Calculation of Effective Dose Conversion Coefficients for Electrons

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1 Calculation of Effective Dose Conversion Coefficients for Electrons S. Tsuda 1, A. Endo 1, Y. Yamaguchi 1 and O. Sato 2 1 Department of Health Physics, Japan Atomic Energy Research Institute (JAERI) Tokai-mura, Ibaraki-ken, , Japan 2 Mitsubishi Research Institute, INC Otemachi, Chiyoda-ku, Tokyo, , Japan 1. INTRODUCTION Radiation protection for high-energy radiation, in the energy range up to GeV order, has come to be important with increases of developments of high-energy accelerators and space mission. Effective dose, recommended by the International Commission on Radiological Protection (ICRP) in its publication 60 (ICRP60) [1], is used as a radiological protection quantity to evaluate radiation risks. Effective doses and organ doses per unit fluence, referred to as the conversion coefficients, have ever been calculated against external radiation as the quantities to transform a measured fluence to effective dose and organ dose. The conversion coefficients have been calculated up to 10 GeV for photons [2, 3] and up to 10 TeV for neutrons [4]. The conversion coefficients for electron, however, are not enough to cover the high-energy region. ICRP74 [5] presented them from 1 MeV to 10 MeV but the irradiation geometry and the kind of organ doses presented are limited. Ferrari et al. [6] calculated the conversion coefficients from 5 MeV up to 10 GeV using FLUKA, the Monte Carlo high energy radiation transport code. However, the data should be checked independently, since FLUKA is not opened to the public. In the present study, we calculated the fluence to effective dose and organ dose conversion coefficients for electrons from 1 MeV to 100 GeV, using the photon electron Monte Carlo simulation code EGS4 [7] and an anthropomorphic phantom. And we evaluated the contribution to dose of photonuclear reaction, which occurs by electromagnetic cascade shower in a human body. 2. METHOD OF CALCULATION 2.1 Effective Dose Effective dose, recommended by ICRP60, is defined as E = w T H T ; (1) T where w T is the tissue weighting factor for tissue or organ, T, and H T is the equivalent dose in tissue or organ, T. The tissue weighting factors are given for 12 tissues or organs and remainder which includes 10 tissues or organs. H T is given by H T = w R D T;R (2) ; R where w R is the radiation weighting factor for radiation R and D T;R is the absorbed dose for tissue or organ, T, due to radiation R. For photons and electrons, w R is assigned to be Mathematical Phantom and Monte Carlo Code Figure 1 shows the flow diagram of the calculation composed of two parts: for electromagnetic cascade shower and for photonuclear reactions. The absorbed dose in each organ or tissue, D T;R, is obtained by dividing deposited energy by its own mass. The equivalent dose in each organ or tissue is converted from the absorbed dose in Eq.(2). Finally, we obtained effective dose in Eq.(1) by using the equivalent doses for the organs or tissues with tissue weighting factors. An anthropomorphic phantom and EGS4 were used to calculate D T;R for each tissue or organ. The phantom [8], designed as hermaphroditic, is shown in Fig.2 and composed of 37 organs or tissues. To incorporate the phantom into the EGS4 code system, UCGEN [9], the generalized user code for EGS4, was used. The user code employs modified MARS geometry package [10] developed at ORNL, and the MIRD-type anthropomorphic phantom was presented with this geometry package. Cut off energies for photons and electrons were set to be 10 kev and 100 kev respectively since each range for photons and electrons with the cut off energies is short as compared with the tissue or organ size in the phantom. Histories were selected to keep the statistical uncertainties below 10% for equivalent doses of organ or tissue given the tissue weighting factors in the energy range over 10 MeV. The phantom was irradiated in a vacuum space by mono-energetic parallel electron beams. Selected irradiation geometries were anterior-posterior (AP), posterior-anterior (PA), Right-lateral (RLAT), Left-lateral (LLAT), isotropic (ISO) and rotational (ROT). When a human body is irradiated by electrons, photons are produced by bremsstrahlung. Photon energy produced by bremsstrahlung increases with the electron energy and photonuclear reactions appear above photon 1

2 energy 10 MeV. It is reported that charged particles produced by the photonuclear reaction contribute to equivalent dose due to their large averaged quality factors up to about 25 [11]. We treated the main elements in a human body such as carbon, nitrogen and oxygen. Major reaction types to be considered are (γ, p), (γ, d), (γ, t), (γ, 3 He), (γ, α) and (γ, n). The cross sections of these six reactions have ever been evaluated up to 140MeV [12]. Using the photon fluence averaged in each organ or tissue, we calculated the absorbed dose in each organ or tissue in Eq.(3) with the cross sections of photonuclear reactions [12] and the energy spectrum of charged particles produced by the reactions: Z E i ZEi where D i = 1 ρ j E γ N j σ ij (E γ ) f j (E i ;E γ ) φ(e γ )de γ de i ; (3) D i : the absorbed dose for charged particle i, such as proton (p), deuteron (d), triton (t), 3 He, and α-particle (α), E i : the energy of charged particle i, N j : the atom number density of j-nucleus in the phantom, σ ij (E γ ): the cross section of j-nucleus for i-particle production reaction at photon energy E γ, f j (E i ;E γ ): the energy spectrum of particle i produced by the reaction between photon with energy E γ and j-nucleus, φ(e γ ): the photon spectrum averaged in each organ or tissue, ρ: the density of the tissue in the phantom. As for recoiled atoms by the reactions, the kinetic energy, Ei Recoil, was calculated by energy conservation law and the absorbed doses were obtained by substituting Ei Recoil for E i in Eq.(3). In this calculation, it was assumed that the recoiled atoms and the second particles deposit their whole energies on the spot of each organ or tissue in the phantom. However, we did not evaluate the contribution of secondary neutrons because of the following reasons. The first is that the contribution of neutron to absorbed dose will be overestimated because neutron can not deposit its whole energies on the spot of each organ or tissue in the phantom. The second is that it is reported that the contribution of neutron produced to dose equivalent is 2.35% at the maximum [11] when the same phantom used in this study are irradiated by photons in the energy range from 1MeV to 10 GeV. 3. RESULTS AND DISCUSSION 3.1 Effective dose calculation Figure 3 shows the effective dose conversion coefficients, E, in various irradiation geometries. The coefficients sharply increase with incident electron energy up to 50 MeV, while those for electron energies over 50 MeV increase gradually. At 50 MeV, the E values are generally in agreement with irradiation geometries. The reason may be that the range of electron with 50 MeV was semi-empirically estimated to be about 16 cm and nearly equal to the thickness of the phantom. The type of geometry with the maximum E is dependent on electron energies. In the energy range below 50 MeV, the E values are higher for AP than for PA geometry. This is because the range of electron is short and most of electron and photon energy are deposited at the near surface of the phantom, where organs or tissues with large w T such as testes and breast are located. For electron energy over 100 MeV, the range of electron becomes longer and the E values for RLAT or ISO become the maximum. And organs or tissues located on the rear of the phantom against its incident direction contribute more to E. The E values for ROT resulted in nearly averaged values for AP and LAT geometry. For LAT geometry, the difference in E between for RLAT and for LLAT resulted from the position of stomach (left-side) and liver (right-side). The w T is 0.12 for stomach and 0.05 for liver, and the E was about 9% higher for RLAT than for LLAT at 100 GeV. 3.2 Evaluation of Dose by Photonuclear Reaction It should be noted that charged particles produced by the interaction between high energy electrons and a human body contribute to doses in addition to the electromagnetic cascade shower calculated by EGS4. We discussed the contribution of photonuclear reactions, which was evaluated as a ratio of the absorbed doses by photonuclear reactions to the absorbed doses by electromagnetic cascade. A calculated result for AP geometry is shown in Fig.4. The predominant charged particles were recoiled ions for (γ, n) and (γ, p) reactions and proton for (γ, p) reaction, due to the larger cross sections than other reactions. The maximum ratio in the energy range up to 500 MeV was about 0.6%. In other cases, the maximum ratio was 0.9% for ISO and 0.8% for ROT geometry. The averaged quality factors of charged particles produced by the photonuclear reactions can be roughly estimated to be 10 from Sato s calculation [11]. Then the contribution of photonuclear reaction to effective dose will be about 6% for AP, 9% for ISO and 8% for ROT geometry. 2

3 3.3 Comparison with Other Data Figure 5 shows a comparison of effective doses with those calculated by Ferrari et al. [6]. We assumed the contribution of photonuclear reaction below photon energy 140 MeV to effective dose to be 10% equally for all irradiation geometries. The value of 10% is a provisional and rough value based on the discussion about the contribution of photonuclear reactions to the absorbed doses by charged particles below 140 MeV to compare with Ferrari s data. The effective dose conversion coefficients for electromagnetic cascade shower in the energy range over 10 MeV were multiplied by 1.1. In the energy range below 10 MeV, E was in a good agreement with Ferrari data and became nearly 10% larger than Ferrari data over 10 MeV. 4. CONCLUSION Effective doses and organ doses per unit fluence for electrons have been calculated from 1 MeV to 100 GeV using the photon-electron Monte Carlo simulation code, EGS4, combined with an anthropomorphic phantom. The contribution of photonuclear reaction below photon energy 140 MeV has been evaluated. The absorbed dose ratio of photonuclear reactions to electromagnetic cascade reached about 0.6% for AP, 0.9% for ISO and 0.8% for ROT geometry. By selecting the averaged quality factors of charged particles produced by the photonuclear reactions to be 10, we temporarily estimated the contribution of photonuclear reactions to effective doses for all geometries to be 10%. The results were generally in agreement with the conversion coefficients for electrons up to 10 GeV calculated by FLUKA and suggest that the methods for calculation such as a phantom used and simulation code cause no significant difference in the effective doses and organ doses. However, using the averaged quality factors for charged particles, we must evaluate the contribution of photonuclear reaction to equivalent doses and effective doses for more detailed discussion. REFERENCES 1) International Commission on Radiological Protection. ICRP Publication 60 (Oxford: Pergamon Press) (1991). 2) O. Sato, et al., Radiat. Prot. Dosim. 62, (1995). 3) A. Ferrari, et al., Radiat. Prot. Dosim. 67, (1996). 4) A. Ferrari, et al., Radiat. Prot. Dosim. 71, (1997). 5) International Commission on Radiological Protection. ICRP Publication 74 (Oxford: Pergamon Press) (1998). 6) A. Ferrari, et al., Radiat. Prot. Dosim. 69, (1997). 7) W.R. Nelson, et al., SLAC-265 (1985). 8) Y. Yamaguchi, J. Nucl. Sci. Tech. 31, (1994). 9) T. Momose, et al., Proceedings of 1st EGS4 User s Meeting in Japan, (1990). 10) J.T. West, et al., NUREG/CR-0200, vol.3, sect.m9 (1993) 11) O. Sato, doctoral dissertation, Tohoku University (1999) 12) T. Fukahori, et al., private communication 3

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5 Âããâàñæóâ áìðâ ØÐóàê âéâàñïìëú ª ª ¾Í Í¾ ÏÌÑ ÆÐÌ ÉÉ¾Ñ ÏÉ¾Ñ ± ² Âéâàñïìë âëâïäö ØÊâÓÚ Figure 3. Effective dose per unit fluence as a function of incident electron energy. «¾ßðìïßâá áìðâ ïþñæì Ø Ú «³ «² «± ««á á Åâ ïâàìæé Åâ Åâ ñ ïâàìæé ñ ñ ïâàìæé γ ë ïâàìæé γ í ïâàìæé «ª «γ í í Âéâàñïìë âëâïäö ØÊâÓÚ Figure 4. The ratio of charged particles by photonuclear reaction to the absorbed dose by electromagnetic cascade shower in AP geometry. The contribution of (γ, d)recoil was too small to see. 5

6 Âããâàñæóâ áìðâ ØíÐóàê âéâàñïìëú µ ³ ± Íïâðâëñ ïâðòéñð ØñâêíìïÞïöÚ ¾Í Í¾ ÏÉ¾Ñ ÆÐÌ ÃâïïÞïæ ¾Í Í¾ ÏÉ¾Ñ ÆÐÌ Âéâàñïìë âëâïäö ØÊâÓÚ ± ² Figure 5. The comparison of effective doses with Ferrari s data. The effective dose conversion coefficients for electromagnetic cascade shower in the energy range over 10MeV were multiplied by

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