Radiation Protection Dosimetry (2005), Vol. 115, No. 1–4, pp. 254–257 doi:10.1093/rpd/nci187
COMPARISON OF DETERMINISTIC AND MONTE CARLO METHODS IN SHIELDING DESIGN A. D. Oliveira and C. Oliveira Departamento de Protecc¸~ao Radiol ogica e Seguranc¸a Nuclear, Instituto Tecnol ogico e Nuclear, EN 10, Apartado 21, 2686-953 Sacavem, Portugal In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions.
INTRODUCTION In routine design of photon radiation shielding or other operational activities in radiation protection, it is widely used as the description of the scattered radiation by the build-up factor, B, given by B ¼ (P þ S)/P, where P and S stands for primary and secondary components of radiation, respectively. Some commercial software packages are often applied, e.g. MicroShield from Grove Engineering Company(1), where several approaches of the buildup factor are used. For the built-in reference materials, data tables are used while for custom or mixed materials the Taylor or geometric progression approximations is used. We used only MicroShield built-in reference materials, water, air and lead in our calculations. One of the advantages of this type of software is the user-friendly interface allowing the definition of geometry, source, build-up and sensitivity analysis in a very simple windows interface. The drawbacks are well known and are recognised in the recommendations of the MicroShield software but the limits of applicability and some details are not very well identified. In order to compare with other well-accepted tools we used, as reference, the MCNP Monte Carlo code(2) and through some case studies we compared both deterministic and Monte Carlo codes. Several geometries were used in the MCNP in order to reproduce the results of MicroShield.
applied both deterministic and Monte Carlo codes in shielding calculations allowing evaluation of the influence of primary energy from 0.03 to 5 MeV in the slab shield thickness. Both codes were also applied to a case study of shielding with a 99Tcm gamma source, widely used in nuclear medicine. For slab materials of water and lead, we calculated the energy fluence (MeV cm2) vs. slab thickness for energies 0.03, 0.07, 0.15, 1 and 5 MeV. In MicroShield software(1), the point of interest was located 100 cm away from the source that emits 106 photons s1. To obtain MCNP(2) results several geometrical configurations have been considered. In MCNP, we simulated the emission of photons and its transport and interactions including the emission of fluorescence and bremsstrahlung photons. The energy cut-off was 1 keV and the results were obtained using the F2 tally, which gives the average energy fluence (using ICRU definitions) in MeV cm2. It was defined as a case study with a cylinder (40 cm height and 15 cm radius) of water with 99 Tcm as source. The aim was the determination of the lead slab thickness for professional exposed (PE) using NCRP Publication 49 standard occupation factors 1, 1/4 and 1/16, named as PE1, PE1/4 and PE1/16, respectively. The geometry of the case study is shown in Figure 1. RESULTS
METHODS We defined very simple geometric conditions with a point source and a slab shield of water and lead, and
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Using the geometric condition of point source we wanted to reproduce the MicroShield results using MCNP, and after several trials with different geometric configurations we concluded that the build-up factor used in MicroShield is obtained with the geometry shown in Figure 2, which is significantly
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DETERMINISTIC AND MONTE CARLO METHODS IN SHIELDING DESIGN
Figure 1. Geometry used in the case study: cylindrical source of water with 99Tcm (40 cm height and 15 cm radius), lead slab and point of interest at 100 cm. Figure 3. Relative deviation between analytical (MS) and Monte Carlo (MC) in the calculation of energy fluence as a function of slab thickness of water, considering only the primary interactions of radiation.
Detector In black
Radiation beam
Figure 2. Monte Carlo geometry: parallel beam, slab shield with the output face as the detector.
different from the conditions shown in Figure 1 with respect to the detection of the radiation. This modification is very important at low energies as we shall see below. The results obtained with both MicroShield (MS) and MCNP (MC) are in very good agreement for high-energy values; however, as the energy decreases to values such as 30–150 keV some discrepancies arise. To quantify the relative differences between MS and MC, we calculated the relative deviation (RD) by the expression RD ¼ 100 (MS MC)/MC. In Figures 3 and 4 the RD for water as a function of slab thickness, with energy as parameter, is shown. In shielding, we have to consider in the calculations both the primary and the secondary components of the radiation. From Figure 4, we can see that for 5 MeV we have an excellent agreement; however, 500 keV was obtained with different geometrical conditions. The geometry shown in Figure 2 used in the MC simulation allows us to obtain the best agreement with the MS software where we defined a point source with a point detector. These discrepancies indicate that the build-up factor used in MS does not correspond to the geometry defined in the dialog box. In the case of lead slab and considering the geometric aspect mentioned above we obtained a good agreement, considering both primary and secondary components of radiation interactions,
