Radiation Protection Dosimetry (2005) Vol. 115, No. 1–4, pp. 298–301 doi:10.1093/rpd/nci119
BREMSSTRAHLUNG DOSES FROM NATURAL URANIUM INGOTS Jeri L. Anderson1, and Nolan E. Hertel2 1 National Institute for Occupational Safety and Health, 4676 Columbia Parkway, Cincinnati, OH 45226, USA 2 G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
INTRODUCTION
METHODS
During the cold war, there were privately owned commercial facilities in the United States that processed or produced radioactive materials for the US Atomic Energy Commission (AEC). These materials were used in the production of atomic weapons. Several of these facilities handled only natural uranium metal in various geometric forms and the processes at these facilities included recasting, rolling, machining and extruding uranium. The authors have undertaken a study to compute the external dose rates on the surfaces of and at distances of 30.48 cm and 1 m from the surfaces of typical geometrical forms in which the natural uranium metal might have been handled. Two different computational approaches, or models, were used to calculate the external dose rate due to bremsstrahlung and natural uranium decay chain gamma rays. In the first approach, MCNP5(1) calculations were performed to obtain the beta-induced bremsstrahlung dose and the gamma ray dose from natural uranium decay and the decay of its progeny. It was necessary to use several variance reduction techniques to obtain bremsstrahlung and photon doses in reasonable run times. The second approach employed the MICROSHIELD(2) point-kernel code. The approaches used to determine these doses rates are described and the dose rates computed by both approaches are reported.
Natural uranium objects
Seven different natural uranium configurations were modelled in the dose rate calculations. They consist of the five cylindrical configurations shown in Table 1 and the two rectangular configurations shown in Table 2. These configurations were typical of the various uranium forms used and produced in uranium metal-working facilities during early AEC operations. MCNP calculations Source terms As a starting point, the natural uranium was assumed to have decayed for 100 d after chemical separation. According to Ref. (3), 238U and 235U specific activities in natural uranium are 12.2 kBq g1 and 555 Bq g1, respectively. 234U was assumed to be in secular equilibrium with 238U at chemical Table 1. Cylindrical natural uranium configurations considered. Item
Long rod Slug Long billet Short billet Cylindrical ingot
geometrical
Inner Radius (cm)
Outer Radius (cm)
Length (cm)
— 1.041 — — —
1.784 2.108 6.35 7.62 16.51
609.8 10.16 71.12 30.48 50.80
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In the past, some privately owned commercial facilities in the United States were involved in producing or processing radioactive materials used in the production of atomic weapons. Seven different geometrical objects, representative of the configurations of natural uranium metal potentially encountered by workers at these facilities, are modelled to determine gamma ray and bremsstrahlung dose rates. The dose rates are calculated using the MCNP5 code and also by using the MICROSHIELD point-kernel code. Both gamma ray and bremsstrahlung dose rates are calculated and combined to obtain a total dose rate. The two methods were found to be in good agreement despite differences in modelling assumptions and method differences. Computed total dose rates on the surface of these objects ranged from 51–84 lSv h1 and 17–95 lSv h1 using the MCNP5 and the MICROSHIELD modeling, respectively. The partitioning of the computed dose rates between gamma rays and bremsstrahlung were the same order of magnitude for each object.
BREMSSTRAHLUNG DOSES FROM NATURAL URANIUM INGOTS
separation and so it must have similarly decayed for a 100-d time period. The specific radionuclide activities in the natural uranium after 100 d of decay are shown in Table 3. The natural uranium beta source spectrum was computed by summing the activityweighted beta spectra for 234Pam, 234Th, 231Th, 223 Fr and 227Ac using the specific activities in Table 3. These beta spectra were taken from the RADDECAY code that is distributed with the MICROSHIELD code. The ICRP Publication 38 dataset in geometrical
Item
Width (cm)
Length (cm)
Thickness (cm)
Rectangular ingot Flat plate
40.64 7.874
60.96 45.72
10.16 0.457
Table 3. Specific activities in 238U and 100 d of decay. 238
238
U Th 234m Pa 234 U 230 Th 226 Ra 234
Elower (MeV)
Eupper (MeV)
Emission (g s1 g1)
0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.10 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1.0 1.5 2.0
0.02 0.03 0.04 0.05 0.06 0.08 0.10 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1.0 1.5 2.0 3.0
1.04Eþ00 2.24E05 8.13Eþ01 2.26E02 1.44Eþ01 4.54Eþ02 8.15Eþ01 7.70Eþ02 9.22Eþ01 3.46Eþ00 1.34Eþ00 1.13Eþ00 1.68Eþ00 6.86Eþ00 3.82Eþ01 1.22Eþ02 2.58Eþ00 3.33E01
235
U chains after
235
U Chain
Nuclide
Table 4. Natural uranium gamma ray source term based on the MICROSHIELD code after 100 days of decay.
U Chain
Specific activity
Nuclide
12.2 kBq g1 11.5 kBq g1 11.5 kBq g1 12.2 kBq g1 3.01E02 Bq g1 1.78E06 Bq g1
U Th 231 Pa 227 Ac 227 Th 223 Fr 223 Ra
235
231
Specific activity (Bq g1) 555 555 3.17E–03 1.35E–05 8.00E–06 1.87E–07 5.55E–06
Figure 1. The differential bin probabilities created for the natural uranium beta source used in the MCNP5 calculations. The uranium decay chain beta spectra taken from the ICRP Publication 38 data in the RADDECAY CODE were activity-weighted to form the composite spectrum.
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Table 2. Rectangular natural uranium configurations considered.
RADDECAY is the ultimate source of these spectra selected. The resulting differential probability distribution function is shown for the beta source in Figure 1. In this figure, the differential bin probabilities are plotted at the average energy of each energy bin. This beta spectrum was input into MCNP5 to create bremsstrahlung photons in the natural uranium objects. The natural uranium gamma ray source term for the MCNP5 code runs also was created using the MICROSHIELD/RADDECAY codes (see Table 4). The energy binning structure in Table 4 is the default one generated by the MICROSHIELD code and is a rather broad group set.
J. L. ANDERSON and N. E. HERTEL Table 5. The dose-equivalent rates ( lSv h1) for the Natural Uranium Objects. MCNP calculations Item
Location
Long rod
2.40Eþ01 1.32Eþ00 4.03E01 3.51Eþ01 2.32E01 2.45E02 3.61Eþ01 3.23Eþ00 5.17E01 3.45Eþ01 2.14Eþ00 2.62E01 4.00Eþ01 5.45Eþ00 8.82E01 3.96Eþ01 9.91Eþ00 1.45Eþ00 2.67Eþ01 8.65E01 9.52E02
(0.4%) (0.4%) (0.4%) (0.5%) (1.1%) (2.0%) (1.1%) (1.2%) (1.7%) (0.7%) (1.2%) (2.1%) (1.8%) (1.6%) (2.5%) (0.4%) (1.1%) (3.0%) (0.9%) (1.6%) (2.6%)
Bremsstrahlung 2.69Eþ01 1.53Eþ00 4.80E01 4.12Eþ01 2.92E01 2.74E02 4.12Eþ01 3.79Eþ00 5.67E01 3.91Eþ01 2.55Eþ00 3.23E01 4.44Eþ01 6.05Eþ00 9.66E01 4.30Eþ01 1.09Eþ01 2.28Eþ00 3.60Eþ01 1.45Eþ00 1.83E01
Total
(4.7%) (5.1%) (4.9%) (1.3%) (2.9%) (4.9%) (2.1%) (2.5%) (3.6%) (1.2%) (2.0%) (3.3%) (3.6%) (5.6%) (8.1%) (2.9%) (6.8%) (21.6%) (1.1%) (3.0%) (5.1%)
5.09Eþ01 2.85Eþ00 8.83E01 7.63Eþ01 5.24E01 5.19E02 7.74Eþ01 7.03Eþ00 1.08Eþ00 7.36Eþ01 4.69Eþ00 5.85E01 8.44Eþ01 1.15Eþ01 1.85Eþ00 8.26Eþ01 2.08Eþ01 3.73Eþ00 6.27Eþ01 2.31Eþ00 2.78E01
(2.5%) (2.7%) (2.7%) (0.7%) (1.7%) (2.8%) (1.2%) (1.4%) (2.1%) (0.7%) (1.2%) (2.1%) (2.1%) (3.1%) (4.4%) (1.5%) (3.6%) (13.2%) (0.7%) (2.0%) (3.5%)
Gamma
Bremsstrahlung
Total
9.18Eþ00 1.65Eþ00 4.98E01 2.09Eþ01 2.92E01 2.95E02 3.35Eþ01 4.08Eþ00 6.18E01 3.41Eþ01 2.71Eþ00 3.26E01 3.55Eþ01 6.30Eþ00 9.85E01 4.43Eþ01 1.23Eþ01 1.83Eþ00 2.35Eþ01 9.72E01 1.07E01
7.91Eþ00 1.92Eþ00 5.72E01 2.55Eþ01 3.65E01 3.65E02 3.68Eþ01 4.71Eþ00 7.02E01 3.87Eþ01 3.15Eþ00 3.76E01 4.30Eþ01 7.62Eþ00 1.24Eþ00 5.04Eþ01 1.43Eþ01 2.06Eþ00 3.68Eþ01 1.68Eþ00 1.84E01
1.71Eþ01 3.57Eþ00 1.07Eþ00 4.65Eþ01 6.56E01 6.59E02 7.03Eþ01 8.79Eþ00 1.32Eþ00 7.27Eþ01 5.87Eþ00 7.02E01 7.85Eþ01 1.39Eþ01 2.22Eþ00 9.47Eþ01 2.65Eþ01 3.88Eþ00 6.03Eþ01 2.65Eþ00 2.91E01
The dose rates are given for the natural uranium decay chain gamma rays and bremsstrahlung photons as well as for the sum of the two components. The percentages to the right of the MCNP results are the statistical uncertainties in the dose rate values. The MICROSHIELD surface dose rates are computed at 1 cm from the surface. The MCNP5 dose rates are computed using track-length estimators and are, therefore, averaged over a volume
Model considerations In order to obtain reasonable execution time for the bremsstrahlung calculations, several variance reduction methods were employed. The source beta spectrum was sampled uniformly in energy using the SB data card in the MCNP5 code. This biasing method ensured that the higher energy beta particles were sampled adequately, since they produce more bremsstrahlung and, on the average, harder photon energies. The bbrem data card was also used with the default values suggested in the manual. This option biases the sampling of the photon energies towards a larger fraction of the available beta energy ensuring that the most penetrating photons are adequately sampled(1). The dose rate tallies were calculated using the ANSI/ANS 6.1.1-1977(4) dose-equivalent conversion coefficients. The dose rates were computed using track-length estimators fluence tallies in small volumes of air about the mid-plane of the radial objects and on the centreline about the largest surface area of the rectangular parallelepiped objects. For both object shapes, spatial biasing was used in order to increase sampling of the beta source near the surface and towards the object’s centre. Several different detector sizes were used and, in general, the
lateral extent of these tally volume sizes ranged from 10 to 25% of the longest linear dimension of the object. The thicknesses of the surface tally volume thickness were all 1 cm; while the detector thicknesses at 30.48 and 100 cm were 1 cm thick and had the same lateral dimensions as the surface detectors.
MICROSHIELD calculations Source term The same natural uranium decay gamma ray source term was used in the MICROSHIELD calculations. The decay option of the program was used to decay the uranium for 100 d. In the MICROSHIELD calculations, the bremsstrahlung activity was attributed entirely to 234Pam beta decay, after 100 d of decay the 234Pam activity is 94.4% of the 238U activity. The average fraction of the beta-particle energy emitted as bremsstrahlung, fb, was determined by the following equation(5), fb ffi
ZTmax ¼ 0:0699, 3000
ð1Þ
where Z is the atomic number of the absorber (92 for uranium) and Tmax is the maximum beta energy,
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Surface 30.48 cm 1m Slug Surface 30.48 cm 1m Long billet Surface 30.48 cm 1m Short billet Surface 30.48 cm 1m Cylindrical Surface ingot 30.48 cm 1m Rectangular Surface ingot 30.48 cm 1m Flat plate Surface 30.48 cm 1m
Gamma
MICROSHIELD calculations
BREMSSTRAHLUNG DOSES FROM NATURAL URANIUM INGOTS 234
RESULTS The resulting dose rates from the two sets of calculations are shown in Table 5. The calculated dose rates for natural uranium decay chain gamma rays and from the bremsstrahlung created by the uranium chain beta decays are similar in magnitude. The MICROSHIELD-computed total surface dose rates are quite close, within 10%, to those determined using the MCNP5 calculations. The two exceptions are the surface dose rates for the long rod and slug; these are 2–3 times lower than the MCNP-calculated dose rates. The MICROSHIELD surface dose rates are computed at 1 cm from the surface owing to potential instability at distances less than that. The 30.48-cm and 100-cm dose rates calculated using MICROSHIELD are an average of 20% higher than those calculated using MCNP. CONCLUSIONS The use of volumetric tallies in the MCNP5 calculations leads to dose rates that are lower than the maximum dose rates from the objects. This is an
obvious consequence of tallying over a volume and particularly true for the surface detector as fluxes will be strongly spatially varying near the source. The average dose rate around each source may be a better estimate of the dose rate to which a randomly oriented worker was exposed during operations of such facilities. However, the dose rates computed herein are higher than the spatially averaged dose rates would be and, therefore, are probably conservative overestimates of worker dose for dosereconstruction purposes. This reduction of dose rates calculated by the MCNP5 code that arises from spatially averaging over a small volume could be a contributor to the differences in dose rates computed at 30.48 cm and 1 m since MICROSHIELD computes the maximum dose rate at these distances. The agreement between the two methods of calculation was striking given the use of point-kernel techniques by the MICROSHIELD code as well as the assumptions used to create bremsstrahlung photon sources for the MICROSHIELD calculations.
REFERENCES 1. X-5 Monte Carlo Team. MCNP—a general Monte Carlo N-particle transport code, version 5. LANL Report No. LA-UR-03-1987 (Los Alamos National Laboratory, Los Alamos, NM) (2003). 2. Grove Engineering. MicroShield Software Program, Version 6.02. Copyright 1992–2003. 3. Benedict, M., Pigford, T. H. and Levi, H. W. Nuclear Chemical Engineering, second edition (Boston, MA: McGraw Hill) (1981), ISBN-0-07-004531-3. 4. American Nuclear Society Standards Committee Working Group ANS-6.1.1. American National Standard for neutron and gamma-ray fluence-to-dose factors. ANSI/ANS 6.1.1-N666 (LaGrange Park, IL: American Nuclear Society) (1977). 5. Chilton, A. B., Shultis, J. K. and Faw, R. E. Principles of Radiation Shielding (Englewood Cliffs, NJ: PrenticeHall Inc.), pp. 109–111 (1984), ISBN-0-13-709907-X.
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2.28 MeV for Pam. Thus, the bremsstrahlung production rate was estimated by multiplying the 234 Pam activity by fb. The average energy of the bremsstrahlung photons was assumed to be 30% of the maximum beta energy, or 0.684 MeV. All the bremsstrahlung photons were emitted at this energy for the MICROSHIELD calculations and were assumed to be uniformly distributed in the natural uranium objects. The air build-up factor was used for dose rate calculations for the uranium decay gamma rays as this resulted in the most conservative dose estimate. The natural uranium build-up factor was used for the calculations of dose rate due to the bremsstrahlung photons, as the one for air resulted in physically unrealistic doses in this case.
