MONTE CARLO CALCULATION OF DOSE
RATE CONVERSION FACTORS FOR EXTERNAL
EXPOSURE TO PHOTON EMITTERS IN SOIL.
A. Clouvas, S. Xanthos, M.AntonopoulosDomis
Nuclear Technology Laboratory, Department of Electrical and Computer
Engineering, Aristotle University of Thessaloniki, GR54006 Thessaloniki, Greece
J. Silva
Universite Pierre et Marie Curie, PARIS VI, Paris, France
The dose rate conversion factors _{ } (absorbed dose rate in air per unit activity per unit of soil mass, nGy/h per Bq/kg) are calculated 1m above ground, for photon emitters of natural radionuclides uniformly distributed in the soil. Three Monte Carlo codes are used: a) The MCNP code of Los Alamos b) The GEANT code of CERN and c) a Monte Carlo code developed in the Nuclear Technology Laboratory of the Aristotle University of Thessaloniki. The accuracy of the Monte Carlo results is tested by the comparison of the unscattered flux obtained by the three Monte Carlo codes with an independent straightforward calculation. All codes and particularly the MCNP calculate accurately the absorbed dose rate in air due to the unscattered radiation. For the total radiation (unscattered plus scattered) the _{ } values calculated from the three codes are in very good agreement between them. The comparison between these results and the results deduced previously by other authors indicates a good agreement (less than 15% of difference) for photon energies above 1500 keV. Antithetically, the agreement is not so good (difference of 2030%) for the low energy photons.
INTRODUCTION
Dose rate conversion factors for external gamma exposure to photon emitters from contaminated soil are very important for radiation physicists and therefore have been studied for more than three decades. The literature on the subject is extensive and in the following discussion only some of the relevant references are considered. The first calculations have been performed by Beck and de Planque (1968) and Beck et al. (1972). They used the polynomial expansion matrix equation method for solving the soil/air transport problem to calculate the exposure rates 1 m above ground level for distributed sources of g emitters in soil. The dose rates in air were calculated for g energies (from 0.25 to 2.75 MeV) for radionuclides commonly found in the natural environment. Conversion factors have been also calculated by Kocher and Sjoreen (1985) using the pointkernel integration method, in which it is assumed that soil is an infinite scattering medium for photons, and employed buildup factors to account for doses from uncollided and scattered photons. Soil properties, including the photon crosssectional data, were approximated by those of concrete. All dose conversion factors were calculated as usual for a point receptor located 1 m above the ground. In the present decade Monte Carlo techniques have been used almost exclusively in order to calculate absorbed dose rate in air. Chen (1991) developed a Monte Carlo algorithm to track the photon transport equation in the soil/air medium. One of the most complete studies of air kerma rate per unit of soil mass for natural sources uniformly distributed in the ground is performed by K. Saito and P. Jacob (1995). The photon transport calculations were carried out using the Monte Carlo program YURI (K. Saito and S. Moriuchi 1985) which has been verified through comparison with various experimental and theoretical data. The results obtained from this work are considered as reference values (ICRU 1994). A question which has to be answered is whether this research and in particular the accuracy of the calculations performed up to now need any further investigation. It is our view that the theoretical calculations of air kerma rates have reached a very mature stage. However, the development of new personal computers with always increasing computation capabilities makes possible the use by small research groups of “heavy” general purpose Monte Carlo codes like the MCNP code or the GEANT code of CERN. This becomes extremely helpful in cases where published data do not match the situation of interest absolutely. To our knowledge, the only calculations with these codes of air kerma rates are the following: The MCNP code has been used by Saito and Jacob (1995) for calculations of air kerma rates for a plane surface source and also for a plane source at a depth where the air kerma is attenuated by one order of magnitude compared with that for the surface plane source. The GEANT code has been used very recently by A. Likar et al. (1998) for calculations of absorbed dose rates in air 1 m above soil for uniform distribution of photon emitters in soil. As it will be discussed in the following sections the geometry used in that work is not the most appropriate for the determination of the dose rate coefficients due to the “huge detector” used. It is understandable, that a smaller “detector” needs much more computing time, a problem that we had to face in the present work. The use of such codes gives also the possibility to test them in relative simple health physics problems.
In the present work we calculated the gamma absorbed dose rate in air 1 m above ground for uniform distribution of natural radionuclides in soil with three different Monte Carlo codes. a) The MCNP code (Briesmeister 1986), b) the GEANT code of CERN (GEANT 1993) and c) a Monte Carlo code developed in the Nuclear Technology Laboratory of the Aristotle University of Thessaloniki, the socalled “MC” code. The aim of the present work is to compare and validate the results reached from the three different Monte Carlo codes.
CALCULATION PROCEDURE
The absorbed gamma dose rate in air _{ } (nGy/h) at a point 1 m above soil for uniform distribution of a gammaray emitter of photon energy E_{0} can be calculated easily, as it will be shown in the following chapter, if the photon flux energy distribution f(E) is known at the given position. The photon flux is comprised by two parts: a) The unscattered flux which is due to photons of energy E_{0} reaching the given position without any interaction with the soil and the air above and b) The scattered flux which is due to photons of energies 0 < E < E_{0} reaching the given position after scattering mainly in soil. Although the calculation of the unscattered flux is straightforward, the calculation of the scattered flux is more complex and needs the solution of the transport equation or use of Monte Carlo transport codes. A short description of the Monte Carlo codes and the implementations of the simulations used are given below.
The MCNP code
The Los Alamos National Laboratory MCNP code is a general purpose Monte Carlo radiation transport code that can numerically simulate neutron, photon and electron transport. For photons, the code takes account of incoherent and coherent scattering, the possibility of fluorescent emission after photoelectric absorption, absorption in pair production with local emission of annihilation radiation and bremsstrahlung. The user supplied information required by MCNP contains information about specific items such as the geometry and the materials characterizing the environment which will be simulated, the source distribution of the radiation and finally the type of the answers desired (e.g. energy distribution of photon flux in a given position).
The geometry of our calculation using the MCNP code is simple and is shown in Fig. 1. The different components incorporated in the simulation are:
· Air: Simulated as a cylinder of 40 m radius and 1.5 m height with atomic composition of 79% N and 21% O and a density of 0.00129 g cm^{3}.
· Soil: Simulated as a cylinder of 40 m radius and 1 m depth with atomic composition of 7.3% Al, 2.1% C, 1.4% Ca, 3.9% Fe, 0.9% K, 0.5% Mg, 0.1% N, 0.6% Na, 50.1% O, 32.7% Si, 0.4% Ti and a density of 1.3 g cm^{3} (Lindsay1979). As it will be shown in the next chapter the radius of 40 m and the soil depth of 1 m are sufficient in order to consider the emission photon geometry as half space geometry. In addition it is known (Saito and Jacob 1995) that the atomic composition of soil is not a critical parameter of the flux energy distribution. We obtained practically the same results for two different atomic compositions: the atomic composition presented here and the one given by Beck et al. (1972).
The source distribution of radiation incorporated in the MCNP code is photon emitters uniformly distributed in the soil with 8 different photon energies between 200 and 3000 keV. The number of photons emitted in each of these 8 simulations was fifty million.
For the determination of the photon flux energy distribution at one meter above soil two virtual detectors were used: a) The point detector which is a standard tally of the MCNP code, gives the energy distribution of the photon flux directly, normalized per starting photon b) A sphere of radius of 40 cm with its center located at 1 m above soil. The MCNP code counts the number of photons as a function of their energy crossing the surface of the sphere and calculates the photon fluence energy distribution, normalized per starting photon, which can be easily transformed into flux per unit activity per unit of soil mass (g cm^{2} s^{1} per Bq/kg). Both virtual detectors are located on the Z axis of the cylinder of radius of 40 m. Special detectors were also used in some cases where the deposited energy of photons per unit mass of air is directly computed.
The GEANT code
The GEANT code was developed by the Application Software Group at CERN. The GEANT program describes the passage of elementary particles through matter. The principal applications of the code are a) the tracking of particles through an experimental setup for simulation of detector response and b) the graphical representation of the setup and of the particle trajectories. The code is used primarily for the simulation “runs” of complex experiments in order to obtain an optimal placement of different detectors and to calculate various efficiencies for the detection of different particles. The code has been used recently for simulation of Ge detectors (Clouvas et al. 1998; Korun et al. 1997). For photons, the code takes into account the photoelectric effect, Compton scattering and pair production. It also includes electronpositron processes of multiple scattering, ionization, bremsstrahlung, and annihilation. Xrays and Auger electrons following the photoelectric effect are also considered. The simulation consists of tracking all particles created initially by the user and all secondary ones that are created along their path as a result of the physical processes taken into account. Each particle history, from its generation to full dissipation of its energy, is stored.
The geometry of our calculation using the GEANT system is simple and is the same as used for the MCNP code (Fig. 1). The atomic composition of the soil and air is the same as used for the MCNP code. The virtual detector is a surface detector (circle of radius 2 m) located 1 m above soil on the Z axis of the cylinder of radius 40 m. As in the MCNP code the source distribution of radiation are photon emitters uniformly distributed in the soil with eight different photon energies between 200 and 3000 keV. The number of photons emitted in each of these 8 simulations was fifty million. The tracing of gamma rays starts at a certain point in the soil and then carried on until the photon disappears or leaves the space considered. The surface detector counts the number of photons crossing the surface as a function of their energy and their angle of incidence. Knowing the number of photons emitted, the area of the surface detector, the number of photons crossing the surface, their corresponding energy and angle of incidence, the photon flux energy distribution per unit activity per unit of soil mass (g cm^{2} s^{1} per Bq/kg) can be calculated.
The MC code
The MC code is a Monte Carlo code that was originally developed for “indoor” environment (4p geometry). However, it can be also used for “outdoor” environment (2p geometry) with minor changes and assumptions. The code was written using standard FORTRAN 77 language so as to be portable for different machine platforms and it was very easily compiled using different vendors of FORTRAN 77 with minor changes. Its main advantage is the reduction in computational time when compared to the other two codes using the same statistics.
The simulated 2p geometry is simple. The soil is simulated as a square slab with a side of 80 m and height of 1 m. The soil material is concrete with the same density 1.3 g cm^{3} as assumed for the soil in the MCNP and GEANT codes. The atomic composition of concrete is almost the same as the soil’s. Above the soil there is air, simulated by a square slab with the same side as the soil (80 m) and a height of 1.5 m. The “detector” is 1 m above the soil and is simulated by a square surface with side of 2 m, located in the center of the square slab which represents the soil.
The mechanisms of interaction of photons with matter taken into account, were the photoelectric effect, Compton scattering and pair production. As far as a photon undergoes a photoelectric effect or a pair production then the photon is considered as lost. For a Compton scattering process the photon is tracked until its energy drops below 10 keV. Cross sections were taken from the Storm and Israel (1970) tables, in the region from 1 keV until 3 MeV. These are a reasonable cut off, as the highest important gamma energy of natural radionuclide is 2614 keV and because photons even below 50 keV contribute a negligible amount to the dose rate. For photons with energy above 1.4 MeV the Koblinger’s method was adopted (Koblinger 1975), for the estimation of the scattered photon’s energy. Knowing this energy the scattering angle cosine (m) is then simply estimated by the formula
_{ } (1)
where _{ }
a and a¢ are the photon energies, (in _{ } MeV units) before and after collision respectively. For photons with energies less than 1.4 MeV a rejection technique was used so as to sample the secondary energy (after scattering) from Klein  Nishina’s formula (Blomquist and Gelbard, 1983). The scattering angle cosine (m) is calculated afterwards by the same way as above.
In order to calculate the fluence, the inverse cosine of the angle of the photons entering the surface detector with respect to the normal axis is summed for photons of the same energy (within the energy bin). The division of this sum by the detector’s area gives the fluence in units of g/cm^{2}. The fluence of photons of energy E arriving at the detector is calculated by the equation
_{ } (2)
where _{ } is the angle between the surface normal and the particle’s trajectory.
Í is the number of particles of energy around E.
Á the area of the surface used as a detector.
Calculating by eqn (2) the fluence for all energies between 1 keV and E_{0} (where E_{0} is the energy of the photons emitted from the soil), the fluence energy distribution can be deduced which is easily converted to photon flux energy distribution per unit activity per unit of soil mass.
RESULTS AND DISCUSSION
Photon flux energy distribution
A typical simulated photon flux energy distribution per 10 keV step as calculated by the point detector of the MCNP code for photons of energy 1500 keV emitted from the soil is shown in Fig. 2a. The photon emitters are uniformly distributed in the soil and the photon flux is normalized per starting photon and per second. The simulated photon flux as calculated by the volume detector (sphere of radius 40 cm) is presented in Fig. 2b. In both spectra the flux due to unscattered photons (peak) and the continuum due to the photon flux energy distribution of the scattered photons can be clearly observed. The comparison between the two simulated fluxes indicates that both detectors give about the same results, the statistics however obtained with the point detector seems to be much better than those of the volume detector. This is due to the fact that a point detector does not rely on particle simulation by random walk as the volume detector. Point detector is a Monte Carlo method wherein the simulation of particle transport from one place to another is deterministically shortcircuited (Briesmeister 1986).
In order to check if the emission photon geometry is a half space geometry the unscattered flux was calculated with the MCNP code for different photon energies, soil radii and soil depth combinations. In Fig. 3 is presented the unscattered flux per unit activity and per soil mass (Bq/kg) (assuming a fractional yield equal to 1) as function of the soil depth and in Fig. 4 as function of the soil radius. From these two figures it is clear that the emission photon geometry can be considered as a half space geometry.
A test of the accuracy of our Monte Carlo results is the comparison of the unscattered flux obtained by the three Monte Carlo codes with the numerical solution of eqn (3) (Beck et al. 1972) calculating the unscattered flux 1 m above soil per activity per unit mass for photon emitters uniformly distributed in the ground (Fig. 5).
_{ } (3)
where S_{0} the intensity of the source in photons/cm^{3} s
z the depth beneath the surface, where the source is distributed
ù = cosè
ñ_{s}_{ }soil’s density
ì_{s} / ñ_{s} mass attenuation coefficient in soil
ñ_{á} air’s density
ì_{á} / ñ_{á} mass attenuation coefficient in air
h detector’s distance from the soil
Eqn (3) can be solved numerically and in the present work, was solved with Mathcad 7 package using Romberg’s algorithm. Table 1 presents the results of the unscattered flux 1 m above soil per activity per unit mass for different photon energies (assuming a fractional yield equal to 1), calculated by the three Monte Carlo codes, by Beck et al. (1972) and by Mathcad 7 package. The comparison between the results indicates that all Monte Carlo codes calculate very well the unscattered radiation and in particular the difference between the results obtained with the MCNP code and by the Mathcad 7 package is less than 2%. It is worth mentioning that the unscattered flux was calculated using Mathcad in order to achieve a better accuracy than Beck did. The good agreement between the unscattered flux calculated by MCNP and by Mathcad indicates that the simulation parameters used (geometry, tallies, materials) by MCNP are correct.
Dose rate conversion factors
Knowing the photon flux energy distribution the dose rate conversion factor _{ } (absorbed dose rate in air per unit activity per unit of soil mass, nGy/h per Bq/kg) for a photon emitter of energy E_{0} uniformly distributed in the ground can be calculated easily by
_{ } (4)
where E_{i} is the average energy of band i, f_{i}(Å_{i}) the photon flux per unit activity per unit of soil mass in energy band i, _{ } the mass absorption coefficient for air at energy band i. The summation starts at the energy band i = 1 (1020 keV) proceeds with a step of 10 keV and ends at the energy band i = n containing the photon energy of E_{0}.
The MCNP code offers the possibility of using a detector which calculates directly the energy deposition in a given volume. For photon emitters uniformly distributed in the ground of photon energy 1500 keV the dose rate conversion factor _{ } was found 0.369 nGy/h per Bq/kg (assuming a fractional yield equal to 1). Calculating first the photon flux, and then by eqn (4) _{ } was found equal to 0.354 nGy/h per Bq/kg. The comparison between the two values (difference of about 4%) indicate that, as it should, the dose rate conversion factors are independent of the method used for their extraction.
Table 2 presents the dose rate conversion factor _{ } calculated by the three Monte Carlo codes for different photon energies. In the same table for comparison reasons, previous results as deduced from the work of Kocher and Sjoreen (1985), Chen (1991), Lickar et al. (1998), Saito and Jacob (1995) are presented. It is clear that the differences between the results obtained from the three Monte Carlo codes of the present work are small (between 1% and 9%) for all photon energies. It is our view that from the three codes the most accurate results are obtained by the MCNP code. This is strongly supported by Table 1 where the best agreement between the results obtained for the unscattered radiation by the three Monte Carlo codes and the direct calculation with the Mathcad 7 package is for the MCNP code. This is probably due to the use of the point detector by the MCNP. The point detector uses the most complicated variance reduction techniques, which are partially deterministic methods. These techniques circumvent the normal random walk process by using deterministiclike techniques such as next event estimators. However they must be used with caution and particularly in case where there is a source or high scattering medium near the detector. This is not our case where the point detector is surrounded by air.
The comparison between the results obtained in the present work by the three codes with the results obtained by other authors indicates a good agreement (less than 15% of difference) for photon energies above 1500 keV. However, the agreement is not so good (difference of 2030%) for the low energy photons. Moreover, it can be seen that the values proposed in the current research are always lower than the ones proposed by the other authors. A possible explanation for that could be the use of different energy bining in the calculation of the flux spectrum. The energy bin in the present work, as mentioned before, was selected to be 10 keV. A value that is considered to be fairly low and can estimate accurately the absorbed dose rate afterwards. Unfortunately there are no data for the bining used by other authors in order to be positive that this is the reason of the difference among the results. Bad statistics could be another reason for this discrepancy although it doesn’t justify the bias of the values. In our case we traced 50x10^{6} photons while others (e.g. Chen) traced only 10000 photons. The precision of the results given in this work is more than 95% for each energy bin of the flux spectrum. That means much better precision for absorbed dose rate estimations. It has to be mentioned that precision refers to the error or uncertainty estimates for the results of Monte Carlo and not to the accuracy. Also the materials used in the present research are different from the ones other authors used. For example Kocher and Sjoreen used concrete instead of soil for their computations. Moreover, the computation methods used are different. Kocher and Sjoreen used the point kernel method while Beck used a polynomial solution to Boltzman’s transfer equation. Also Saito and Jacob made their calculation using their own Monte Carlo code without comparisons to well known standard codes like MCNP and GEANT. Finally it is interesting to compare the results deduced from the present work by the GEANT code with those obtained by the recent work of Lickar et al. (1998) using the above mentioned code. Despite the fact that they use a completely different geometry, with a huge detector (2 km) which probably makes some problems in their calculation, (their value at 3 MeV is underestimated in comparison with the extrapolation at this energy deduced from their values of 0.2 MeV2 MeV) the difference between the results are 7%26%.
Table 3 presents the dose rate conversion factors (absorbed dose rate in air per unit activity per unit of soil mass, nGy/h per Bq/kg) 1 m above ground, due to natural radionuclides and to ^{137}Cs (from the Chernobyl accident) distributed uniformly in the ground, as extracted from the three Monte Carlo codes. The intensity (photon emission probability per 100 decays) is also presented for the photopeaks of each radionuclide. Although the most important peaks (intensities larger than 1%) are presented in this table, the total dose rate conversion factor for each series takes into account all known peaks (approximately 300 peaks for each series (Chu S. Y. F. et al. 1999)). As expected (from Table 2), the differences between the dose rate conversion factors obtained from the three codes are small (less than 5%).
In Table 4 the dose rate conversion factors of specific radionuclides presented in Table 3 are compared with previous results of Saito and Jacob (1995) and Beck et al. (1972). The differences between the results of this research and the results obtained by other researchers are 18% for Uranium series 15% for Thorium series and 10% for ^{40}K.
CONCLUSION
The dose rate conversion factors (absorbed dose rate in air per unit activity per unit of soil mass, nGy/h per Bq/kg) were calculated 1 m above ground for photon emitters of natural radionuclides uniformly distributed in the soil. Three Monte Carlo codes were used a) the MCNP code of Los Alamos b) the GEANT code of CERN and c) a Monte Carlo code developed in the Nuclear Technology Laboratory of the Aristotle University of Thessaloniki. All codes and particularly the MCNP calculate very well the absorbed dose rate in air due to the unscattered radiation. The difference between the values deduced by the MCNP code and the precise solution of the corresponding integral (eqn 3) is less than 2%. For the total radiation (unscattered plus scattered) the results obtained from the three codes are in very good agreement between them. The comparison between the results obtained in the present work by the three codes and the results obtained previously by other authors indicate a good agreement (less than 15% of difference) for photon energies above 1500 keV. However, the agreement is not so good (difference of 2030%) for the low energy photons (e.g. 200 keV). The very good agreement of the dose rate conversion factors calculated by the three independent Monte Carlo codes used in the present work, indicates that the corresponding values reported in ICRU (1994) may be reexamined.
ACKNOWLEDGMENTS
This work was financially supported by the Greek General Secretariat of Research and Technology
FIGURE CAPTION
Figure 1. Simulated geometry by the MCNP code.
Figure 2. Photon flux at 1 m above soil surface as deduced by the MCNP code with (a) a point detector and (b) a volume one for photon emitter of energy of 1500 keV uniformly distributed in the soil. The flux is normalized per emitted photon per second.
Figure 3. Unscattered flux normalized per emitted photon of energy of 1500 keV (per cm^{3} s) as a function of soil’s depth.
Figure 4. Unscattered flux normalized per emitted photon of energy of 1000 keV (per cm^{3} s) as a function of soil’s radius.
Figure 5. Theoretical model (eqn 3) used in calculating unscattered flux.
REFERENCES
· Beck, H. L.; DeCampo, J.; Gogolak, C. In situ Ge(Li) and NaI(Tl) gammaray spectrometry. New York: U.S DOE, Environmental Measurements Lab.; HASL258; 1972.
· Beck, H. L.; Planque, G. The radiation field in air due to distributed gamma ray sources in ground. New York: U.S. DOE, Environmental Measurements Lab.; HASL195; 1968.
· Blomquist, P. N.; Gelbard, E.M. An Assessment of Existing KleinNishina Monte Carlo Sampling Methods. Nucl. Sci. Eng. 83:380384l 1983.
· Briesmeister, J. F. (Ed.) MCNPA General Monte Carlo NParticle Transport Code, version 4A. Los Alamos: NM; Los Alamos National Laboratory; LA12625M.; 1993.
· Chen, S. Y. Calculation of effective doseequivalent responses for external exposure from residual photon emitters in soil. Health Phys. 60:411426; 1991.
· Chu, S. Y. F.; Ekstrom, L. P.; Firestone, R. B. WWW Table of Radioactive Isotopes, database version 2/28/99 from URL http://nucleardata.nuclear.lu.se http://nucleardata.nuclear.lu.se/ nucleardata/toi.
· Clouvas, A.; Xanthos, S.; AntonopoulosDomis, M.; Silva, J. Monte Carlo based method for conversion of insitu gamma ray spectra obtained with a portable Ge detector to an incident photon flux energy distribution. Health Phys. 74:216230; 1998.
· GEANT Detector Description and Simulation Tool, Geneva: CERN; Program Library Long Writeup W5013; 1993.
· International Commission on Radiation Units and Measurements. Gamma – ray spectrometry in the Environment, Bethesda, MD:ICRU Report 53; 1994
· Koblinger, L. Direct Sampling from the Klein Nishina Distribution for Photon Energies above 1.4 MeV. Nuclear Science Engineering 56:218219; 1975.
· Kocher, D. C.; Sjoreen, A. L. Dose rate conversion factors for external exposure to photon emitters in soil. Health Phys. 48:193205; 1985.
· Korun, M.; Lickar, A.; Vidmar, T. Monte Carlo calculation of the spatial dependence of the coaxial HPGe detector efficiency for point sources. Nucl. Instr. Meth. A 390:203208; 1997.
· Likar, A.; Vidmar, T.; Pucelj, B. Monte Carlo determination of gammaray dose rate with the geant system. Health Phys. 75:165169; 1998.
· Lindsay, W. L. Chemical equilibria in soils. Wiley & Sons, New York; 1979.
· Saito, K.; Jacob, P. Gamma ray fields in the air due to sources in the ground. Radiat. Protect. Dosim. 58:2945; 1995.
· Saito, K.; Moriuchi, S. Development of a Monte Carlo code for the calculation of gamma ray transport in the natural environment. Radiat. Protect. Dosim. 12:2128; 1985.
· Storm, E.; Israel, H. Photon cross sections from 1 keV to 100 MeV for elements Z=1 to Z=100. Nuclear Data Tables A 7:565681; 1970.
Table 1. Unscattered flux obtained by the Monte Carlo codes of the present work, numerical solution of the eqn 3 and as calculated by Beck et al. (1972) 

ã cm^{2} s^{1} per emitted photon gr^{1} s^{1} 

Energy (keV) 
GEANT 
MCNP 
MC 
Mathcad 
Beck 
200 
4.33 
3.63 
4.31 
3.67 
3.91 
400 
5.14 
4.86 
5.86 
4.92 
4.93 
800 
7.22 
6.67 
6.91 
6.81 
6.74 
1000 
8.18 
7.45 
7.59 
7.56 
7.53 
1500 
9.94 
9.21 
9.84 
9.36 
9.27 
2000 
10.95 
10.72 
10.75 
10.90 
10.81 
2500 
12.66 
12.10 
12.10 
12.03 
12.17 
3000 
13.74 
13.21 
13.08 
13.44 
13.74 
Table 2. Conversion Factors obtained by the Monte Carlo codes of the present work and as deduced by Kocher and Sjoreen (1985), Chen (1991), Likar et al. (1998), Saito and Jacob (1995) 

nGy/h per emitted photon kg^{1} s^{1} 

Energy (keV) 
MCNP 
GEANT 
MC 
Kocher 
Chen 
Lickar 
Saito 
200 
0.0282 
0.0308 
0.0304 
0.0363 
0.0380 
0.0414 
0.0420 
400 
0.0743 
0.0768 
0.0791 
0.1015 
0.0997 
0.0985 

800 
0.1733 
0.1841 
0.1790 
0.2205 
0.2135 
0.2070 

1000 
0.2228 
0.2364 
0.2317 
0.2765 
0.2614 
0.2660 
0.2793 
1500 
0.3539 
0.3740 
0.3559 
0.4139 
0.4053 
0.3970 
0.4128 
2000 
0.4857 
0.5018 
0.4779 
0.5498 
0.5662 
0.5410 
0.5792 
2500 
0.6271 
0.6557 
0.6212 
0.6590 

3000 
0.7554 
0.7911 
0.7460 
0.8071 
0.7979 
0.7370 
0.8603 
Table 3. Conversion Factors for different radionuclides estimated by the Monte Carlo codes of the present work. Only the most important peaks are presented here. However all the known peaks are taken in to account for the computation of the total conversion factor of the series 

nGy/h per Bq/kg 

Nuclide 
Energy 
percentage per disintegration 
MCNP 
MC 
GEANT 
^{232}Th series 

^{228}Ac 
129.1 
3.03 
0.00036 
0.00040 
0.00044 
^{228}Ac 
154.2 
1.02 
0.00018 
0.00020 
0.00021 
^{228}Ac 
209.4 
4.71 
0.00143 
0.00154 
0.00155 
^{228}Ac 
270.3 
3.9 
0.00173 
0.00185 
0.00183 
^{228}Ac 
328 
3.48 
0.00201 
0.00214 
0.00210 
^{228}Ac 
338.4 
12.4 
0.00746 
0.00795 
0.00777 
^{228}Ac 
409.4 
2.31 
0.00177 
0.00188 
0.00183 
^{228}Ac 
463 
4.8 
0.00430 
0.00455 
0.00450 
^{228}Ac 
562.3 
1.02 
0.00116 
0.00122 
0.00123 
^{228}Ac 
755.2 
1.14 
0.00185 
0.00191 
0.00196 
^{228}Ac 
794.8 
5.01 
0.00862 
0.00891 
0.00915 
^{228}Ac 
835.6 
1.88 
0.00342 
0.00354 
0.00364 
^{228}Ac 
840.2 
1.02 
0.00187 
0.00193 
0.00199 
^{228}Ac 
911.1 
30 
0.06024 
0.06249 
0.06395 
^{228}Ac 
964.6 
5.64 
0.01207 
0.01254 
0.01281 
^{228}Ac 
968.9 
18.1 
0.03894 
0.04046 
0.04132 
^{228}Ac 
1459.2 
1.08 
0.00371 
0.00373 
0.00392 
^{228}Ac 
1495.8 
1.09 
0.00385 
0.00387 
0.00406 
^{228}Ac 
1587.9 
3.84 
0.01448 
0.01449 
0.01522 
^{228}Ac 
1620.6 
1.51 
0.00582 
0.00582 
0.00611 
^{228}Ac 
1630.4 
2.02 
0.00784 
0.00783 
0.00823 
^{212}Bi 
727.3 
6.66 
0.01031 
0.01071 
0.01096 
^{212}Bi 
785.5 
1.11 
0.00188 
0.00195 
0.00200 
^{212}Bi 
1620.5 
1.49 
0.00575 
0.00574 
0.00603 
^{224}Ra 
241 
3.7 
0.00139 
0.00150 
0.00149 
^{208}Tl 
377.4 
2.34 
0.00162 
0.00172 
0.00168 
^{208}Tl 
510.7 
8.1 
0.00818 
0.00865 
0.00863 
^{208}Tl 
583.1 
31 
0.03673 
0.03870 
0.03903 
^{208}Tl 
860.5 
4.32 
0.00813 
0.00842 
0.00864 
^{208}Tl 
2614.5 
36 
0.23635 
0.23391 
0.24721 
^{212}Pb 
238.6 
44.6 
0.01657 
0.01777 
0.01771 
^{212}Pb 
300.1 
3.42 
0.00175 
0.00187 
0.00184 
Total 
0.51678 
0.52389 
0.54373 

^{238}U series 

^{214}Pb 
241.9 
7.6 
0.00288 
0.00309 
0.00308 
^{214}Pb 
295.2 
18.9 
0.00948 
0.01013 
0.00996 
^{214}Pb 
352 
36.3 
0.02297 
0.02448 
0.02388 
^{226}Ra 
186 
3.9 
0.00098 
0.00105 
0.00108 
^{214}Bi 
609.4 
42.8 
0.05348 
0.05625 
0.05691 
^{214}Bi 
665.6 
1.4 
0.00195 
0.00204 
0.00207 
^{214}Bi 
768.4 
4.8 
0.00793 
0.00822 
0.00843 
^{214}Bi 
806.2 
1.1 
0.00192 
0.00199 
0.00204 
^{214}Bi 
934 
3.1 
0.00640 
0.00664 
0.00679 
^{214}Bi 
1120.4 
15 
0.03816 
0.03924 
0.04043 
^{214}Bi 
1155.3 
1.7 
0.00448 
0.00459 
0.00475 
^{214}Bi 
1238.2 
6.1 
0.01740 
0.01774 
0.01842 
^{214}Bi 
1281 
1.5 
0.00445 
0.00452 
0.00471 
^{214}Bi 
1377.7 
4.3 
0.01384 
0.01400 
0.01463 
^{214}Bi 
1401.6 
1.5 
0.00492 
0.00497 
0.00520 
^{214}Bi 
1408 
2.6 
0.00857 
0.00866 
0.00907 
^{214}Bi 
1509.3 
2.2 
0.00784 
0.00788 
0.00828 
^{214}Bi 
1661.4 
1.16 
0.00460 
0.00459 
0.00482 
^{214}Bi 
1729.8 
3.2 
0.01326 
0.01318 
0.01385 
^{214}Bi 
1764.6 
16.7 
0.07074 
0.07021 
0.07375 
^{214}Bi 
1847.6 
2.3 
0.01025 
0.01014 
0.01065 
^{214}Bi 
2118.7 
1.3 
0.00675 
0.00665 
0.00700 
^{214}Bi 
2204.3 
5.3 
0.02880 
0.02843 
0.02993 
^{214}Bi 
2448 
1.65 
0.01011 
0.01000 
0.01056 
Total 
0.38092 
0.38668 
0.39996 

^{137}Cs 
661.6 
85.1 
0.11761 
0.12084 
0.12424 
^{40}K 
1460.8 
11 
0.03780 
0.03808 
0.03995 
Table 4. Conversion Factors for different radionuclides deduced by the Monte Carlo codes of the present work and as deduced by Saito and Jacob (1995), Beck et al. (1972) 

nGy/h per Bq/kg 

Nuclide 
MCNP 
MC 
GEANT 
SAITO 
BECK 

^{232}Th series 

^{228}Ac 
0.18526 
0.19120 
0.19594 
0.22100 
0.27800 

^{212}Bi 
0.02256 
0.02305 
0.02383 
0.02720 
0.02120 

^{224}Ra 
0.00156 
0.00167 
0.00167 
0.00214 

^{208}Tl 
0.28944 
0.28871 
0.30312 
0.32600 
0.32100 

^{212}Pb 
0.01796 
0.01926 
0.01917 
0.02770 
0.02120 

Total 
0.51678 
0.52389 
0.54373 
0.60400 
0.66600 

^{238}U series 

^{214}Pb 
0.04150 
0.04413 
0.04342 
0.05460 
0.04720 

^{226}Ra 
0.00092 
0.00099 
0.00100 
0.00125 

^{214}Bi 
0.33849 
0.34156 
0.35554 
0.40100 
0.37800 

Total 
0.38092 
0.38668 
0.39996 
0.46300 
0.43000 

^{40}K 
0.03780 
0.03808 
0.03995 
0.04170 
0.04220 
