|Year : 2012 | Volume
| Issue : 3 | Page : 156-163
Accelerator radiation protection: Recourse to nuclear reaction models
Chemical Sciences Division, Saha Institute of Nuclear Physics, Kolkata, West Bengal, India
|Date of Web Publication||5-Sep-2013|
Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata - 700 064, West Bengal
Source of Support: These studies have been carried out with logistic
support from CBAUNP (XI paln) and BARD (XII plan) projects, Saha
Institute of Nuclear Physics, Kolkata, India., Conflict of Interest: None
Nuclear reaction models play a very crucial role in theoretical estimation of radiation environment in accelerator facilities where experimental data are scantily available. In this paper, we discuss the exciton and hybrid models for pre-equilibrium reaction, the Weiskopf-Ewing formalism for compound nuclear emissions and quantum molecular dynamics (QMD) model for spallation reactions. The choice of Fermi gas or Gilbert Cameron level density results in a variation of 21% in the neutron yield from p + Cu reaction at 20 MeV. The surface effects, which are more pronounced at higher energies influence the organ absorbed dose at most to 5% even at 60 MeV for the same reaction. The code EMPIRE and the hybrid model code ALICE give a reasonable estimate of dose and induced activity in proton accelerator facilities up to about 200 MeV until when pion production is not significant. The code HION can be a preferred choice for neutron dose simulation in low energy heavy ion (HI) accelerators. However, the model needs improvement for more accurate estimation of the angular distribution. QMD model can be used to estimate the induced activity and absorbed dose for proton and HI reactions at several hundreds of MeV to GeV per nucleon.
Keywords: Accelerator safety, neutron dosimetry, nuclear reaction models, organ dose
|How to cite this article:|
Nandy M. Accelerator radiation protection: Recourse to nuclear reaction models. Radiat Prot Environ 2012;35:156-63
| Introduction|| |
Accelerators - electron and positive ion-in 21 st century are based on state-of-the-art technology. One of the wonders of scientific as well as technological developments of 20 th century these machines cater to various facets of modern civilization, e.g., in medical science for diagnosis and therapy of malignant tissue, in basic science research to probe nuclear, subnuclear particles, characterization of atomic and molecular layers, in industrial application for sterilization of surgical equipment, food products, for power production, in agriculture, use of synchrotron radiation to probe material properties and crystal structures of macro-molecules, etc. These multi-faceted use of accelerators, often in the public domain, call for detailed safety planning of the entire facility. The key player in this planning is the prompt radiation produced during normal operation, radiation field that might be encountered in the case of any accidental beam-on condition and the post-operation radiation environment. The latter is generated from the radioactivation of the accelerator components and accelerators housing. In the design and planning stage of any accelerator facility, in the absence of any experimental data for a similar system, estimation of the possible radiation environment, its transport and the whole design need to be done through theoretical and numerical simulations of the actual scenario. In carrying out these simulations, the designer has two options available for estimation of the source term: Nuclear reaction model calculations or use of empirical formalisms. Calculation of the source term in the framework of nuclear reaction models is a preferred choice,  of the two as it is based on the theory of the actual process that results in the radiation dose or activity more rigorously.
In the case of positive ion accelerators, the prompt radiation is composed of neutrons and photons while in the case of electron accelerators photons dominate this radiation field. The post-operation exposure is attributed to the emission from radionuclides formed in the facility due to the interaction of the primary beam and the secondary radiation. Nuclear reaction model codes give the cross-section of particle emission or radionuclides formed at different beam energies. In accelerator facilities, except for the experimental targets for basic research, one encounters thick stopping targets for all other interactions. The cross-section for production of particles, photons and radionuclides obtained from reaction model calculations are converted to thick target yield. Absorbed dose is estimated from the particle and photon yield by folding it with the fluence-to-dose conversion coefficients. Activity build-up, saturation activity and residual activity are calculated from radionuclide yield as a function of irradiation time and subsequent cooling time.
| Theoretical Simulation: Nuclear Reaction Models|| |
Nuclear reaction models suitable to be used for various energy ranges are reliable means for calculating the energy-angle distribution of photon, neutron or other particle emission or production of radionuclides in accelerators. In the case of positive ion accelerators, these models are used to calculate all the source terms while for electron accelerators, they are mainly used to determine photo-neutron production and neutron activation. There are several nuclear reaction model codes available for such calculations. However, the applicability of these codes may be may be specific for nucleon emissions from specific reactions and it is important to choose the appropriate one from among them. We shall discuss the importance and application of reaction models and codes used for positive ion induced reactions.
Proton induced reactions
E proj < 200 MeV
0In the case of proton accelerators up to about 200 MeV beam energy, the main reaction processes involved are direct (DIR), pre-equilibrium (PEQ) and compound nuclear or equilibrium (EQ) emissions. DIR reactions are modeled through coupled channel calculations.  Distorted wave Born approximation (DWBA).  Reaction models developed for calculating PEQ reactions are exciton model,  Harp-Miller-Berne (HMB) model,  hybrid model,  multi-step direct (MSD),  multi-step compound (MSC) processes.  Compound nuclear reactions are calculated using Weisskopf-Ewing  or Hauser-Feshbach theory.  Some of the codes used for estimation of neutron and photon yield for proton energies up to 200 MeV are ALICE, ,,, TALYS,  PRECO-2000,  EMPIRE,  CASCADE  and PACE. 
Compound nuclear and PEQ reactions
In Weisskopf-Ewing formalism, the evaporation cross-section for a particle of type "b" is given by
where is the probability of the compound nucleus in the state "a" to decay through a reaction channel "b" and is given by the ratio of the channel width for "b" to the total decay width. The level density of the compound nucleus (CN) as well as the residual nucleus plays a very important role in determining this decay probability. In Hauser-Feshbach treatment of EQ emissions, evaporation cross-section is determined by similar formalism, taking into consideration angular momentum conservation.
Among the different PEQ models used for source term estimation, the hybrid and the exciton models are the two most widely used formalisms. Both the models consider that in the target + projectile composite system, energy of the incident particle is shared through two-body interactions. Each stage of this energy sharing process is characterized by the number of particle-hole (exciton) pairs present. Exciton model can use either of the two approaches-closed form and master equation. Nuclear reaction model codes ALICE and TALYS calculate PEQ emissions in the framework of hybrid model while EMPIRE has provisions to invoke hybrid, exciton or MSD and MSC models. In implementing hybrid or exciton model in the computer codes, never come-back approximation is used. This suggests that at each stage of the equilibration process, exciton pairs can either be created or the number remains unchanged, annihilation of the particle-hole pairs is not considered. In their original forms, the hybrid and the exciton model could not predict PEQ emission probability of cluster particles. The most important difference between these two models is that the hybrid model explicitly calculates the probability of all possible energy distribution of the excited composite system, but exciton model assumes that all energy distributions are equally probable, constrained only by energy conservation. As a result, the exciton model used to fail to reproduce the back angle cross-sections.
In the hybrid model, PEQ emission cross-section of a nucleon of type ν is given by,
D n = probability of reaching n exciton state without prior emission.
Xνn = fraction of excited particles of type n in n exciton state.
= probability of one excited particle to have the energy ε, with the remaining excitation energy U distributed among other excited particles.
= emission probability with energy ε. Here, γc(ε) is the emission rate and is total two body collision rate.
In the closed form exciton model this cross-section is given by,
Here, γ+n(ε), γ-n(ε), γ0n(ε) and are the two-body collision rates for creation, annihilation of exciton pairs and for the number of exciton pairs remaining unchanged, respectively.
The emission rate is calculated from the principle of detailed balance. In calculating the two-body interaction rate, hybrid model uses an empirical formalism while exciton model calculates it using the Fermi's golden rule.
This difference in considering the pre-emission energy distribution of the exciton and hybrid models is manifested in the emission cross-section of the PEQ particles in the fact that high energy emissions were under predicted in the exciton model. This has been reported by Chakravarty et al.,  in calculating the excitation function of 200 Tl from the alpha induced reaction on 197 Au. In the said reaction 200 Tl is formed through a single neutron emission. In the energy range of 30-60 MeV studied in that work PEQ emission has a significant contribution, which increases as the energy increases. It has been observed from the excitation function curve for 200 Tl that while ALICE calculation reproduced the measured excitation function fairly well, the under prediction of the exciton model calculation (GNASH  ) increased at higher projectile energies.
In the recent versions of several computer codes, e.g., EMPIRE, master equation approach of exciton model is used. In this approach, time evolution of the exciton states is followed. Emission probability cross-section of an ejectile is given from the emission rate folded by the life-time of that state. Total emission cross-section is calculated from the product of this probability and the absorption cross-section summed over all possible spins of the composite system and all exciton states.
The nuclear density is not uniform throughout the physical volume of the nucleus. The diffuseness of the nuclear surface influences the emission probability if the interaction takes place at the surface. In order to take into account the effect of diffuse nuclear surface on the emission probability of particles, hybrid model was modified to geometry dependent hybrid (GDH) model.  In GDH model the emission cross-section of (1) is expressed as a sum of cross-sections over a range of impact parameters.
In [Figure 1]a, we show a comparison of double-differential neutron yield calculated in ALICE using the hybrid model + evaporation with different level density option for p + Cu reaction at 20 MeV. The total neutron yield varies by 21% for two different choices of the level densities. The Gilbert-Cameron level density option gives larger neutron yield, which results in a larger computed dose. In [Figure 1]b, we have compared the measured values,  for energy integrated angular distribution of neutron yield for the same reaction with those calculated using Fermi gas and Gilbert Cameron level densities. It is observed, that though the shape of the distribution is not reproduced by the calculations, the measured values are reproduced within a maximum disagreement of about 28% by GDH model calculations in ALICE.
In order to investigate the influence of the diffuse nuclear surface on neutron dose to human tissue, we have studied the of p + Cu reaction at 60 MeV using ALICE. The choice of energy has been dictated by the fact that surface effects become more pronounced at higher beam energies. The double differential neutron yield is folded by the fluence-to-dose conversion factors as tabulated in ICRP (International Commission on Radiological Protection) 74,  for antero-posterior (AP) exposure in an accidental condition. In [Table 1], we have given a comparison of hybrid model and GDH + hybrid model calculations for the whole body ambient dose equivalent H* (10) and organ absorbed doses D. From the table, we observe that the organ doses calculated using two different options of ALICE vary between 1.5% and 5% while the variation in total ambient dose equivalent is negligible. The results suggest that at the energy range considered properties of the diffuse nuclear surface do not influence the biological dose.
|Table 1: H* (10) and organ dose D from P + Cu reaction at 60 MeV for 1 μA beam current at a distance of 1 m from the target|
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In the proton energy range up to 200 MeV DIR reaction channel also contribute significantly to the emission of particles. Nuclear reaction model code PRECO-2000 takes into account DIR reaction contribution along with exciton model MSD and MSC PEQ emission. In [Figure 2], we have shown the angular distribution of neutron yield from p + Cu reaction at 20 MeV calculated with the hybrid model code ALICE and the exciton model code PRECO-2000.
|Figure 2: Comparison of neutron yield from p + Cu at 20 MeV calculated with ALICE-91 and PRECO-2000|
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From the figure, we observe that the total neutron yield calculated by PRECO-2000 is twice that calculated by ALICE. One factor contributing to this variation in the angular distribution of neutron yield is the absorption cross-section for the projectile as calculated by the two codes. If the yield calculated by the two codes is normalized at 1.5 MeV (the lowest energy point in our ALICE calculations) the yield calculated by PRECO-2000 is larger than that calculated by ALICE at higher neutron energies (except at forward angle). PRECO-2000 calculation of neutron spectrum has a broad hump-like structure which resembles some earlier measurements (not published) indicating DIR emissions. At higher energies, neutron dose estimation will be more influenced by these emissions.
The variations in neutron yield calculated by various reaction model codes are important for radiation protection point of view because of the following reason. As has been mentioned earlier in this article that in the absence of measured data, one has to fall back on theoretical simulation to estimate the radiation environment in any accelerator facility-be it for designing a new facility or for ensuring radiation safety protocol. The variation in the neutron yields calculated by different reaction model codes for the same reaction would translate into a difference in the whole body and organ absorbed doses as rendered by the different models.
Induced activity calculations
Prompt radiation field is not the only entity to take recourse of nuclear reaction models to be estimated. Residual activity in experimental targets, accelerator components calls for proper strategic planning for post-operation handling of targets, maintenance works. Long-lived radioactivity induced in the walls and accelerator parts is crucial to plan decommissioning of run-down facilities. Yield of various radionuclides produced by photon, neutron and charged particle induced reactions and consequently the activity induced is also calculated with the help of nuclear reaction models. In [Figure 3], we show induced activity of some radionuclides produced by proton induced reaction on Fe target at 200 MeV. The activities are calculated using ALICE and EMPIRE. From [Figure 3], we see that EMPIRE gives a lower yield of the radionuclides considered compared with that given by ALICE. The mismatch between the two calculations increases as we go further away from the projectile + target composite system. This disagreement between the two sets of calculations is again attributed to the fact that exciton model (used in EMPIRE) underpredicts high energy PEQ emission. At 200 MeV projectile energy high energy multi-particle emission is likely to have a significant contribution in formation of residual nuclide.
|Figure 3: Activity build-up of some radionuclides for 250 MeV p + Fe reaction at 1 mA beam current|
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E proj =200 MeV/amu - 3 GeV
As the proton projectile gains higher energies, pion production becomes significant and cannot be dealt with properly in the framework of most of these codes. Accelerator driven subcritical system (ADSS) finds very important application of nuclear reactions at 800 MeV to few GeV of incident proton energy. ADSS employs proton induced spallation reaction at a few GeV. Safety design of these systems involves source term estimation in two steps-multiple fragmentations (spallation) of the target and n + γ emission through a fast process followed by statistical decay of the primary fragments. The radiation environment in ADSS and other facilities involving spallation reaction is estimated in the framework of quantum molecular dynamics (QMD) theory, intra-nuclear cascade or Monte Carlo calculations. A few nuclear reaction model codes used for this purpose are JAERI Quantum Molecular Dynamics (JQMD), Bertini, INCL4, PHITS, followed by statistical decay codes such as ABLA, GEM, GEMINI, etc. Many authors have investigated spallation reaction and its application in the framework of these models, a few of which are available in references. ,,
We have studied the spallation reaction and its contribution to the radiation environment in ADSS facilities. Radionuclide production and the neutron field have been studied using the QMD model. , The model simulates the nuclear reaction in an event-by-event basis. The nucleons are represented by Wigner densities of Gaussian wave packets. Pauli exclusion principle is taken into account, which ensures that collisions, which lead to already occupied or partially occupied final states are forbidden. The Hamiltonian H consists of kinetic energy, Skryme, Coulomb, Yukawa interaction part and the symmetry energy. At each stage of the relaxation process, relative importance of mean field effects and nucleon-nucleon collisions decides which amongst EQ, PEQ and spallation mechanisms will dominate the reaction process.
Lead (Pb) and lead-bismuth eutectic (LBE) are the two preferred targets for ADSS. In the case of LBE target, a potential radiation hazard is posed by the production of 210 Po, which is a α-emitter. We have estimated neutron ambient dose equivalent H* (10) and organ absorbed dose D for 800 MeV proton induced reaction on Pb target. In [Table 2], we have shown the values of H* (10) and dose to different organs from this reaction in an accidental scenario. The distance from target to the point of observation considered for these calculations is 1 m and the beam current is 1 mA.
|Table 2: Calculated H* (10) and organ dose D at AP geometry due to neutrons emitted from the P+Pb reaction at 800 MeV for 1 mA beam current at a distance of 1 m from the target|
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In some of our earlier works, , we have estimated the induced activity production by proton beam on Pb and LBE targets in the energy range of 1-2 GeV. It has been found from our study that 3 H, which may lead to ground water contamination, is produced with an activity of ~2 × 10 6 MBq for 30 days of irradiation of LBE with 1 mA proton beam. For the same system of study, activity of 210 Po is ~8 × 10 6 MBq. In the case of Pb target also 3 H activity is of the order of ~10 6 MBq.
Heavy ion reactions
HI reactions have found a wide range of applications in producing isotopes of different elements from a single reaction, preparation of implanted targets (in HI therapy), study of nuclear structure and reaction dynamics and ion therapy of malignant tissues. This has prompted practitioners of accelerator radiation protection to put a high premium on the study of radiation environment in HI accelerators. Detailed microscopic models are available to study HI reactions and analyze equation of state, nuclear density, etc., but these models are too complicated and their computation time rather large to be used for accelerator radiation protection.
We have developed a model to follow the reaction process and particle emission in HI reactions at low energies. The model HION,  considers that reaction starts even before the projectile and the target particles undergo any two-or three-body interaction. This becomes possible due to potential redistribution as the two nuclei approach each other. In the later stages, the energy sharing between the nucleons proceed through two-body interaction. The composite system is considered to be composed of two systems - a hot spot, where the nucleon motion is described by a finite temperature Fermi distribution and a cold spot where the nucleons follow a zero temperature Fermi distribution. In following the relaxation process, energy and linear momentum conservation have been taken into account.
In our earlier work, we calculated neutron yield from a thick Ta target due to 16 O 5+ beam at 7.2 A MeV energy with HION and compared the results with our measured data.  The calculated results showed very good agreement with the experimental data at the three angles of observation 0°, 30° and 60°. In another work, we have compared the angle-integrated energy distribution of neutron dose calculated with HION for 12 C incident on Ag and Ti targets at 12 A MeV.  It was observed that for both the reactions the calculated dose under predicted the measured values below 22 MeV neutron energy. At higher energies, the agreement is good for Ti target, but for Ag target experimental data are slightly over predicted by the calculations.
As has been mentioned, ion therapy with HIs employs energies of several hundreds of MeV per nucleon. One of the widely used reaction models used to study particle fluence, dose, etc., is the QMD model, which has already been described. QMD is incorporated in many transport codes, e.g., FLUKA, , GEANT4,  etc., used for radiation field simulation in accelerator facilities. In [Figure 4], we have shown the distribution of dose equivalent in 10 cm. Thick tissue due to a carbon beam of energy 800 MeV/amu, which is a typical energy regime used for ion therapy at National Institute of Radiological Sciences (NIRS), Chiba, Japan. The dose distribution is calculated using the combined particle interaction and transport code FLUKA. In simulating the dose, it is assumed that the 12 C beam is with a field size of 4 cm × 4 cm (in the X-Y plane) and is incident on the tissue along the Z-direction at Z = 0.0 cm. [Figure 4] shows the dose equivalent distribution (pSv) in the X-Z plane. The Bragg peak occurs at a depth of ~11 cm with a dose of ~15 pSv/ion. In this calculation, we have used a plane 10 cm thick slab of tissue. However similar estimation of absorbed dose and dose equivalent distribution from HI reactions at energies of few hundreds of MeV to a few GeV per nucleon using the transport codes and standard human phantom constitutes an important part of treatment planning for HI therapy.
|Figure 4: Distribution of dose equivalent in tissue in the X-Z plane from 12C beam at 800 MeV/amu|
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In the case of electron accelerators, photons and photoneutrons dominate the prompt radiation field. High energy photon yield through bremsstrahlung is estimated in the framework of born approximation while photoneutron production is calculated using giant dipole resonance and quasi-deuteron formation cross-section.
| Conclusion|| |
This paper has discussed the role of nuclear reaction theory, models and codes in accelerator radiation protection. It is evident that in the absence of evaluated and validated measured data, determination of the source term for radiation field in an accelerator facility largely depends on the reaction mechanism involved and consequently on reaction models. Different parameters and options of the reaction model codes influence the neutron yield, dose and induced activity significantly. At 20 MeV proton energy, ALICE calculations with Fermi-gas and Gilbert-Cameron level density formalisms result in a 21% variation in neutron yield and its distribution. Level density of the residual nuclide influences the low energy evaporation emissions, so this effect is expected to decrease at higher energies. The properties of diffuse nuclear surface has a less pronounced effect on the neutron emission and consequently on absorbed and ambient dose. DIR emissions contribute to high energy neutron yield and consequently enhance neutron dose in the forward direction. Nuclear reaction model codes ALICE and EMPIRE can be used to give a fairly good estimate of the neutron field in proton accelerators with beam energies up to 200 MeV. The code HION can be used to predict neutron distribution at low energy HI accelerators, but the code needs improvement to determine the angular distribution of emitted particles more accurately. At high energies, both for proton and HI induced reactions application of the QMD model is a good choice for estimation of prompt radiation field as well as induced activity.
| References|| |
|1.||Nandy M, Sarkar PK. Estimation of induced activity in thick lead-bismuth and iron alloy targets by 30MeV protons. Nucl Instrum Methods Phys Res A 2007;583:248. |
|2.||Tamura T. Coupled-Channel Approach to Nuclear Reactions. Annu Rev Nucl Sci 1969;19:99. |
|3.||Ray Satehler G. Outline of the development of the theory of direct nuclear reactions. Rev Mod Phys 1978;50:1. |
|4.||Griffin JJ. Statistical Model of Intermediate Structure. Phys Rev Lett 1966;17:478. |
|5.||Harp GD, Miller JM, Berne BJ. Attainment of Statistical Equilibrium in Excited Nuclei. Phys Rev 1968;165:1166. |
|6.||Blann M. Importance of the Nuclear Density Distribution on Pre-equilibrium Decay. Phys Rev Lett 1972;28:757. |
|7.||Feshbach H, Kerman A, Koonin S. The statistical theory of multi-step compound and direct reactions. Ann Phys 1980;125:429. |
|8.||Weisskopf VF, Ewing DH. On the Yield of Nuclear Reactions with Heavy Elements. Phys Rev 1940;57:472. |
|9.||Hauser W, Feshbach H. The Inelastic Scattering of Neutrons. Phys Rev 1952;87:366. |
|10.||Blann M. Lawrence Livermore National Laboratory Report UCID 19614, 1982. Blann M. ICTP Workshop Report No. SMR/284-1; 1988. |
|11.||Blann M. Hybrid Model for Pre-Equilibrium Decay in Nuclear Reactions. Phys Rev Lett 1971;27:337. Blann M. Hybrid Model For Pre-Equilibrium Decay in Nuclear Reactions. Phys Rev Lett 1971;27:700E. |
|12.||Blann M. A priori pre-equilibrium decay models. Nucl Phys A 1973;213:570. |
|13.||Koning AJ, Hilaire S, Duijvestjjn MC. TALYS: Comprehensive nuclear reaction modeling. Proceedings of the International Conference on Nuclear Data for Science and Technology-ND 2004. In: Haight RC, Chadwick MB, Kawano T, Talou P, editors, Sep. 26 to Oct. 1, 2004, Santa Fe, USA. AIP, Vol. 769. 2005. p. 1154. |
|14.||Walker CK. Users Manual for PRECO-2000 Exciton Model Preequilibrium Code with Direct Reactions, Triangle Universities Nuclear Laboratory Report (unnumbered), 2001. |
|15.||Herman M, Capote R, Carlson BV, Oblozinsky P, Sin M, Trkov A, et al. EMPIRE: Nuclear Reaction Model Code System for Data Evaluation. Nucl Data Sheets 2007;108:2655. |
|16.||Pulhofer F. On the interpretation of evaporation residue mass distributions in heavy-ion induced fusion reactions. Nucl Phys A 1977;280:267. |
|17.||Gavron A. Statistical model calculations in heavy ion reactions. Phys Rev C Nucl Phys 1980;21:230. |
|18.||Chakravarty N, Sarkar PK, Nandy M, Ghosh S. Excitation function measurement and reaction mechanism analysis for alpha-induced reactions on 197 Au. J Phys G 1998;24:151. |
|19.||Young PG, Arthur ED, Chadwick MB. International Centre for Theoretical Physics Workshop on Computation and Analysis of Nuclear Data Relevant to Nuclear Energy and Safety (Trieste, Italy) H4.SMR614/1, 1992. |
|20.||Blann M, Vonach HK. Global test of modified precompound decay models. Phys Rev C 1983;28:1475. |
|21.||Sunil C, Shanbhag AA, Nandy M, Maiti M, Bandyopadhyay T, Sarkar PK. Direction distribution of ambient neutron dose equivalent from 20 MeV protons incident on thick Be and Cu targets. Radiat Prot Dosimetry 2009;136:67-73. |
|22.||22 ICRP. Conversion Coefficients for use in Radiological Protection against External Radiation. ICRP Publication 74, Annals of the ICRP. Vol. 26 (3-4). Oxford: Elsevier Science; 1996. |
|23.||Leray S, Borne F, Crespin S, Fréhaut J, Ledoux X, Martinez E, et al. Spallation neutron production by 0.8, 1.2, and 1.6 GeV protons on various targets. Phys Rev C 2002;65:044621. |
|24.||Ledoux X, Borne F, Boudard A, Brochard F, Crespin S, Drake D, et al. Spallation Neutron Production by 0.8, 1.2, and 1.6 GeV Protons on Pb Targets. Phys Rev Lett 1999;82:4412. |
|25.||Iwamoto Y, Satoh D, Hagiwara M, Yashima H, Nakane Y, Tamii A, Measurements and Monte Carlo calculations of neutron production cross-sections at 180° for the 140 MeV proton incident reactions on carbon, iron, and gold. Nucl Instrum Methods Phys Res A 2010;620:484. |
|26.||Niita K, Chiba S, Maruyama T, Maruyama T, Takada H, Fukahori T, et al. Analysis of the (N,xN′ ) reactions by quantum molecular dynamics plus statistical decay model. Phys Rev C 1995;52:2620. |
|27.||Maruyama T, Niita K, Maruyama T, Iwamoto A. On the IMF Multiplicity in Au+Au Reactions. Prog Theor Phys 1997;98:87. |
|28.||Nandy M, Sunil C. Estimation of induced activity in an ADSS facility. Radioactive Waste. Croatia: ISBN: 978-953-51-0551-0. Ch. 6. InTech: Dr. Abdel-Rahman R, editor. 2012; |
|29.||Nandy M, Lahiri C. Radioactivity generation in Pb target by protons: A comparative study from MeV to GeV. Indian J Pure Appl Phys 2012;50:761. |
|30.||Nandy M, Ghosh S, Sarkar PK. Angular distribution of preequilibrium neutron emissions from heavy-ion reactions. Phys Rev C 1999;60:044607. |
|31.||Nandy M, Bandyopadhyay T, Sarkar PK. Measurement and analysis of neutron spectra from a thick Ta target bombarded by 7.2A MeV 16 O ions. Phys Rev C 2001;63:034610(1-6). |
|32.||Nandy M, Sarkar PK, Sanami T, Shibata T, Takada M. Neutron dose distribution from 12 C induced reactions on Ti and Ag using proton recoil scintillator. Radiat Meas 2010;45:1276. |
|33.||Ferrari A, Sala PR, Fasso A, Ranft J. FLUKA: A multi-particle transport code CERN-2005-10, INFN/TC 05/11, SLAC-R-773, 2005. |
|34.||Fasso A, Ferrari A, Roesler S, Sala PR, Ballarini F, Ottolenghi A, et al. The physics models of FLUKA: Status and recent developments. Computing in High Energy and Nuclear Physics 2003 Conference (CHEP2003), La Jolla, CA, USA, March 24-28, 2003 (paper MOMT005), eConf C0303241, 2003. arXiv: hep-ph/0306267. |
|35.||Agostinelli S, Allison J, Amako K, Apostolakis J, Araujo H, Arce P, et al. Geant4: A simulation toolkit. Nucl Instrum Methods Phys Res A 2003;506:250. |
[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2]