04 8.11E+04 6.83E+04 7.77E+04 7.68E+04 7.47E+04 6.12E+04 8.96E+05
1.49 m.f.p. Steel
SAM-F
Integrated experimental angular flux
1.57E+06 6.93E+05 4.89E+05 3.86E+05 3.98E+05 2.90E+05 1.97E+05 1.93E+05 1.49E+05 1.35E+05 1.19E+05 8.67E+04 7.90E+04 8.23E+04 8.31E+04 8.13E+04 6.09E+04 7.50E+04 6.89E+04 7.02E+04 8.96E+05
8.08E+04 3.55E+05 3.32E+05 2.62E+05 2.25E+05 1.91E+05 1.39E+05 1.26E+05 1.18E+05 6.62E+04 4.59E+04 4.96E+04 5.31E+04 5.31E+04 5.64E+04 5.14E+04 5.66E+04 6.06E+04 4.66E+04 3.91E+04 4.32E+05
0.97 m.f.p. Graphite
SAM-F
Integrated experimental angular flux
5.60E+05 5.98E+05 3.78E+05 2.52E+05 2.69E+05 1.39E+05 1.18E+05 1.07E+05 7.96E+04 8.12E+04 8.58E+04 6.57E+04 7.62E+04 5.19E+04 5.16E+04 5.53E+04 3.56E+04 4.09E+04 5.07E+04 4.12E+04 4.32E+05
8.73E+05 7.34E+05 5.48E+05 3.81E+05 2.78E+05 2.36E+05 1.79E+05 1.66E+05 1.62E+05 9.47E+04 6.72E+04 4.80E+04 6.30E+04 6.30E+04 6.31E+04 4.52E+04 6.52E+04 8.71E+04 6.85E+04 5.32E+04 9.44E+05
1.21 m.f.p. Lead
SAM-F
Integrated experimental angular flux
SAM-F
1.46E+06 6.07E+05 5.06E+05 3.26E+05 4.18E+05 2.29E+05 2.08E+05 1.35E+05 1.44E+05 9.82E+04 1.07E+05 1.09E+05 5.50E+04 1.24E+05 8.10E+04 7.15E+04 1.00E+05 6.l l E+04 5.87E+04 1.05E+05 9.44E+05
1.11E+05 2.62E+04 3.06E+04 4.20E+04 1.19E+05 1.25E+05 6.59E+04 7.79E+04 8.69E+04 4.53E+04 4.24E+04 4.12E+04 5.72E+04 5.72E+04 6.04E+04 4.79E+04 5.67E+04 7.01E+04 5.20E+04 3.78E+04 6.95E+05
1.85E+04 7.50E+04 1.12E+05 1.16E+05 4.66E+05 1.22E+05 1.23E+05 1.10E+05 8.69E+04 6.85E+04 7.91E+04 7.98E+04 5.70E+04 4.70E+04 6.78E+04 4.94E+04 2.56E+04 2.86E+04 3.95E+04 2.88E+04 6.95E+05
1O;
o
lo ~
>
0.5
1.0
1.5
2.0
2.5
5.0
Energy, E ( M e V )
Fig. 5. Scalar flux variation with penetration thickness (5, 10 and 15 cm) of aluminium.
572
Technical Notes
F-7
I
SAM-F
I
r~
RADAK
10 7
L
u >
L71-10 6 I
~ -- -I
/
E
I__j
2
o
I
I ,
I I I_
J
10 5
I
L
O3
1.49 ~ o 0.0
0.5
1.0
Energy,
1.5
20
2.5
30
E(MeV)
Fig. 6. Scalar flux variation with penetration thickness (2.5 and 5 cm) of steel.
IJ
1d-
r - ~ RAOAK [7
[7
SAM-F
RADAK
F 7 SAM-V
% > lo6
"l I
o ~. 10~
o
i1 ml Ii
o
r-1 m L
io5
o. r-
-
10`=
=
104
[u
rr
~7
I Io~
oo 03
O3
10
~)1.OI
I
Q5
I
1.O Energy,
]
1,5
I
2O
]
2.5
I
5.0
E (MeV)
Fig. 7. Scalar flux with a penetration thickness of 15 cm (0.97 m.f.p.) of graphite.
j10 .
I
• 0.5
0
I 1.0
[ 1.5
I 2.0
I 25
I 30
Energy, E (MeV)
Fig. 8. Scalar flux with a penetration thickness of 2.5 cn~ (1.21 m.f.p.) of lead.
Technical Notes Angular flux spectra are presented which can be used to evaluate calculational methods.
Acknowledgement~The authors would like to thank Mr A. G. Davies for his help in constructing and operating the ~4Na facility; the Radiation Information Shielding Centre, Oak Ridge, Tenn., U.S.A. for the computer package on SAM-CE; the Atomic Energy Authority, Winfrith, for the unfolding code RADAK; and the staff of the Universities Research Reactor Centre, Risley, Warrington, for their close cooperation throughout the project.
573 REFERENCES
Banal J. (1983) A TKE 42, 197. Bishop G. B. and Banal J. (1985) Ann. nucl. Energy 12, 593. Bishop G. B. and Marafie A. M. (1978) Nucl. lnstrum. Meth. 150, 505. Dahlstrom T. S. and Thompson W. E. (1962) Report USN RDL-TR-558. Grimstone M. J. (1976) Report AEEW-M.1455. Kappos I., Bishop G. B. and Tsagas N. F. (1986) Ann. nucl. Energy 13, 511. Lichtenstein H. et al. (1979) Report ORNL-RSIC-CCC- 187. Watts R. S. and Pena H. G. (1972) J. nucl. Med. Biol. 16, 51.
0306-4549/86 $3.00+0.00 Copyright © 1986 PergamonJournals Ltd
TECHNICAL
NOTES
PENETRATION OF 2.75 MeV ?-RAYS THROUGH SHIELDING SLABS OF GRAPHITE, ALUMINIUM, STEEL AND LEAD I. KAPPOS, t G. B. BISHOP2 and N. F. TSAGASt ~Department of Electrical Engineering, Democritos University of Thrace, 67100 Xanthi, Greece 2Department of Mechanical Engineering, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, England (Received I0 April 1986) Abstract--Experimentally determined angular and scalar flux spectra are presented for 2.75 MeV source photons of disc geometry penetrating shielding slabs of graphite, aluminium, steel and lead. The scalar flux spectra are compared with calculated values using the SAM-FMonte Carlo code. The data presented can be used in the assessment of calculational methods.
INTRODUCTION Carefully derived data for y-ray penetration through shielding materials is required for the assessment of calculational methods. Angular and scalar flux are particularly useful for this purpose to test fine structure analysis, and integrated values can readily be determined from the spectra. Recent publications of benchmark angular and scalar flux spectra are available for y-ray source energies of 662 keV (Banai, 1983), 1.43 MeV (Kappos et aL, 1986) and 6.13 MeV (Bishop and Banai, 1985). To extend the source energy range, angular and scalar flux spectra are presented for 2.75 MeV ?-rays penetrating single material shielding slabs of graphite, aluminium, steel and lead. No monoenergetic y-ray-emitting radioisotope is available at 2.75 MeV but the decay of 24Na produces two y-rays at energies 2.75 and 1.37 MeV. The activated Na2CO3 solution used for the measurements therefore provided a uniform disc source of y-rays at both energies. Activated NHnVO3 solution emitting 1.43 MeV y-rays was also available. The emerging angular spectra for the Na2CO 3 and NH4VO 3 solutions were compared and spectra for 2.75 MeV source photons were derived by subtraction. Scalar flux spectra have also been evaluated by suitable integration of the angular flux spectra.
diated for a period of 7 h in a region of thermal-neutron flux 1.4" 10~2 neutron/cm:" s. After overnight decay the sample was fired into the rabbit-tube terminal within the leadshielded hot cell. The NazCO~ powder was then transferred by remote handling equipment into 5 1. of distilled water in a storage tank, stirred and dissolved. The radioactive solution was then pumped by means of a remotely operated electrical pump to the disc radiator in the shielded cell via a shielded small-bore pipe running in ducting underground. The volume of the disc radiator was 3.32 1. and pumping continued until the radiator was completely filled and excess solution collected in a lead-shielded overflow tank. This ensured that the disc radiator was completely full of the active solution. The initial source strength within the radiator was 9.583" 109 Bq and angular flux measurements were made for periods of up to three half-lives of 24Na (45 h) with suitable corrections for decay. At the end of each set of measurements, the solution was forced back to the storage tank within the hot cell by means of a simple foot pump. The solution was then stored until the activity level had reduced to discharge values. A cross-section of the 24Na facility is shown in Fig. 1.
DESCRIPTION OF THE EXPERIMENTAL FACILITY DETERMINATION OF ANGULAR FLUX SPECTRA AT 2.75 MeV The 24Na facility installed at the Universities Research Reactor Centre (Risley, Warrington, Ches.) provides a uniAngular flux measurements were taken with a leadform disc source, 0.86 m active diameter, of mixed 2.75 and collimated 5.08 cm dia × 5.08 cm NaI(T1) scintillation detec1.37 MeV y-rays at one end of a concrete shielded cell. The tor coupled to an amplifier and multichannel pulse-height 24Na is produced by irradiating Na in the form of Na2CO3 analyser. A schematic plan view of the source-shield~letecpowder in the core of the reactor using the rabbit-tube tor arrangement is shown in Fig. 2. Measurements were facility. 24Na is produced by the 23Na(n,y)24Na reaction taken at polar angles of 0 °, 15°, 30°, 45 ° and 60 ° for shielding which has an activation cross-section of 0.40 barn. It decays slabs of aluminium (5, 10 and 15 cm), steel (2.5 and 5 cm), graphite (15 cm) and lead (2.5 cm). with a half-life of 15 h emitting 2.75 and 1.37 MeV y-rays Before the output pulse-height distributions can be with equal intensity. For these experiments, 7 g of Na:CO3 powder was irra- unfolded using the code RADAK (Grimstone, 1976) a col559
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Technical Notes
561
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limated detector response matrix must be established. The detector spectrometer was carefully calibrated using eleven monoenergetic 7-ray-emitting radioisotopes covering the entire energy range up to the higher source energy 2.75 MeV. Suitable calibration isotopes are given by Bishop and Marafie (1978). A method of generating a collimated detector response matrix from the calibration response functions has been described by Bishop and Banai (1985). The matrix must be normalized to the detector intrinsic efficiency and collimator integrated effective aperture. In the latter case, the method of Dahlstrom and Thompson (1962) has been modified to an exponential model following analysis of the observations of Watts and Pena (1972). The energy group structure and normalization factors used in constructing a 21 x 33 response matrix are given in Table 1. Table 2 gives the values of the response matrix elements. The standard deviation on each element was typically of the order of 1% due to the statistics of emission of the source photons. The unfolded pulse-height distributions produced angular flux spectra for the mixture of 1.37 and 2.75 MeV source photons. To obtain the spectra for a monoenergetic source
energy of 2.75 MeV the contribution from the 1.37 MeV source photons must be subtracted. To do this, the angular flux spectra obtained for the penetration of 1.43 MeV source photons, from the decay of 52V, through similar sourceshield~letector configurations was used. First, the 1.43 MeV spectra were normalized to the same source strength as the 1.37 MeV photons. Then, the spectra were adjusted so that the energy structure coincided with the 1.37 MeV spectra. The modified 1.43 MeV spectra were then subtracted from the combined 2.75 and 1.37 MeV spectra, leaving an angular flux distribution representing 2.75 MeV photon penetration. The 1.43 MeV spectra was chosen since this energy level was very close to the lower source energy from 24Na. Since the reaction cross-sections at 1.43 and 1.37 MeV are very close, only a small error is introduced by this subtraction procedure. Due to the physical dimensions of the detector lead collimator, it was not possible to take measurements at polar angles greater than 60° . Values of the angular flux spectra above this angle have been calculated using the method given by Kappos et al. (1986). The angular flux spectra for 2.75 MeV source photons are presented in Tables 3~5 for selected
562
Technical Notes Table 1. Energy group structure of the response matrix
Bin No.
Mid-bin energy, E, (MeV)
l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.15957 0.24282 0.32607 0.40932 0.49257 0.57582 0.65907 0.74232 0.82557 0.92963 1.07532 1.24182 1.40832 1.57482 1.74132 1.90782 2.07432 2.24082 2.40732 2.57382 2.75410
Upper and lower boundaries (MeV) 0.201195 0.284445 0.367695 0.450945 0.534195 0.617445 0.700695 0.783945 0.867195 0.992070 1.158570 1.325070 1.491570 •.658070 1.824570 1.991070 2.157570 2.324070 2.490570 2.657070 2.851130
0.117945 0.201195 0.284445 0.367695 0.450945 0.534195 0.617445 0,700695 0.783945 0.867195 0.992070 1.158570 1.325070 1.481570 1.658070 1.824570 1.991070 2.157570 2.324070 2.490570 2.657070
shield thicknesses of aluminium, steel, graphite and lead, respectively. The data include derived values for polar angles of 70 ~' and 80 °. Complete values for all the shields used can be obtained from the authors. Figures 3 and 4 show graphically the angular spectral distributions emerging from 1.52 m.f.p, aluminium and 0.75 m.f.p, steel shields, respectively. DETERMINATION OF SCALAR FLUX SPECTRA Because of the two 7-ray energies emitted in the 24Na decay, it was not possible to measure the scalar flux spectra emerging from the shielding slabs due to the 2.75 MeV photons. The scalar flux spectra were therefore obtained by integration of the angular flux spectra for polar angles of 0°-90 ° . The relationship between scalar flux ~(x, E), where x is the shield thickness and E the photon energy, and the angular flux O(x, E, 0), where 0 is the polar angle, is given by
• (x, E) = ~ ~(x, E, f~) d~, which for semi-infinite geometry becomes q~(x, E) = 2re
q)(x, E, 0)" sin 0" d0.
Bin width, AE, (MeV) 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.08325 0.124875 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.16650 0.19406
Intrinsic efficiency of the detector 1.0000 0.9965 0.9825 0.9575 0.9350 0.9100 0.8862 0.8613 0.8400 0.8175 0.7888 0.7625 0.7400 0.7213 0.7050 0.6920 0.6772 0.6700 0.6610 0.6525 0.6470
Aperture normalization coefficient, A~, (cmz" sr) 0.03855 0.03916 0.03983 0.04099 0.04215 0.04308 0.04458 0.04469 0.04568 0.04670 0.04814 0.04943 0.05069 0.05200 0.05280 0.05361 0.05427 0.05475 0.05515 0.05546 0.05578
was taken as 180. The values for the derived scalar flux spectra obtained by this method are included in Tables 3-6 for the selected shields and further values are available. For direct comparison, calculations have been made using the Monte Carlo code SAM-F (Lichtenstein et al., 1979), of the scalar flux spectra emerging from each shield. For each shield thickness, 106 case histories were considered, which gave typically 5 15% SD on the calculated values for elements of the angular flux spectra. Comparisons were made with the experimentally derived values. Table 7 gives values for shields of 1.01 m.f.p, aluminium, 1.49 m.f.p, steel, 0.97 m.f.p, graphite and 1.21 m.f.p, lead. The calculated values have been normalized to a c o m m o n source strength. Figures 5-8 compare the derived experimental values with SAM-F calculated values for each shield of aluminium, steel, graphite and lead, respectively. CONCLUDING COMMENTS The stripping away of the modified 1.43 MeV source photon energy angular flux spectra from the spectra obtained using the mixed source energy from 24Na, resulted in spectra representing 2.75 MeV source photon energy. Continuous angular flux spectra were obtained and by suitable integration, scalar flux spectra were derived. These spectra
were compared directly with calculated values using the In order to compute the scalar flux, it was necessary to estimate the angular fluxes between the measured angles and between 60 ° and 90 °. The method of Kappos et al. (1986) was used. After the evaluation of q~(x, E, 0) for all 0 the integration was done arithmetically using the formula
~(x,E) = 2~ ~ q~(x,E, Oi)'sin 0i'A0,, i-I
where n, the number of integration steps between 0 and rr/2
s~a~-F code and reasonable agreement was achieved, except for the lead shield. The main discrepancies at the lower end of the spectra were due to unfolding errors aggravated by the stripping process. For lead shields, the presence o f annihilation and bremsstrahlung photons plus the dominance of photoelectric reactions at lower photon energies, results in a severe test on both the calculated and derived methods giving much larger values for the standard deviation on the scattered components of the spectrum.
1
3.86E--02 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Energy group No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
8.32E 3.07E 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 03 02
6.76E--03 3.33E-03 2.89E - 02 I.~E-~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3 6.26E--03 3.86E-03 1.47E - 03 2.~E-02 I. ~ E - 03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4 5.28E-03 5.22E-03 3.07E - 03 2.07E-03 2. M E - 02 3. ~ E - ~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
5 4.51E--03 4.51E-03 4.53E - 03 2.55E-03 2.03 E - 03 2 . ~ E - 02 5.26E-~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
6
Response function N o .
4.02E--03 4 . 0 2 E - 03 4.02E - 03 4.08E-03 2.16E - 03 1. M E -- 03 1.85E-02 9.02E- ~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
7 3.57E--03 3.57E-03 3.59E - 03 3.68E-03 3.70E - 03 1.91E - 03 1.62E-03 l . ~ E - 02 8.75E- ~ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
8
3.28E-03 3.28E-03 3.28 E - 03 3.33E-03 3. ~ E - 03 3 . ~ E - 03 1.74E-03 1 . ~ E - - 03 1.39E - ~ 1.1 I E - 0 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
9
Table 2.21 x 33 response m a t r i x at 2.75 M e V , normalized to unity, detector intrinsic efficiency, collimator integrated effective aperture a n d energy g r o u p width
contm~doverleaf
2.96E-- 03 2 . ~ E - 03 2.96E - 03 2.97E--03 3 . ~ E -- 03 3.19E - 03 3.27E-03 1.91 E - - 03 1.21E 1.25E-02 1.23E-03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
10
LO
Z O
t%
11
2.62E-03 2.62E-03 2.62E-03 2.62E-03 2.62E-03 2.64E-03 2.73E-03 2.91E-03 2.73E--03 1.38E--03 1.40E-03 1.00E- 02 1.08E-03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Energy group No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
2.31E-03 2.31E-03 2.31E-03 2.33E-03 2.29E-03 2.29E-03 2.24E-03 2.33E-03 2.44E-03 2.64E-03 2.39E-03 1.19E 03 1.23E-03 8.30E 03 1.10E-03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
12 2.08E-03 2.09E-03 2.11E-03 2.15E-03 2.18E--03 2.18E--03 2.13E--03 2.11E--03 2.12E-03 2.20E--03 2.24E--03 2.38E--03 2.05E--03 1.19E-03 1.24E-03 6.07E--03 1.01E--03 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
13 1.94E-03 1.94E--03 1.95E-03 1.97E-03 2.05E-03 2.02E--03 1.97E--03 1.95E-03 1.94E 03 1.92E 03 1.93E 03 2.05E-03 2.03E-03 2.11E-03 1.79E-03 1.05E-03 1.13E-03 4.89E--03 8.91E--04 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
14 1.80E-03 1.81E-03 1.81E-03 1.84E--03 1.91E--03 1.86E--03 1.88E-03 1.89E-03 1.80E-03 1.74E-03 1.74E-03 1.72E--03 1,71E--03 1.89E--03 1.SlE-03 1.84E- 03 1.54E-03 8.81E-04 9.95E-04 4.16E-03 5.91E-04 0.0 0.0 0,0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
15 1.60E-03 1.60E--03 1.60E--03 1.61E-03 1.75E-03 1.65E-03 1.63E-03 1.63E-03 1.70E 03 1.77E 03 1.63E 03 1.58E-03 1.57E-03 1.56E-03 1.54E-03 1.80E--03 1.70E-03 1.69E-03 1.39E-03 7.74E--04 9.28E-- 04 3.53E--03 8 . 6 6 E - 04 0,0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
16
17 1.41E-03 1.41E--03 1.41E-03 1.42E-03 1.57E--03 1.44E-03 1.42E- 03 1.43E-03 1.43E-03 1.44E-03 1.52E-03 1.66E--03 1.48E-03 1.45E-03 1.45E-03 1.43E-03 1.42E-03 1.76E-03 1.63E 03 1.59E-03 1.28E 03 6.79E-04 8.93E 04 3.27E-03 8 . 5 2 E - 04 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Response function No.
Table 2--continued
1.25E-03 1.26E-03 1.26E-03 1.27E--03 1.43E--03 1.29E-03 1.26E- 03 1.26E-03 1.27E 03 1.27E 03 1.28E-03 1.28E-03 1.39E--03 1.59E-03 1.38E-03 1.36E--03 1.36E--03 1.33E--03 1.33E-03 1.75E-03 1.60E-03 1.53E--03 1.21E-03 6 . 4 0 E - 04 8 . 7 9 E - 04 3.11E--03 8.57E--04 0.0 0.0 0.0 0.0 0.0 0.0
18 1.09E-03 1.11E-03 1.12E--03 1.13E--03 1.32E--03 1.17E-03 1.12E-03 1.12E--03 1.13E--03 1.13E--03 1.13E--03 1.14E-03 |.14E-03 1.15E-03 1.27E-03 1.54E 03 1.29E-03 1.29E-03 1.28E-03 1.25E--03 1.26E--03 1.77E--03 1.58E-03 1.48E--03 1.16E--03 5.90E--04 8 . 7 6 E - 04 2.97E-03 8.72E--04 0.0 0.0 0.0 0.0
19
9.35E-04 9.51E--04 9.66E 04 9.91E-04 1.22E-03 1.04E-03 1.00E--03 1.00E--03 1.00E-03 1.01E-03 1.01E-03 1.01E--03 1.01E--03 1.02E--03 1.02E-03 1.02E- 03 1.17E--03 1.51E--03 1.22E- 03 1.23E-03 1.23E-03 1.20E--03 1.20E--03 1.81E-03 1.60E 03 1.47E--~)3 1.12E 03 5.50E-04 8.86E-04 2.88E--03 9.01E-04 0.0 0.0
20
7.71E-04 7.90E-04 8.09E--04 8.40E-04 l,llE-03 9.15E-04 8.87E 04 8.90E--04 8.93E 04 8.95E--04 8.98E-04 9.00E-04 9.03E-04 9.06E-04 9.08E--04 9.11E-04 9.13E-04 9.16E-04 1.09E--03 1.53E--03 1.17E-03 1.21E-03 1.21E--03 1.17E--03 1.18E-03 1.91E-03 1.66E-03 1.49E--03 1.12E-03 5.20E-04 9.26E-04 2.87E--03 9.86E - 04
21
Z o
W
,H
Energy (MeV)
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
Bin No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
Width (MeV)
8.42E+ 05 7.99E + 05 5.98E + 05 4.30E + 05 3.24E+05 2.83E+05 2.11E+05 1.90E + 05 1.83E+05 1.01E+05 7.28E+04 8.94E+04 7.55E + 04 7.55E+04 8.11E+04 6.83E+ 04 7.77E + 04 7.68E+04 7.47E+04 6.12E+04 8.96E+05
Scalar flux 2.31E+05 2.12E + 05 1.51E + 05 1.09E + 05 9.36E+04 8.84E+04 7.17E+04 6.16E + 04 6.20E+04 3.31E+04 2.49E+04 2.63E+04 1,97E + 04 1.97E+04 1.98E+04 1.44E + 0 4 1.77E + 04 1.88E+04 1.42E+04 1.13E+04 2.61E+05
0.0
2.22E+05 2.07E + 05 1.44E + 05 1.0BE + 05 8.91E+04 8.08E+04 6.38E+04 5.76E + 04 5.53E+04 2.96E+04 2.22E+04 2.51E+04 1.84E + 04 1.84E+04 1.81E+04 1.63E+ 04 1.89E + 04 1.71E+0,:I 1.46E+04 1.03E+04 2.61E+05
15.0
1.87E+ 05 1.76E + 05 1.26E + 05 9.29E + 04 7.51E+04 6.60E+04 4.88E+04 4.43E + 04 4.42E+04 2.36E+04 1.84E+04 2.01E+04 1.78E + 04 1.78E+04 1.90E+04 1.32E+04 1.53E + 04 1.47E+04 1.34E+04 1.06E+04 2.15E+05
30.0
1.95E+05 1.85 E + 05 1.38E + 05 1.00E + 05 7.42E+04 6.63E+04 4.82E+04 4.35E + 04 4.19E+04 2.29E+04 1.54E+04 2.31E+04 1.79E + 04 1.79E+04 2.07E+04 1.65E+ 04 1.87E + 04 1.61E+04 1.87E+04 1.47E+04 2.20E+05
45.0
1.65E+05 1.58 E + 05 1.22E + 05 8,59E + 04 6.24E+04 5.31E+04 4.00E+04 3.56E + 04 3.39E+04 1.92E+04 1.39E+04 1.59E+04 1.44E + 04 1.44E+04 1.49E+04 1.39E+04 1.58E + 04 1.79E+04 1.57E+04 1.37E+04 1.59E+05
60.0
Angular fluxes (photon/MeV • cm 2" s" st)
Table 3. Angular flux spectra emerging from a 1.01 m.f.p, aluminium shield
1.12E+05 1.08E + 05 8.37E + 04 5.94E + 04 4.16E+04 3.51E+04 2.52E+04 2.29E + 04 2.17E+04 1.22E+04 8.56E+03 1.13E+04 1.02E + 04 1.02E+04 1.14E+04 1.01E + 0 4 1.12E + 04 1.12E+04 1.19E+04 1.02E+04 1.12E+05
70.0
3.83E+ 04 3.72E + 04 2.94E + 04 2.07E + 04 1.41E+04 1.17E+IM 8.27E+03 7.56E + 03 7.13E+03 4.05E+03 2.80E+03 3.82E+03 3.55E + 03 3.55E+03 4.00E+03 3.65E+03 4.00E + 03 4.02E+03 4.45E+03 3.86E+03 3.75E+04
80.0
L,h
O
--]
Energy (MeV)
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
Bin No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
Width (MeV)
8.08E + 04 3.55E + 05 3.32E+05 2.62E+05 2.25E + 05 1.91E+05 1.39E+05 1.26E + 05 1.18E+05 6.62E+04 4.59E + 04 4.96E + 04 5.31E+04 5.31E+04 5.64E + 04 5.14E+04 5.66E+04 6.06E+04 4.66E+ 04 3.91E + 04 4.32E + 05
Scalar flux 2.60E + 04 1.01E + 05 9.08E+04 7.10E+04 6.61E + 04 6.17E+04 4.85E+04 4.49E + 04 4.34E+04 2.38E+04 1.72E + 04 1.80E+04 1.52E+04 1.52E+04 1.56E + 04 1.18E+04 1.40E+04 1.44E+04 1.22E+04 9.67E + 03 1.52E + 05
0.0 2.16E + 04 9.67E + 04 8.62E+04 6.77E+04 6.32E + 04 5.78E+04 4.31E+04 4.06E + 04 3.81E+04 2.10E+04 1.39E + 04 1.49E+04 1.48E+04 1.48E+04 1.61E + 04 1.30E+04 1.48E+04 1.57E+04 1.31E+04 8.82E + 03 1.48E + 05
15.0 2.09E + 04 9.25E + 04 8.36E+04 6.65E+04 6.03E + 04 5.18E+04 3.87E+04 3.56E + 04 3.41E+04 1.83E+04 1.32E + 04 1.49E+04 1.47E+04 1.47E+04 1.54E + 04 1.37E+04 1.59E+04 1.51E+04 1.12E+04 9.63E + 03 1.40E + 05
30.0 1.77E + 04 8.20E + 04 7.69E+04 6.17E+04 5.16E + 04 4.42E+04 3.17E+04 2.87E + 04 2.64E + 04 1.48E+04 1.05E + 04 1.17E+04 1.32E+04 1.32E+04 1.40E + 04 1.24E+04 1.30E+04 1.42E+04 1.18E+04 9.69E + 03 1.08E + 05
45.0 1.75 E + 04 7.36E + 04 7.10E+04 5.52E+04 4.59E + 04 3.75E+04 2.65E+04 2.39E + 04 2.22E+04 1.29E+04 8.65E 4- 03 8.98E+03 1.00E+04 1.00E + 04 1.07E + 04 1.04E+04 1.15E+04 1.29E+04 9.32E+03 8.29E + 03 6.88E + 04
60.0
Angular fluxes (photon/MeV • em:" s" sr)
Table 4. Angular flux spectra emerging from a 1.49 m.f.p, steel shield
8.37E + 03 3.81E + 04 3.68E+04 2.91E+04 2.36E + 04 1.89E+04 1.31E+04 1.17E + 04 1.07E+04 6.t8E+03 4.23E + 03 4.58E+03 5.54E+03 5.54E+03 5.95 E 4- 03 5.99E+03 6.36E+03 7.04E+03 5.13E+03 4.62E + 03 3.79 E + 04
70.0
1.39E + 03 6.43E + 03 6.29E+03 4.97E+03 3.95 E + 03 3.09E+03 2.11E+03 1.88 E + 03 1.71E+03 9.91E+02 6.74E + 02 7.31E+02 9.25E+02 9.25E+02 9.98E + 02 1.05E+03 1.09E+03 1.23E+03 8.74E+02 8.11E + 02 5.95E 4- 03
80.0
Z Q
o~
9 10 11 12 13 14 15 16 17 18 19 20 21
8
5 6 7
4
2 3
1
Bin No.
Scalar flux
8.73E + 05 7.ME + 05 5.48E + 05 3.81E+05 2.78 E + 05 2.36E+05 1.79E+05 1.66E + 05 1.62E + 05 9.47E+04 6.72E + 04 4.80E+04 6.30E+ 04 6.30E+04 6.31E+04 4.52E+04 6.52E + 04 8.71E+04 6.85E+04 5.32E+04 9.44E+05
Width (MeV)
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
Energy (MeV)
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
2.36E + 05 1.98E + 05 1.39E + 05 1.02E+05 7.99E + 04 7.62E+04 5.95E+04 5.75E + 04 5.35E + 04 3.45E+04 2.00E + 04 1.45E+04 1.80E+04 1.80E+04 1.68E+04 1.10E+04 1.47E + 04 1.65E+04 1.49E+04 1.11E+04 2.75E+05
0.0 2.27E + 05 1.89E + 05 1.34E + 05 9.66E+ 04 7.60E + 04 6.90E+04 5.43E+04 5.02E + 04 4.94E + 04 2.68E+04 1.96E + 04 1.04E+04 1.64E+ 04 1.64E+04 1.50E+04 1.06E+04 1.48E + 04 1.99E+04 1.55E+04 1.06E+04 2.72E+05
15.0 2.19E + 05 1.84E + 05 1.31E + 05 9.36E+04 7.27E + 04 6.23E+04 4.82E+04 4.30E + 04 4.42E + 04 2.51E+04 1.74E + 04 9.97E +03 1.70E+04 1.70E+04 1.73E+04 1.16E+04 1.67E + 04 1.75E+04 1.46E+04 1.16E+04 2.61E+05
30.0 1.97E + 05 1.66E + 05 1.24E + 05 8.69E + 04 6.24E + 04 5.46E+04 4.04E+04 3.79E + 04 3.65E + 04 2.18E+04 1.59E + 04 1.05E+04 1..50E+ 04 1.50E+04 1.53E+04 1.16E+04 1.60E + 04 1.74E+04 1.67E+04 1.11E+04 2.29E+05
45.0 1.71E + 05 1.44E + 05 1.12E + 05 7.58E+04 5.30E + 04 4.34E+04 3.29E+IM 3.09E + 04 2.96E + 04 1.75E+04 1.23E + 04 1.1 I E + 0 4 1.15E+04 1.15E+04 1.15E+04 8.16E+03 1.22E + 04 2.08E+04 1.40E+04 1.23E+04 1.64E+05
60.0
Angular fluxes (photon/MeV • cm 2"s" sr)
Table 5. Angular flux spectra emerging from a 0.97 m.f.p, graphite shield
1.12E + 05 9.46E + 04 7.34E + 04 4.96E+04 3.43 E + 04 2.75E+04 2.05E+04 1.89E + 04 1.85E + 04 1.07E+04 8.07E + 03 6.43E+03 7.82E+03 7.82E+03 8.16E+03 6.07E+03 9.04E + 03 1.32E+04 9.86E+03 8.00E+03 1.13E+05
70.0
3.48E + 04 2.95E + 04 2.32E + 04 1.55E+04 1.05E + 04 8.24E+03 6.09E+03 5.60E + 03 5.50E + 03 3.15E+03 2.44E + 03 2.03E+03 2.40E+ 03 2.40E+03 2.54E+03 1.92E+03 2.90E + 03 4.43E+03 3.22E+03 2.67E+03 3.42E+04
80.0
o
Z
g.
o
,-q
0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.0832 0.0833 0.1249 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1665 0.1940
0.1596 0.2428 0.3261 0.4093 0.4926 0.5758 0.6591 0.7423 0.8256 0.9297 1.0754 1.2419 1.4084 1.5749 1.7414 1.9078 2.0744 2.2409 2.4074 2.5739 2.7541
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Width (MeV)
Energy (MeV)
Bin No.
1.11E+03 2.62E + 04 3.06E + 04 4.20E + 04 1.19E + 05 1.25E + 05 6.59E + 04 7.79E + 04 8.69E+04 4.53E+04 4.24E + 04 4.12E+04 5.72E+04 5.72E+04 6.04E+ 04 4.79E + 04 5.67E+04 7.01E+04 5.20E+04 3.78E + 04 6.95 E + 05
Scalar flux 3.42E+03 1. I 1E + 04 5.49 E + 03 6.97E + 03 2.92E + 04 3.70E + 04 2.45E + 04 2.75E + 04 3.10E+ 04 1.69E+04 1.33 E + 04 1.21E+04 1.33E+04 1.33E+04 1.22E+04 8.27E + 03 1.15E+04 1.41E+04 9.44E+03 6.81E + 03 2.01E + 05
0.0 1.77E+03 9.57E + 03 4.56E + 03 5.79E + 03 2.78E + 04 3.39E + 04 2.04E + 04 2.46E + 04 2.69E+ 04 1.33E+04 1.23E + 04 9.83E+03 1.36E+04 1.36E+04 1.29E+04 7.93E + 03 1.15E+04 1.29E+04 9.84E+03 6.56E + 03 1.99E + 05
15.0 1.82E+03 1.07E + 04 5.65E + 03 7.50E + 03 2.75E + 04 2.92E + 04 1.68E + 04 2.09E + 04 2.34E+04 1.27E+04 1.24E + 04 1.06E+04 1.28E+04 1.28E+04 1.42E+04 9.59E + 03 1.16E+04 1.72E+04 1.17E+04 8.09 E + 03 1.88 E + 05
30.0 1.08E+01 6.18 E + 03 6.67E + 03 8.61E + 03 2.49E + 04 2.63E + 04 1.34E + 04 1.62E + 04 1.83E+ 04 9.31E+03 9.12E + 03 8.46E+03 1.31E+04 1.31E+04 1.35E+04 1.09E + 04 1.23E+04 1.52E+04 1.15E+04 7.78 E + 03 1.61E + 05
45.0 6.03E--01 3.38 E + 03 7.36E + 03 1.07E + 04 2.57E + 04 2.61E + 04 1.30E + 04 1.47E + 04 1.63E+ 04 8.62E+03 7.64E + 03 8.58E+03 1.16E+04 1.16E+04 1.23E+04 1.06E + 04 1.27E+04 1.47E+04 1.10E+04 8.69E + 03 1.24E + 05
60.0
Angular fluxes (photon/MeV- cm 2. s" sr)
Table 6. Angular flux spectra emerging from a 1.21 m.f.p, lead shield
2.58E--01 2.41E + 03 5.18 E + 03 7.39 E + 03 1.67E + 04 1.60E + 04 7.45E + 03 8.84E + 03 9.85E+03 5.10E+03 5.03 E + 03 5.35E+03 8.07E+03 8.07E+03 9.01E+03 7.95 E + 03 8.72E+03 1.07E+04 8.22E+03 6.13 E + 03 8.56E + 04
70.0
2.02E 02 6.96E + 02 1.92E + 03 2.80E + 03 5.66E + 03 5.22E + 03 2.32E + 03 2.75E + 03 3.07E+03 1.59E+03 1.59E + 03 1.76E+03 2.75E+03 2.75E+03 3.15E+03 2.92E + 03 3.09E+03 3.80E+03 2.95E+03 2.23E + 03 2.75E + 04
80.0
o
7~
-]
oo
Technical Notes
"C
106
c~
E 10 5
10 4
3
10:3
3 < IO
2
O0
0.5
1.0 Energy,
1..5
2.0
2.5
3.0
E (MeV)
Fig. 3. Angular flux variation through 1.52 m.f.p. (15 cm) of aluminium, for photons emitted at 2.75 MeV, measured using the disc radiator.
569
570
Technical Notes
~0 6
"2 ca'
~o~
=o ~4
~0 D
0
<
2 10 OO
05
10
1.5
20
2.5
3.0
Energy, E ( M e V )
Fig. 4. Angular flux variation through 0.75 m.f.p. (2.5 cm) of steel, for photons emitted at 2.75 MeV, measured using the disc radiator.
571
Technical Notes
Table 7. Comparison of scalar flux spectra for selected shields 1.01 m.f.p. Aluminium Integrated experimental angular flux 8.42E+05 7.99E+05 5.98E+05 4.30E+05 3.24E+05 2.83E+05 2.11E+05 1.90E+05 1.83E+05 1.01E+05 7.28E+04 8.94E+04 7.55E+04 7.55E+04 8.11E+04 6.83E+04 7.77E+04 7.68E+04 7.47E+04 6.12E+04 8.96E+05
1.49 m.f.p. Steel
SAM-F
Integrated experimental angular flux
1.57E+06 6.93E+05 4.89E+05 3.86E+05 3.98E+05 2.90E+05 1.97E+05 1.93E+05 1.49E+05 1.35E+05 1.19E+05 8.67E+04 7.90E+04 8.23E+04 8.31E+04 8.13E+04 6.09E+04 7.50E+04 6.89E+04 7.02E+04 8.96E+05
8.08E+04 3.55E+05 3.32E+05 2.62E+05 2.25E+05 1.91E+05 1.39E+05 1.26E+05 1.18E+05 6.62E+04 4.59E+04 4.96E+04 5.31E+04 5.31E+04 5.64E+04 5.14E+04 5.66E+04 6.06E+04 4.66E+04 3.91E+04 4.32E+05
0.97 m.f.p. Graphite
SAM-F
Integrated experimental angular flux
5.60E+05 5.98E+05 3.78E+05 2.52E+05 2.69E+05 1.39E+05 1.18E+05 1.07E+05 7.96E+04 8.12E+04 8.58E+04 6.57E+04 7.62E+04 5.19E+04 5.16E+04 5.53E+04 3.56E+04 4.09E+04 5.07E+04 4.12E+04 4.32E+05
8.73E+05 7.34E+05 5.48E+05 3.81E+05 2.78E+05 2.36E+05 1.79E+05 1.66E+05 1.62E+05 9.47E+04 6.72E+04 4.80E+04 6.30E+04 6.30E+04 6.31E+04 4.52E+04 6.52E+04 8.71E+04 6.85E+04 5.32E+04 9.44E+05
1.21 m.f.p. Lead
SAM-F
Integrated experimental angular flux
SAM-F
1.46E+06 6.07E+05 5.06E+05 3.26E+05 4.18E+05 2.29E+05 2.08E+05 1.35E+05 1.44E+05 9.82E+04 1.07E+05 1.09E+05 5.50E+04 1.24E+05 8.10E+04 7.15E+04 1.00E+05 6.l l E+04 5.87E+04 1.05E+05 9.44E+05
1.11E+05 2.62E+04 3.06E+04 4.20E+04 1.19E+05 1.25E+05 6.59E+04 7.79E+04 8.69E+04 4.53E+04 4.24E+04 4.12E+04 5.72E+04 5.72E+04 6.04E+04 4.79E+04 5.67E+04 7.01E+04 5.20E+04 3.78E+04 6.95E+05
1.85E+04 7.50E+04 1.12E+05 1.16E+05 4.66E+05 1.22E+05 1.23E+05 1.10E+05 8.69E+04 6.85E+04 7.91E+04 7.98E+04 5.70E+04 4.70E+04 6.78E+04 4.94E+04 2.56E+04 2.86E+04 3.95E+04 2.88E+04 6.95E+05
1O;
o
lo ~
>
0.5
1.0
1.5
2.0
2.5
5.0
Energy, E ( M e V )
Fig. 5. Scalar flux variation with penetration thickness (5, 10 and 15 cm) of aluminium.
572
Technical Notes
F-7
I
SAM-F
I
r~
RADAK
10 7
L
u >
L71-10 6 I
~ -- -I
/
E
I__j
2
o
I
I ,
I I I_
J
10 5
I
L
O3
1.49 ~ o 0.0
0.5
1.0
Energy,
1.5
20
2.5
30
E(MeV)
Fig. 6. Scalar flux variation with penetration thickness (2.5 and 5 cm) of steel.
IJ
1d-
r - ~ RAOAK [7
[7
SAM-F
RADAK
F 7 SAM-V
% > lo6
"l I
o ~. 10~
o
i1 ml Ii
o
r-1 m L
io5
o. r-
-
10`=
=
104
[u
rr
~7
I Io~
oo 03
O3
10
~)1.OI
I
Q5
I
1.O Energy,
]
1,5
I
2O
]
2.5
I
5.0
E (MeV)
Fig. 7. Scalar flux with a penetration thickness of 15 cm (0.97 m.f.p.) of graphite.
j10 .
I
• 0.5
0
I 1.0
[ 1.5
I 2.0
I 25
I 30
Energy, E (MeV)
Fig. 8. Scalar flux with a penetration thickness of 2.5 cn~ (1.21 m.f.p.) of lead.
Technical Notes Angular flux spectra are presented which can be used to evaluate calculational methods.
Acknowledgement~The authors would like to thank Mr A. G. Davies for his help in constructing and operating the ~4Na facility; the Radiation Information Shielding Centre, Oak Ridge, Tenn., U.S.A. for the computer package on SAM-CE; the Atomic Energy Authority, Winfrith, for the unfolding code RADAK; and the staff of the Universities Research Reactor Centre, Risley, Warrington, for their close cooperation throughout the project.
573 REFERENCES
Banal J. (1983) A TKE 42, 197. Bishop G. B. and Banal J. (1985) Ann. nucl. Energy 12, 593. Bishop G. B. and Marafie A. M. (1978) Nucl. lnstrum. Meth. 150, 505. Dahlstrom T. S. and Thompson W. E. (1962) Report USN RDL-TR-558. Grimstone M. J. (1976) Report AEEW-M.1455. Kappos I., Bishop G. B. and Tsagas N. F. (1986) Ann. nucl. Energy 13, 511. Lichtenstein H. et al. (1979) Report ORNL-RSIC-CCC- 187. Watts R. S. and Pena H. G. (1972) J. nucl. Med. Biol. 16, 51.