- Email: [email protected]
JAM
Nuclear Instruments and Methods in Physics Research B 184 (2001) 406±420
www.elsevier.com/locate/nimb
High-energy particle transport code NMTC/JAM Koji Niita
a,b,*
, Hiroshi Takada b, Shin-ichiro Meigo b, Yujiro Ikeda
b
a
b
Research Organization for Information Science and Technology, Tokai-mura, Naka-gun, Ibaraki-ken 319-1106, Japan Center for Neutron Science, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan Received 30 January 2001; received in revised form 11 July 2001
Abstract We have developed a high-energy particle transport code NMTC/JAM, which is an upgraded version of NMTC/ JAERI97. The applicable energy range of NMTC/JAM is extended in principle up to 200 GeV for nucleons and mesons by introducing the high-energy nuclear reaction code JAM for the intra-nuclear cascade part. We compare the calculations by NMTC/JAM code with the experimental data of thin and thick targets for proton-induced reactions up to several tens of GeV. The results of the NMTC/JAM code show excellent agreement with the experimental data. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 24.10.Lx; 25.40.-h Keywords: NMTC/JAM; Monte Carlo simulation; High-energy particle transport; Intra-nuclear cascade model; Hadron±hadron cross-sections; Nucleon±nucleus cross-sections
1. Introduction Several projects aiming at the development of an intense pulsed spallation neutron source with a power of 1±5 MW are under progress in the world [1]. Japan Atomic Energy Research Institute (JAERI) and High Energy Accelerator Research Organization (KEK) have jointly proposed the high-intensity proton accelerator project [2], which is the multi-purpose utilization of intense second-
* Corresponding author. Tel.: +81-29-282-5336/6101; fax: +81-29-282-6496. E-mail address: [email protected] (K. Niita).
ary particle beams for materials and life science, nuclear and particle physics and basic technologies for accelerator-based nuclear transmutation of long-lived radioactive wastes. It is planned to build a 600 MeV proton linac, 3 GeV proton rapid cycling synchrotron and 50 GeV proton synchrotron and associated experimental facilities to carry out these multi-purpose scienti®c activities and technology developments. At present, the neutronics design study of a pulsed spallation source driven by 3 GeV protons with a power of 1 MW is being conducted by JAERI [3]. The beam line and related shielding design of the accelerator facilities are also under way. It is very important to estimate source distributions and transport phenomena of various
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 7 8 4 - 4
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particles, especially neutrons, as precisely as possible and to make a target±moderator±re¯ector system of the neutron source facility extracting its maximum neutronics performance given by 1 MW proton beams. Moreover, it is required to do some neutronics design studies of the facilities for the 50 GeV proton synchrotron. For the neutronics design study, a nucleon±meson transport code NMTC/JAERI97 [4] has been employed in combination with the neutron transport code MCNP [5] as a standard code system in JAERI. This manner is essentially similar to the code system adopted in the neutronics design study [6] in the SNS project [7]. As described in [4], some function of the geometry con®guration, neutron transport calculation part and tally function were upgraded in the development of NMTC/JAERI97 from its original version. However, the code still had some limitations. The most critical one is the highest applicable energy limited to 3.5 GeV for protons and neutrons and 2.5 GeV for pions because of the limit of the Bertini model [8] for nuclear reaction calculations. Hence, it was required to extend the applicable energy range of NMTC/JAERI97 for the neutronic design study of the facility related to the 50 GeV proton synchrotron. In order to satisfy this requirement, we have introduced the high-energy nuclear reaction code JAM [9] into the intra-nuclear reaction calculation part of NMTC/JAERI97. With implementation of JAM, the particle transport part has been improved to treat all established hadronic states including resonances as well as their anti-particles listed in [10]. This new code system has been named NMTC/JAM. Here we also upgraded the nucleon±nucleus non-elastic, elastic and dierential elastic cross-section data by employing new systematics. Moreover, the Coulomb scattering of a traveling charged particles has been also upgraded and a new function treating the ¯ight of charged particles in the magnetic ®eld has been implemented so that the user could employ NMTC/JAM for design study of proton beam lines. In the nuclear reaction calculation part, a new evaporation model GEM [11], treating light nuclei emission up to magnesium, has been included to improve the light nuclide yield such as Be isotopes production in structural materials by
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the spallation reaction. User interfaces such as input data preparation and output ®le information has also been improved to be more user-friendly than NMTC/JAERI97. The overview and code manual of NMTC/JAM has already been published in [12]. This paper focuses on the main features of JAM in Section 2, upgrading of the cross-section data in Section 3 and some comparisons with experimental data for thin and thick target systems in Section 4. We summarize the paper in Section 5. 2. High-energy nuclear reaction code JAM 2.1. Main features of JAM Jet AA Microscopic Transport Model (JAM) [9] is a hadronic cascade model, which explicitly treats all established hadronic states including resonances with explicit spin and isospin as well as their anti-particles. We have parameterized all hadron±hadron cross-sections based on the resonance model and string model by ®tting the available experimental data. Below p the energy in the center-of-mass system (c.m.) s < 4 GeV, the inelastic hadron±hadron collisions are described by the resonance formations and their decays and at higher energies, string formation and their fragmentation into hadrons are assumed. We have parameterized the resonance formation cross-sections in terms of the extended Breit± Wigner form and used the established data [10] for its decay channels p and probabilities. At an energy range above s > 4±5 GeV, the (isolated) resonance picture breaks down because the width of the resonance becomes wider and the discrete levels get closer. Thephadronic interactions at the energy range 4±5 < s < 10±100 GeV where it is characterized by the small transverse momentum transfer is called ``soft process'' and string phenomenological models are known to describe the data for such soft interactions well. The hadron± hadron collision leads to a string-like excitation longitudinally. In actual description of the string formation, we follow the prescription adopted in the HIJING model [13±15]. The strings are assumed to hadronize via quark±antiquark or
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diquark±antidiquark creation. As for the fragmentation of the strings, we adopted the Lund fragmentation model PYTHIA6.1 [16,17]. In Fig. 1, we show the ®tted total cross-section with experimental data [10] and inelastic components of pp collisions as a function of c.m. energy. Inelastic cross-sections are assumed to be ®lled up with p the resonance formations (gray region) up to s 3±4 GeV. At higher energies, the dierence between experimental inelastic cross-sections and resonance formation cross-sections are assigned to the string formation. The following resonance excitation channels are implemented for the nucleon±nucleon scattering in JAM: (1) (2) (3) (4) (5) (6) (7) (8) (9)
NN NN NN NN NN NN NN NN NN
! N D 1232, ! NN , ! D 1232D 1232, ! N D , ! N D 1232, ! D 1232D , ! N N , ! N D , ! D D .
Here N and D represent higher baryonic states below 2 GeV/c2 . In the same ®gure, we also plot the contributions from the above channels (1)
(dashed line), (2) (dot-dot-dashed line), (4) (long dashed line) and the sum of the other channels (dot-dashed line) to the resonance formation cross-section. For nuclear reactions in JAM, we use the full cascade method described in the following. Each hadron has its position and momentum and moves along a straight line until it meets the next hadron± hadron collision, decay or absorption. The initial position of each nucleon is sampled by the parameterized distribution of nuclear density. Fermi motion of nucleons is assigned according to the local Fermi momentum as a function of the density. We do not take into account the mean ®eld eects except for the initial nucleons. The initial nucleons in the target nucleus stay in the initial positions until the collision with the other hadrons. The interaction probabilities of hadron±hadron are determined by the method of so-called ``closest distance approach''; if the minimum relative distance for any pair of particles becomes less p pthan the interaction range speci®ed by r s=p, p where r s is the p total cross-section for the pair at the c.m. energy s, then particles are assumed to collide. This cascade method has been widely used to simulate high-energy nucleus±nucleus collisions. However, geometrical interpretation of the cross-section violates causality and the time ordering of the collisions in general diers from one reference-frame to another. These problems have been studied by several authors [18±21]. We have adopted the similar procedure as that in [18±20,22] for the collision criterion to mimic the referenceframe dependence. Pauli-blocking for the ®nal nucleons in two-body collisions are also considered. For the comparison with the alternative methods of the cascade, we have compared the results of JAM with that of Glauber-type calculations in [9]. It is found that the rescattering eect, which is not considered in Glauber-type calculations, is of importance both for the explanation of the high transverse momentum tail and for the multiplicity of produced particles. 2.2. Elementary cross-sections of hadron±hadron
Fig. 1. Fitted total cross-section and inelastic components of pp collision as a function of c.m. energy.
There are a lot of adjustable parameters in the resonance model and string model in JAM.
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However, the number of the adjustable parameters in the models is relatively small compared with the number of ®nal channels at high energy, because the number of ®nal channels even in a proton± proton scattering increases drastically as a function of energy (see Fig. 11). Furthermore, they are not completely free parameters but restricted by the basic physical observables and arguments as the mean energies and widths of the resonances, the detailed balance principle and the kinematical conditions of the scattering. The detail of the parameterization of hadron±hadron cross-sections in JAM is described in [9]. Here we demonstrate typical examples of the elementary hadron±hadron cross-sections obtained by JAM and compare results with the experimental data. In Fig. 2, we show the calculated rapidity y distributions and the transverse momentum distributions of protons and positive and negative pions for proton±proton collisions at 12 GeV/c and also the data from [23]. It is found that the proton stopping behavior and the pion yields are well described by JAM. In the JAM model, fast
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protons come from resonance decays and mid-rapidity protons from string fragmentation. Fig. 3 shows the energy dependence of the exclusive pion production cross-sections in pp reactions. We compare the results obtained from the simulation with the experimental data [24]. Overall agreement is achieved in these exclusive pion productions. Smooth transition from the resonance picture to the string picture at Ecm 3±4 GeV is realized since no irregularity of the energy dependence is present in the calculated results. For another example of hadron±hadron crosssections, we plot, in Fig. 4, the total and elastic p p and K p cross-sections parameterized by JAM (upper panel) and the energy dependence of the exclusive cross-sections of K p ! p0 K and K n ! p R0 (lower panel). Data are taken from [10,25]. It is recognized that JAM shows a good capability for calculating the cross-sections even for the K; K; R. These examples indicate that the parameterization of the elementary hadron±hadron crosssections in JAM is accurate enough for the highenergy particle transport calculations.
Fig. 2. Rapidity y distributions (left panel) and the transverse momentum distributions (right panel) of proton, p and p in pp collisions at 12 GeV/c. Histograms are the results obtained from JAM, while the data are from [23].
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Fig. 3. Energy dependence of the exclusive pion production cross-sections for proton±proton reactions as a function of c.m. energy. Solid lines are the results obtained from JAM, while the data are from [24].
Fig. 4. Parameterization of the total and elastic p p and K p cross-sections (upper panel) and the energy dependence of the exclusive cross-sections of K p ! p0 K and K n ! p R0 (lower panel). Data are taken from [10,25].
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3. Upgrade of the nucleon±nucleus cross-sections We have included the JAM code into the intranuclear cascade part of NMTC/JAERI97. For this purpose, it is important to use reliable data of total non-elastic and elastic nucleon±nucleus cross-sections for simulating nucleon and meson transport in media. Although the cascade model itself, i.e. the JAM or Bertini code, can calculate the total non-elastic nucleon±nucleus cross-sections by the simulations, the results do not always reproduce the experimental data (see Fig. 5). If the deviation from the experimental data is even small in a nucleon±nucleus reaction, this aect the ¯ight length of nucleons in the material very much. Therefore, we should normalize the dierential cross-sections obtained by the cascade models by the total nonelastic nucleon±nucleus cross-sections given by the evaluated nuclear data or the systematics. As for the elastic cross-sections, on the other hand, the cascade model can calculate neither the total crosssections nor the double dierential cross-sections. We should use the evaluated nuclear data or the systematics for the total and also the double differential cross-sections of elastic nucleon±nucleus reactions. In NMTC/JAERI97, Pearlstein's systematics [26±28] is used for total non-elastic and elastic cross-sections of neutron±nucleus reactions, while for proton±nucleus reactions, elastic collision is not considered and total non-elastic cross-section is not normalized but determined by the simulations of the Bertini model [8]. We have then made new systematics for proton and neutron-induced total non-elastic and elastic cross-sections based on Pearlstein's systematics introducing the additional energy, target mass and angle-dependent factors. In Fig. 5, we plot the results of new systematics (bold solid lines) for the total non-elastic crosssection of p C and p Pb. In the same ®gure, we also show the evaluated nuclear data of LA150 [29] (bold gray dashed lines), the original Pearlstein's systematics (dashed lines) and the simulation results of the Bertini model (solid lines up to 3.5 GeV) and JAM code (solid line above 3.5 GeV). Experimental data are extracted from EXFOR [30]. The present results well follow the ex-
Fig. 5. Total non-elastic cross-section of p C (upper panel) and p Pb (lower panel). The results of new systematic is denoted by bold solid lines. The results of LA150 [29] (bold gray dashed lines), the original Pearlstein's systematics (dashed lines) and the simulation results of the Bertini model (solid lines up to 3.5 GeV) and JAM code (solid line above 3.5 GeV) are also shown compared with the experimental data extracted from EXFOR [30].
perimental data and also LA150 data, while the results of the original Pearlstein's systematics overestimates the data below 100 MeV. The connection of the simulation results between Bertini and JAM is not smooth and in the low-energy region, the results of Bertini are too high. This is one of the reasons for creating the new systematics and using it for the normalization of the total nonelastic cross-sections. We have also created new systematics based on Pearlstein's systematics [26±28] for nucleon±
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Fig. 6. Angular distribution of the elastic cross-sections compared with the experimental data [30] and LA150. The results of the new systematic is denoted by solid lines.
nucleus elastic angular distributions. Fig. 6 shows the results of the new systematics of the angular distribution of the elastic cross-sections. We compare the present results with the experimental data [30] and LA150. The present results reproduce the experimental data for all of the targets and the incident energies above 150 MeV up to 1 GeV. Even below 150 MeV, the present results have enough accuracy for the transport calculations. Indeed, Fig. 7 shows the elastic angular distributions of various targets with 55 MeV (left panel) and 75 MeV (right panel) neutrons. Experimental data are taken from [31]. Although, for some targets, the present results underestimate the experimental data at the angular regions above the second peak, the agreement with the data is excellent around the ®rst peak.
4. Comparison with experimental data For validation, we compare the results of NMTC/JAM with experimental data of thin and thick targets. In addition, we compare them with
the results of LCS2.7 [32] calculations. Since LCS2.7 also uses the Bertini model for the intranuclear cascade part and employs the scaling law in order to extend the upper limit of the energy of the Bertini model, we can then compare the results of NMTC/JAM and LCS2.7 in higher-energy regions above 3.5 GeV. 4.1. Thin target In Fig. 8, we plot the invariant transverse mass distribution of proton (left panel), p (middle panel) and K (right panel) from protons on thin Au targets at 13.7 GeV. The results of JAM (histograms) and data [33] are plotted for each rapidity y bin quoted in the ®gure. For all ejectiles, the results of JAM agree well with the experimental data [33]. The agreement is also shown in the other targets of Be, Al and Cu in [9]. Next, comparisons are shown for the reactions of the incident energies around 3 GeV. Fig. 9 shows the double dierential cross section of neutrons from p (3 GeV) + 208 Pb (left panel) and invariant cross-section of p from p (3.17
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Fig. 7. Angular distribution of the elastic cross-sections. The results of the new systematic is denoted by solid lines. The incident energy of the neutron is 55 MeV (left panel) and 75 MeV (right panel). Targets are 208 Pb, 90 Zr, 56 Fe, 28 Si and 12 C from upward, respectively.
Fig. 8. Invariant transverse mass distribution of proton (left panel), p (middle panel) and K (right panel) from protons on thin Au targets at 13.7 GeV. The results of JAM (histograms) and data [33] are plotted for each rapidity y bin quoted in the ®gure.
GeV) + 208 Pb (right panel). The histograms are the results of NMTC/JAM, while data are taken from [34,35]. The results of NMTC/JAM (left panel)
reproduce the neutron yields from the beam energy region down to 1 MeV where the neutrons come from the evaporation process. In NMTC/
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Fig. 9. Double dierential cross-section of neutrons from p (3 GeV) + 208 Pb (left panel) and invariant cross-section of p from p (3.17 GeV) + 208 Pb (right panel). The histograms are the results of NMTC/JAM, while data are taken from [34,35].
JAM, the statistical decay process is implemented after the intranuclear cascade process described by JAM. It is found that the results of NMTC/JAM are almost comparable to that of NMTC/JAERI97 and also LCS2.7 for the thin target systems at the incident energies below 3.5 GeV. For detail comparisons of NMTC/JAM and LCS2.7, we have calculated the neutron yields from proton-induced thin target reactions at 1.5 and 24 GeV. In Fig. 10, we plot the results of invariant cross-sections of neutrons from p + 208 Pb at 1.5 GeV (left panels) and 24 GeV (right panels) calculated by NMTC/JAM (full squares) and LCS2.7 (histograms). In the upper panels the energy spectra are shown, while the angular distributions are shown in the lower panels. The angle bins for the energy spectra are denoted in the ®gures. The neutron energies of the angular distribution in the lower panels are 148 MeV for 1.5 GeV incident energy and 360 MeV for 24 GeV,
which are denoted by the dashed lines in the upper panels. The low-energy neutron spectra below 10 MeV are almost identical for both incident energies. This means that the residual nucleus after the intranucleus cascade process described by the JAM and Bertini models are not so dierent. However, the neutron spectra above 10 MeV dier very much with each other for the 24 GeV case, though both are the same for 1.5 GeV. This is due to the dierent description of hadron±hadron cross-sections in the JAM and Bertini models for the 24 GeV case. As show in Section 2, JAM can reproduce the elementary cross-sections of hadron±hadron reactions in the energy range of several 10 GeV. However, the Bertini model is originally based on the parameterized cross-sections of nucleon±nucleon reactions up to 3.5 GeV, where the two pion production channel is the highest inelastic channel. In LCS2.7, thus, the scaling law is employed to extend this upper limit of energy of the Bertini model. However, this
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Fig. 10. Invariant cross-sections of the neutrons from p + 208 Pb at 1.5 GeV (left panels) and 24 GeV (right panels) calculated by NMTC/ JAM (full squares) and LCS2.7 (histograms). In the upper panels the energy spectra are shown, while the angular distributions are shown in the lower panels. The angle bins for the energy spectra are denoted in the ®gures. The neutron energies of the angular distribution in the lower panels are 148 MeV for 1.5 GeV incident energy and 360 MeV for 24 GeV, which are denoted by the dashed lines in the upper panels.
®gure shows that the scaling law is not adequate for the higher energy than 3.5 GeV. Particularly the angular distribution of neutrons from the 24 GeV case (lower right panel) has a strange shape, only forward and backward neutrons are produced by the cascade process in LCS2.7.
To clarify this situation, we plot, in Fig. 11, the pp inelastic cross-section as a function of energy obtained by the JAM code. In this ®gure, we divide the total inelastic cross-section into the fractions of individual channels characterized by the number of produced pions. The gray region
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Fig. 11. pp inelastic cross-section as a function of energy obtained by JAM code. The total inelastic cross-section is divided into individual channel characterized by the number of produced pions. The gray region denotes the component with three pions and more or with another mesons like g; K.
denotes the component with three pions and more or with another mesons like g; K. The fraction of the gray region is 25% at 3.5 GeV and 85% at 24 GeV. Therefore, it is the very limit that we use the original Bertini model up to 3.5 GeV. Moreover, the scaling law of LCS2.7 is obviously inadequate above 3.5 GeV as long as it does not take into account the higher inelastic channels above two pion production.
In NMTC/JAERI97, the EVAP [36] code is used for evaporation and the ®ssion process. It is reported in [11] that the results of EVAP underestimate light nuclei production. Therefore, we have implemented the GEM [11] code, which is a simulation program of the generalized evaporation and ®ssion model, in the nuclear reaction calculation part. The GEM code can treat light nuclei emission up to magnesium taking into account the excitation of the ejectiles. The detail of the GEM model has been discussed in [11]. Here we compare the results of the nuclear reaction calculation by JAM coupled with GEM with experimental data of thin targets for validation. Fig. 12 shows the isotope production crosssections of He, Li and Be from the Ag(p,x) reaction at 480 MeV. The experimental data are taken from [37]. The results of JAM coupled with GEM reproduce the experimental data. The isotopes of Li and Be are hardly produced by the other evaporation models, e.g. the EVAP code in this reaction. 4.2. Thick target We have applied NMTC/JAM to thick target analysis. There do not exist many reliable experimental data of neutron yields from thick targets
Fig. 12. Isotope production cross-sections of He, Li and Be from the Ag(p,x) reaction at 480 MeV. The experimental data are taken from [37]. The results of JAM with GEM are shown by the solid lines.
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with proton beams above 3 GeV. We have picked up two experiments carried out at KEK and AGS for the comparison with NMTC/JAM calculations. For thick target analysis, we have used the same parameters of the JAM models as for thin target analysis. In the actual calculations of thick targets, however, the Bertini model was employed for the intra-nuclear cascade part below 3.5 GeV by using the in-medium nucleon±nucleon cross-sections [4] and JAM was used above 3.5 GeV. This connection between the Bertini and JAM models is due to the reduction in the calculation time. The CPU time of the JAM calculation for one nuclear reaction, which depends on the incident energies and target mass, is about 10 times longer than that of the Bertini model. However, below 3.5 GeV, the results of the dierential cross-sections of the produced particles and nuclei calculated by both models are almost the same, as long as we normalize the total non-elastic cross-sections by the new systematics. Thus we have used the Bertini model below 3.5 GeV. The total CPU time is 0.621 s per one history (17.25 h for 100 000 history) on an Alpha workstation (600 MHz) for the large mercury target system with the 24 GeV proton beam mentioned below. This calculation time is not so long for the various calculations of neutronics design study with realistic geometry. We have ®rst applied NMTC/JAM to the neutron production from lead targets with 12 GeV protons. The experiment has been done in KEK by means of the Mn-bath moderation method with 20 and 10 cm diameter and 60 cm long cylindrical lead targets [38]. Measurements were performed while changing the length of the target in steps of 10 cm in order to obtain the target length dependence of the neutron yields. We have calculated the neutron yield tracing the experimental conditions by NMTC/JAM combined with MCNP4A for the neutron below 20 MeV. We have used the cross-section data of JENDL-3.2 [39] for MCNP4A. Fig. 13 shows the neutron yields as a function of the number of neutrons per incident proton (n/p) as a function of the target length. The open circles (10 cm diameter case) and solid circles (20 cm diameter case) with error bars are data taken from [38], the solid lines are the results of
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Fig. 13. Neutron yields from lead target with 12 GeV protons as a unit of the number of neutrons per incident proton (n=p) as a function of the target length. The open circles (10 cm diameter) and solid circles (20 cm diameter) with error bars are data taken from [38], the solid lines are the results of NMTC/JAM, while the dashed lines denote that of LCS2.7, respectively.
NMTC/JAM, while the dashed lines denote that of LCS2.7, respectively. The results of NMTC/JAM reproduced quit well the experimental data. On the other hand, the results of LCS2.7 overestimate the neutron yields at deeper positions in the target. It might be due to the failure of the scaling law used in LCS2.7 at 12 GeV as discussed in the previous section. Next, a comparison is done for experiments under the AGS spallation target experiment (ASTE) collaboration [41]. This experiment has been carried out using a thick mercury target, which is a 20 cm diameter and 130 cm long cylinder and detecting the reaction rate distributions along the cylindrical surface of the target by activation techniques at incident proton energies of 1.6, 12 and 24 GeV. Various activation detectors such as the 115 In n; n0 115m In, 93 Nb(n; 2n)92m Nb and 209 Bi(n; xn) reactions with threshold energies ranging from 0.3 to 70.5 MeV were employed to obtain the reaction rate data for estimating
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spallation source neutron characteristics of the mercury target. In the calculation, the reaction rate is obtained from the neutron ¯ux multiplied by the activation cross-sections. We have used dosimetry cross-section set of [40]. Fig. 14 shows the distribution of the 209 Bi(n,4n)206 Bi reaction rates along the cylindrical surface of mercury target bombarded with 1.6, 12 and 24 GeV protons. The threshold of this reaction is 23 MeV, while the most eective energies of neutron for this reaction is about 30 MeV. Other results are shown in Fig. 15 for the 27 Al n; a24 Na reaction rate. The threshold of this reaction is 3.3 MeV, while the most eective energies of neutrons for this reaction is about 10 MeV. The results of NMTC/JAM, denoted by the solid histograms in these ®gures, reproduce the experimental distribution quite well for all positions and all energies,
Fig. 15. Distribution of the 27 Al n; a24 Na reaction rates along the cylindrical surface of a mercury target bombarded with 1.6, 12 and 24 GeV protons. The solid histograms denote the results of NMTC/JAM.
Fig. 14. Distribution of 209 Bi(n,4n)206 Bi reaction rates along the cylindrical surface of a mercury target bombarded with 1.6, 12 and 24 GeV protons. The solid histograms denote the results of NMTC/JAM, while the dashed lines show the results of LCS2.7, respectively.
though the result at 1.6 GeV in Fig 14 slightly underestimates the data. In Fig. 14, we also plot the results of LCS2.7 by the dashed lines. The results of LCS2.7 at 1.6 GeV in Fig 14 is almost the same as that of NMTC/ JAM. This is reasonable, since NMTC/JAM also uses the Bertini model for the intra-nuclear cascade part as in LCS2.7 at this energy. As we increase the incident energy, however, the discrepancy between them becomes large. The results of NMTC/JAM still reproduce the experimental distributions quite well for all positions. The results of LCS2.7, however, overestimate the reaction rate particularly at deeper positions. This trend is very similar to the results shown in Fig. 13. Accordingly, the peak position is shifted to the deeper position in the LCS2.7 results. Therefore, it also might be due to the inadequacy of the scaling law used in LCS2.7 at 12 GeV. As discussed in Fig. 10, the high-energy neutrons produced in proton-
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induced reactions at the energies above 3.5 GeV by LCS2.7 are restricted in the very forward angle and backward angle. Then these high-energy neutrons stay in the target and collide with the other nuclei again and again. By these facts, it can be explained that the neutron yields by LCS2.7 overestimate the data particularly at deeper positions, at incident energies above 3.5 GeV. On the other hand, the results of NMTC/JAM can predict precisely the peak position of the reaction rate as well as the absolute values of various reaction rates for all incident energies. 5. Summary We have developed a high-energy nucleon± meson transport code NMTC/JAM, which is an upgraded version of NMTC/JAERI97. We have introduced two new physical models in NMTC/ JAM, the high-energy nuclear reaction code JAM for the intra-nuclear cascade part and the generalized evaporation model GEM for the evaporation and ®ssion process. The JAM code can extend the applicable energy range of NMTC/JAM in principle up to 200 GeV for nucleons and mesons. While the GEM code enables us to calculate the light nucleus production like Be isotopes from the excited residual nucleus. These nuclei as well as the ®ssion products are very important in view of the radiation safety for estimating induced radiation activities and dose rate in the spallation neutron source facility driven by high-intensity proton beam. For the validation of JAM, we have compared the elementary hadron±hadron cross-sections and the particle production cross-sections from thin targets with the experimental data. It is found that JAM can reproduce the experimental data for the energy range up to several tens of GeV. For the particle transport part of NMTC/JAM, we have upgraded the nucleon±nucleus non-elastic and elastic cross-sections by employing new systematics. We have compared the calculations by NMTC/JAM code with the experimental data of thick targets measured at KEK-PS and AGS for proton-induced reactions up to several tens of GeV. The results of the NMTC/JAM code show
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excellent agreement with the experimental data. From these new calculation functions and the code validation, NMTC/JAM enables us to carry out the radiation transport analysis of a large-scale target system with complex geometry more accurately and easily than before.
Acknowledgements The authors would like to thank Dr. S. Furihata of MRI for supplying the GEM code. They also thank Dr. Y. Nara for his useful comments on the JAM code. They are grateful to Dr. T. Fukahori and Dr. S. Chiba for their useful discussions about parameterization of the nucleon±nucleus cross-sections. References [1] B.R. Appleton, in: Proceedings of the 14th Meeting of the International Collaboration on Advanced Neutron Sources, Illinois, Vol. I, ANL-98-33, Argonne National Laboratory, 1998. [2] S. Nagamiya, in: Proceedings of Ninth International Conference on Radiat. Shielding, ICRS-9, Tsukuba, Japan, 17±22 October 1999, J. Nucl. Sci. Technol. (Suppl. 1) (2000) 40. [3] N. Watanabe, M. Teshigawara, T. Kai, M. Harada, H. Sakata, Y. Ikeda, M. Kaminaga, R. Hino, Y. Oyama, in: Proceedings of ICONE-8 8th International Conference on Nuclear Engineering, 2±6 April 2000 Baltimore, MD USA, ICONE-8457. [4] H. Takada, N. Yoshizawa, K. Kosako, K. Ishibashi, An Upgraded Version of the Nucleon Meson Transport Code; NMTC/JAERI97, JAERI-Data/Code 98-005, 1998. [5] J.F. Briesmeister (Ed.), MCNP General Monte Carlo NParticle Transport Code, Los Alamos National Laboratory, LA-12625-Mm, 1997. [6] For Example, F.C. Di®lippo, L.A. Charlton, J.M. Aragones (Eds.), in: Proceedings of International Conference M&C '99, Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, Madrid, Spain, 27±30 September 1999, Senda Editrial, S. A., Vol. 2, 1999, pp. 949±954. [7] For example, J.R. Alonso, in: AccApp'98, 2nd International Topical Mtg. on Nucl. Application of Accelerator Technology, American Nuclear Society, Gatlinburg, TN, 20±23 September 1998, pp.197±201. [8] H.W. Bertini, Monte Carlo calculation on intranuclear cascade, ORNL-3833, Oak Ridge National Laboratory, 1963.
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[9] Y. Nara, N. Otuka, A. Ohnishi, K. Niita, S. Chiba, Phys, Rev. C61, 024901 (2000). Available from http://hadron31.tokai.jaeri.go.jp/jam/. [10] Particle-Data-Group: Phys. Rev. D 54 (1996). [11] S. Furihata, Nucl. Instr. and Meth. B 171 (2000) 251. [12] K. Niita, S. Meigo, H. Takada, Y. Ikeda, High energy particle transport code NMTC/JAM, JAERI-Data/Code 2001-007, 2001. [13] X.N. Wang, M. Gyulassy, Phys. Rev. D 44 (1991) 3501. [14] X.N. Wang, Phys. Rep. 280 (1997) 287. [15] X.N. Wang, M. Gyulassy, Comp. Phys. Comm. 83 (1994) 307. Available from http://www-nsdth.lbl.gov/simxnwang/ hijing/. [16] T. Sj ostrand, Comp. Phys. Comm. 82 (1994) 74. [17] PYTHIA 5.7 and JETSET 7.4 Physics and Manual. Available from http://thep.lu.se/tf2/sta/torbjorn/Welcome.html. [18] B. Zhang, Comp. Phys. Comm. 109 (1997) 70. Available from http://nt1.phys.columbia.edu/people/bzhang/ZPC/ zpc.html. [19] B. Zhang, Y. Pang, Phys. Rev. C 56 (1997) 2185. [20] B. Zhang, M. Gyulassy, Y. Pang, Phys. Rev. C 58 (1998) 1175. [21] G. Kortemeyer, W. Bauer, K. Haglin, J. Murray, S. Pratt, Phys. Rev. C 52 (1995) 2714. [22] B. Andersson, A. Tai, B.-H. Sa, Z. Phys. C 70 (1996) 499. [23] Bonn±Hamburg±M unchen Collaboration, V. Blobel et al., Nucl. Phys. B 69 (1974) 454. [24] A. Baldni, V. Flaminio, W.G. Moorhead, D.R.O. Morrison (Eds.), Total Cross-sections for Reactions of High Energy Particles, Vol. 12a and b, Springer, Berlin, 1988. [25] High Energy Reactions Analysis Group, CERN Report CERN-HERA 83-01 and 83-02, 1983 (unpublished).
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www.elsevier.com/locate/nimb
High-energy particle transport code NMTC/JAM Koji Niita
a,b,*
, Hiroshi Takada b, Shin-ichiro Meigo b, Yujiro Ikeda
b
a
b
Research Organization for Information Science and Technology, Tokai-mura, Naka-gun, Ibaraki-ken 319-1106, Japan Center for Neutron Science, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan Received 30 January 2001; received in revised form 11 July 2001
Abstract We have developed a high-energy particle transport code NMTC/JAM, which is an upgraded version of NMTC/ JAERI97. The applicable energy range of NMTC/JAM is extended in principle up to 200 GeV for nucleons and mesons by introducing the high-energy nuclear reaction code JAM for the intra-nuclear cascade part. We compare the calculations by NMTC/JAM code with the experimental data of thin and thick targets for proton-induced reactions up to several tens of GeV. The results of the NMTC/JAM code show excellent agreement with the experimental data. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 24.10.Lx; 25.40.-h Keywords: NMTC/JAM; Monte Carlo simulation; High-energy particle transport; Intra-nuclear cascade model; Hadron±hadron cross-sections; Nucleon±nucleus cross-sections
1. Introduction Several projects aiming at the development of an intense pulsed spallation neutron source with a power of 1±5 MW are under progress in the world [1]. Japan Atomic Energy Research Institute (JAERI) and High Energy Accelerator Research Organization (KEK) have jointly proposed the high-intensity proton accelerator project [2], which is the multi-purpose utilization of intense second-
* Corresponding author. Tel.: +81-29-282-5336/6101; fax: +81-29-282-6496. E-mail address: [email protected] (K. Niita).
ary particle beams for materials and life science, nuclear and particle physics and basic technologies for accelerator-based nuclear transmutation of long-lived radioactive wastes. It is planned to build a 600 MeV proton linac, 3 GeV proton rapid cycling synchrotron and 50 GeV proton synchrotron and associated experimental facilities to carry out these multi-purpose scienti®c activities and technology developments. At present, the neutronics design study of a pulsed spallation source driven by 3 GeV protons with a power of 1 MW is being conducted by JAERI [3]. The beam line and related shielding design of the accelerator facilities are also under way. It is very important to estimate source distributions and transport phenomena of various
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 7 8 4 - 4
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particles, especially neutrons, as precisely as possible and to make a target±moderator±re¯ector system of the neutron source facility extracting its maximum neutronics performance given by 1 MW proton beams. Moreover, it is required to do some neutronics design studies of the facilities for the 50 GeV proton synchrotron. For the neutronics design study, a nucleon±meson transport code NMTC/JAERI97 [4] has been employed in combination with the neutron transport code MCNP [5] as a standard code system in JAERI. This manner is essentially similar to the code system adopted in the neutronics design study [6] in the SNS project [7]. As described in [4], some function of the geometry con®guration, neutron transport calculation part and tally function were upgraded in the development of NMTC/JAERI97 from its original version. However, the code still had some limitations. The most critical one is the highest applicable energy limited to 3.5 GeV for protons and neutrons and 2.5 GeV for pions because of the limit of the Bertini model [8] for nuclear reaction calculations. Hence, it was required to extend the applicable energy range of NMTC/JAERI97 for the neutronic design study of the facility related to the 50 GeV proton synchrotron. In order to satisfy this requirement, we have introduced the high-energy nuclear reaction code JAM [9] into the intra-nuclear reaction calculation part of NMTC/JAERI97. With implementation of JAM, the particle transport part has been improved to treat all established hadronic states including resonances as well as their anti-particles listed in [10]. This new code system has been named NMTC/JAM. Here we also upgraded the nucleon±nucleus non-elastic, elastic and dierential elastic cross-section data by employing new systematics. Moreover, the Coulomb scattering of a traveling charged particles has been also upgraded and a new function treating the ¯ight of charged particles in the magnetic ®eld has been implemented so that the user could employ NMTC/JAM for design study of proton beam lines. In the nuclear reaction calculation part, a new evaporation model GEM [11], treating light nuclei emission up to magnesium, has been included to improve the light nuclide yield such as Be isotopes production in structural materials by
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the spallation reaction. User interfaces such as input data preparation and output ®le information has also been improved to be more user-friendly than NMTC/JAERI97. The overview and code manual of NMTC/JAM has already been published in [12]. This paper focuses on the main features of JAM in Section 2, upgrading of the cross-section data in Section 3 and some comparisons with experimental data for thin and thick target systems in Section 4. We summarize the paper in Section 5. 2. High-energy nuclear reaction code JAM 2.1. Main features of JAM Jet AA Microscopic Transport Model (JAM) [9] is a hadronic cascade model, which explicitly treats all established hadronic states including resonances with explicit spin and isospin as well as their anti-particles. We have parameterized all hadron±hadron cross-sections based on the resonance model and string model by ®tting the available experimental data. Below p the energy in the center-of-mass system (c.m.) s < 4 GeV, the inelastic hadron±hadron collisions are described by the resonance formations and their decays and at higher energies, string formation and their fragmentation into hadrons are assumed. We have parameterized the resonance formation cross-sections in terms of the extended Breit± Wigner form and used the established data [10] for its decay channels p and probabilities. At an energy range above s > 4±5 GeV, the (isolated) resonance picture breaks down because the width of the resonance becomes wider and the discrete levels get closer. Thephadronic interactions at the energy range 4±5 < s < 10±100 GeV where it is characterized by the small transverse momentum transfer is called ``soft process'' and string phenomenological models are known to describe the data for such soft interactions well. The hadron± hadron collision leads to a string-like excitation longitudinally. In actual description of the string formation, we follow the prescription adopted in the HIJING model [13±15]. The strings are assumed to hadronize via quark±antiquark or
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diquark±antidiquark creation. As for the fragmentation of the strings, we adopted the Lund fragmentation model PYTHIA6.1 [16,17]. In Fig. 1, we show the ®tted total cross-section with experimental data [10] and inelastic components of pp collisions as a function of c.m. energy. Inelastic cross-sections are assumed to be ®lled up with p the resonance formations (gray region) up to s 3±4 GeV. At higher energies, the dierence between experimental inelastic cross-sections and resonance formation cross-sections are assigned to the string formation. The following resonance excitation channels are implemented for the nucleon±nucleon scattering in JAM: (1) (2) (3) (4) (5) (6) (7) (8) (9)
NN NN NN NN NN NN NN NN NN
! N D 1232, ! NN , ! D 1232D 1232, ! N D , ! N D 1232, ! D 1232D , ! N N , ! N D , ! D D .
Here N and D represent higher baryonic states below 2 GeV/c2 . In the same ®gure, we also plot the contributions from the above channels (1)
(dashed line), (2) (dot-dot-dashed line), (4) (long dashed line) and the sum of the other channels (dot-dashed line) to the resonance formation cross-section. For nuclear reactions in JAM, we use the full cascade method described in the following. Each hadron has its position and momentum and moves along a straight line until it meets the next hadron± hadron collision, decay or absorption. The initial position of each nucleon is sampled by the parameterized distribution of nuclear density. Fermi motion of nucleons is assigned according to the local Fermi momentum as a function of the density. We do not take into account the mean ®eld eects except for the initial nucleons. The initial nucleons in the target nucleus stay in the initial positions until the collision with the other hadrons. The interaction probabilities of hadron±hadron are determined by the method of so-called ``closest distance approach''; if the minimum relative distance for any pair of particles becomes less p pthan the interaction range speci®ed by r s=p, p where r s is the p total cross-section for the pair at the c.m. energy s, then particles are assumed to collide. This cascade method has been widely used to simulate high-energy nucleus±nucleus collisions. However, geometrical interpretation of the cross-section violates causality and the time ordering of the collisions in general diers from one reference-frame to another. These problems have been studied by several authors [18±21]. We have adopted the similar procedure as that in [18±20,22] for the collision criterion to mimic the referenceframe dependence. Pauli-blocking for the ®nal nucleons in two-body collisions are also considered. For the comparison with the alternative methods of the cascade, we have compared the results of JAM with that of Glauber-type calculations in [9]. It is found that the rescattering eect, which is not considered in Glauber-type calculations, is of importance both for the explanation of the high transverse momentum tail and for the multiplicity of produced particles. 2.2. Elementary cross-sections of hadron±hadron
Fig. 1. Fitted total cross-section and inelastic components of pp collision as a function of c.m. energy.
There are a lot of adjustable parameters in the resonance model and string model in JAM.
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However, the number of the adjustable parameters in the models is relatively small compared with the number of ®nal channels at high energy, because the number of ®nal channels even in a proton± proton scattering increases drastically as a function of energy (see Fig. 11). Furthermore, they are not completely free parameters but restricted by the basic physical observables and arguments as the mean energies and widths of the resonances, the detailed balance principle and the kinematical conditions of the scattering. The detail of the parameterization of hadron±hadron cross-sections in JAM is described in [9]. Here we demonstrate typical examples of the elementary hadron±hadron cross-sections obtained by JAM and compare results with the experimental data. In Fig. 2, we show the calculated rapidity y distributions and the transverse momentum distributions of protons and positive and negative pions for proton±proton collisions at 12 GeV/c and also the data from [23]. It is found that the proton stopping behavior and the pion yields are well described by JAM. In the JAM model, fast
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protons come from resonance decays and mid-rapidity protons from string fragmentation. Fig. 3 shows the energy dependence of the exclusive pion production cross-sections in pp reactions. We compare the results obtained from the simulation with the experimental data [24]. Overall agreement is achieved in these exclusive pion productions. Smooth transition from the resonance picture to the string picture at Ecm 3±4 GeV is realized since no irregularity of the energy dependence is present in the calculated results. For another example of hadron±hadron crosssections, we plot, in Fig. 4, the total and elastic p p and K p cross-sections parameterized by JAM (upper panel) and the energy dependence of the exclusive cross-sections of K p ! p0 K and K n ! p R0 (lower panel). Data are taken from [10,25]. It is recognized that JAM shows a good capability for calculating the cross-sections even for the K; K; R. These examples indicate that the parameterization of the elementary hadron±hadron crosssections in JAM is accurate enough for the highenergy particle transport calculations.
Fig. 2. Rapidity y distributions (left panel) and the transverse momentum distributions (right panel) of proton, p and p in pp collisions at 12 GeV/c. Histograms are the results obtained from JAM, while the data are from [23].
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Fig. 3. Energy dependence of the exclusive pion production cross-sections for proton±proton reactions as a function of c.m. energy. Solid lines are the results obtained from JAM, while the data are from [24].
Fig. 4. Parameterization of the total and elastic p p and K p cross-sections (upper panel) and the energy dependence of the exclusive cross-sections of K p ! p0 K and K n ! p R0 (lower panel). Data are taken from [10,25].
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3. Upgrade of the nucleon±nucleus cross-sections We have included the JAM code into the intranuclear cascade part of NMTC/JAERI97. For this purpose, it is important to use reliable data of total non-elastic and elastic nucleon±nucleus cross-sections for simulating nucleon and meson transport in media. Although the cascade model itself, i.e. the JAM or Bertini code, can calculate the total non-elastic nucleon±nucleus cross-sections by the simulations, the results do not always reproduce the experimental data (see Fig. 5). If the deviation from the experimental data is even small in a nucleon±nucleus reaction, this aect the ¯ight length of nucleons in the material very much. Therefore, we should normalize the dierential cross-sections obtained by the cascade models by the total nonelastic nucleon±nucleus cross-sections given by the evaluated nuclear data or the systematics. As for the elastic cross-sections, on the other hand, the cascade model can calculate neither the total crosssections nor the double dierential cross-sections. We should use the evaluated nuclear data or the systematics for the total and also the double differential cross-sections of elastic nucleon±nucleus reactions. In NMTC/JAERI97, Pearlstein's systematics [26±28] is used for total non-elastic and elastic cross-sections of neutron±nucleus reactions, while for proton±nucleus reactions, elastic collision is not considered and total non-elastic cross-section is not normalized but determined by the simulations of the Bertini model [8]. We have then made new systematics for proton and neutron-induced total non-elastic and elastic cross-sections based on Pearlstein's systematics introducing the additional energy, target mass and angle-dependent factors. In Fig. 5, we plot the results of new systematics (bold solid lines) for the total non-elastic crosssection of p C and p Pb. In the same ®gure, we also show the evaluated nuclear data of LA150 [29] (bold gray dashed lines), the original Pearlstein's systematics (dashed lines) and the simulation results of the Bertini model (solid lines up to 3.5 GeV) and JAM code (solid line above 3.5 GeV). Experimental data are extracted from EXFOR [30]. The present results well follow the ex-
Fig. 5. Total non-elastic cross-section of p C (upper panel) and p Pb (lower panel). The results of new systematic is denoted by bold solid lines. The results of LA150 [29] (bold gray dashed lines), the original Pearlstein's systematics (dashed lines) and the simulation results of the Bertini model (solid lines up to 3.5 GeV) and JAM code (solid line above 3.5 GeV) are also shown compared with the experimental data extracted from EXFOR [30].
perimental data and also LA150 data, while the results of the original Pearlstein's systematics overestimates the data below 100 MeV. The connection of the simulation results between Bertini and JAM is not smooth and in the low-energy region, the results of Bertini are too high. This is one of the reasons for creating the new systematics and using it for the normalization of the total nonelastic cross-sections. We have also created new systematics based on Pearlstein's systematics [26±28] for nucleon±
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Fig. 6. Angular distribution of the elastic cross-sections compared with the experimental data [30] and LA150. The results of the new systematic is denoted by solid lines.
nucleus elastic angular distributions. Fig. 6 shows the results of the new systematics of the angular distribution of the elastic cross-sections. We compare the present results with the experimental data [30] and LA150. The present results reproduce the experimental data for all of the targets and the incident energies above 150 MeV up to 1 GeV. Even below 150 MeV, the present results have enough accuracy for the transport calculations. Indeed, Fig. 7 shows the elastic angular distributions of various targets with 55 MeV (left panel) and 75 MeV (right panel) neutrons. Experimental data are taken from [31]. Although, for some targets, the present results underestimate the experimental data at the angular regions above the second peak, the agreement with the data is excellent around the ®rst peak.
4. Comparison with experimental data For validation, we compare the results of NMTC/JAM with experimental data of thin and thick targets. In addition, we compare them with
the results of LCS2.7 [32] calculations. Since LCS2.7 also uses the Bertini model for the intranuclear cascade part and employs the scaling law in order to extend the upper limit of the energy of the Bertini model, we can then compare the results of NMTC/JAM and LCS2.7 in higher-energy regions above 3.5 GeV. 4.1. Thin target In Fig. 8, we plot the invariant transverse mass distribution of proton (left panel), p (middle panel) and K (right panel) from protons on thin Au targets at 13.7 GeV. The results of JAM (histograms) and data [33] are plotted for each rapidity y bin quoted in the ®gure. For all ejectiles, the results of JAM agree well with the experimental data [33]. The agreement is also shown in the other targets of Be, Al and Cu in [9]. Next, comparisons are shown for the reactions of the incident energies around 3 GeV. Fig. 9 shows the double dierential cross section of neutrons from p (3 GeV) + 208 Pb (left panel) and invariant cross-section of p from p (3.17
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Fig. 7. Angular distribution of the elastic cross-sections. The results of the new systematic is denoted by solid lines. The incident energy of the neutron is 55 MeV (left panel) and 75 MeV (right panel). Targets are 208 Pb, 90 Zr, 56 Fe, 28 Si and 12 C from upward, respectively.
Fig. 8. Invariant transverse mass distribution of proton (left panel), p (middle panel) and K (right panel) from protons on thin Au targets at 13.7 GeV. The results of JAM (histograms) and data [33] are plotted for each rapidity y bin quoted in the ®gure.
GeV) + 208 Pb (right panel). The histograms are the results of NMTC/JAM, while data are taken from [34,35]. The results of NMTC/JAM (left panel)
reproduce the neutron yields from the beam energy region down to 1 MeV where the neutrons come from the evaporation process. In NMTC/
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Fig. 9. Double dierential cross-section of neutrons from p (3 GeV) + 208 Pb (left panel) and invariant cross-section of p from p (3.17 GeV) + 208 Pb (right panel). The histograms are the results of NMTC/JAM, while data are taken from [34,35].
JAM, the statistical decay process is implemented after the intranuclear cascade process described by JAM. It is found that the results of NMTC/JAM are almost comparable to that of NMTC/JAERI97 and also LCS2.7 for the thin target systems at the incident energies below 3.5 GeV. For detail comparisons of NMTC/JAM and LCS2.7, we have calculated the neutron yields from proton-induced thin target reactions at 1.5 and 24 GeV. In Fig. 10, we plot the results of invariant cross-sections of neutrons from p + 208 Pb at 1.5 GeV (left panels) and 24 GeV (right panels) calculated by NMTC/JAM (full squares) and LCS2.7 (histograms). In the upper panels the energy spectra are shown, while the angular distributions are shown in the lower panels. The angle bins for the energy spectra are denoted in the ®gures. The neutron energies of the angular distribution in the lower panels are 148 MeV for 1.5 GeV incident energy and 360 MeV for 24 GeV,
which are denoted by the dashed lines in the upper panels. The low-energy neutron spectra below 10 MeV are almost identical for both incident energies. This means that the residual nucleus after the intranucleus cascade process described by the JAM and Bertini models are not so dierent. However, the neutron spectra above 10 MeV dier very much with each other for the 24 GeV case, though both are the same for 1.5 GeV. This is due to the dierent description of hadron±hadron cross-sections in the JAM and Bertini models for the 24 GeV case. As show in Section 2, JAM can reproduce the elementary cross-sections of hadron±hadron reactions in the energy range of several 10 GeV. However, the Bertini model is originally based on the parameterized cross-sections of nucleon±nucleon reactions up to 3.5 GeV, where the two pion production channel is the highest inelastic channel. In LCS2.7, thus, the scaling law is employed to extend this upper limit of energy of the Bertini model. However, this
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Fig. 10. Invariant cross-sections of the neutrons from p + 208 Pb at 1.5 GeV (left panels) and 24 GeV (right panels) calculated by NMTC/ JAM (full squares) and LCS2.7 (histograms). In the upper panels the energy spectra are shown, while the angular distributions are shown in the lower panels. The angle bins for the energy spectra are denoted in the ®gures. The neutron energies of the angular distribution in the lower panels are 148 MeV for 1.5 GeV incident energy and 360 MeV for 24 GeV, which are denoted by the dashed lines in the upper panels.
®gure shows that the scaling law is not adequate for the higher energy than 3.5 GeV. Particularly the angular distribution of neutrons from the 24 GeV case (lower right panel) has a strange shape, only forward and backward neutrons are produced by the cascade process in LCS2.7.
To clarify this situation, we plot, in Fig. 11, the pp inelastic cross-section as a function of energy obtained by the JAM code. In this ®gure, we divide the total inelastic cross-section into the fractions of individual channels characterized by the number of produced pions. The gray region
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Fig. 11. pp inelastic cross-section as a function of energy obtained by JAM code. The total inelastic cross-section is divided into individual channel characterized by the number of produced pions. The gray region denotes the component with three pions and more or with another mesons like g; K.
denotes the component with three pions and more or with another mesons like g; K. The fraction of the gray region is 25% at 3.5 GeV and 85% at 24 GeV. Therefore, it is the very limit that we use the original Bertini model up to 3.5 GeV. Moreover, the scaling law of LCS2.7 is obviously inadequate above 3.5 GeV as long as it does not take into account the higher inelastic channels above two pion production.
In NMTC/JAERI97, the EVAP [36] code is used for evaporation and the ®ssion process. It is reported in [11] that the results of EVAP underestimate light nuclei production. Therefore, we have implemented the GEM [11] code, which is a simulation program of the generalized evaporation and ®ssion model, in the nuclear reaction calculation part. The GEM code can treat light nuclei emission up to magnesium taking into account the excitation of the ejectiles. The detail of the GEM model has been discussed in [11]. Here we compare the results of the nuclear reaction calculation by JAM coupled with GEM with experimental data of thin targets for validation. Fig. 12 shows the isotope production crosssections of He, Li and Be from the Ag(p,x) reaction at 480 MeV. The experimental data are taken from [37]. The results of JAM coupled with GEM reproduce the experimental data. The isotopes of Li and Be are hardly produced by the other evaporation models, e.g. the EVAP code in this reaction. 4.2. Thick target We have applied NMTC/JAM to thick target analysis. There do not exist many reliable experimental data of neutron yields from thick targets
Fig. 12. Isotope production cross-sections of He, Li and Be from the Ag(p,x) reaction at 480 MeV. The experimental data are taken from [37]. The results of JAM with GEM are shown by the solid lines.
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with proton beams above 3 GeV. We have picked up two experiments carried out at KEK and AGS for the comparison with NMTC/JAM calculations. For thick target analysis, we have used the same parameters of the JAM models as for thin target analysis. In the actual calculations of thick targets, however, the Bertini model was employed for the intra-nuclear cascade part below 3.5 GeV by using the in-medium nucleon±nucleon cross-sections [4] and JAM was used above 3.5 GeV. This connection between the Bertini and JAM models is due to the reduction in the calculation time. The CPU time of the JAM calculation for one nuclear reaction, which depends on the incident energies and target mass, is about 10 times longer than that of the Bertini model. However, below 3.5 GeV, the results of the dierential cross-sections of the produced particles and nuclei calculated by both models are almost the same, as long as we normalize the total non-elastic cross-sections by the new systematics. Thus we have used the Bertini model below 3.5 GeV. The total CPU time is 0.621 s per one history (17.25 h for 100 000 history) on an Alpha workstation (600 MHz) for the large mercury target system with the 24 GeV proton beam mentioned below. This calculation time is not so long for the various calculations of neutronics design study with realistic geometry. We have ®rst applied NMTC/JAM to the neutron production from lead targets with 12 GeV protons. The experiment has been done in KEK by means of the Mn-bath moderation method with 20 and 10 cm diameter and 60 cm long cylindrical lead targets [38]. Measurements were performed while changing the length of the target in steps of 10 cm in order to obtain the target length dependence of the neutron yields. We have calculated the neutron yield tracing the experimental conditions by NMTC/JAM combined with MCNP4A for the neutron below 20 MeV. We have used the cross-section data of JENDL-3.2 [39] for MCNP4A. Fig. 13 shows the neutron yields as a function of the number of neutrons per incident proton (n/p) as a function of the target length. The open circles (10 cm diameter case) and solid circles (20 cm diameter case) with error bars are data taken from [38], the solid lines are the results of
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Fig. 13. Neutron yields from lead target with 12 GeV protons as a unit of the number of neutrons per incident proton (n=p) as a function of the target length. The open circles (10 cm diameter) and solid circles (20 cm diameter) with error bars are data taken from [38], the solid lines are the results of NMTC/JAM, while the dashed lines denote that of LCS2.7, respectively.
NMTC/JAM, while the dashed lines denote that of LCS2.7, respectively. The results of NMTC/JAM reproduced quit well the experimental data. On the other hand, the results of LCS2.7 overestimate the neutron yields at deeper positions in the target. It might be due to the failure of the scaling law used in LCS2.7 at 12 GeV as discussed in the previous section. Next, a comparison is done for experiments under the AGS spallation target experiment (ASTE) collaboration [41]. This experiment has been carried out using a thick mercury target, which is a 20 cm diameter and 130 cm long cylinder and detecting the reaction rate distributions along the cylindrical surface of the target by activation techniques at incident proton energies of 1.6, 12 and 24 GeV. Various activation detectors such as the 115 In n; n0 115m In, 93 Nb(n; 2n)92m Nb and 209 Bi(n; xn) reactions with threshold energies ranging from 0.3 to 70.5 MeV were employed to obtain the reaction rate data for estimating
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spallation source neutron characteristics of the mercury target. In the calculation, the reaction rate is obtained from the neutron ¯ux multiplied by the activation cross-sections. We have used dosimetry cross-section set of [40]. Fig. 14 shows the distribution of the 209 Bi(n,4n)206 Bi reaction rates along the cylindrical surface of mercury target bombarded with 1.6, 12 and 24 GeV protons. The threshold of this reaction is 23 MeV, while the most eective energies of neutron for this reaction is about 30 MeV. Other results are shown in Fig. 15 for the 27 Al n; a24 Na reaction rate. The threshold of this reaction is 3.3 MeV, while the most eective energies of neutrons for this reaction is about 10 MeV. The results of NMTC/JAM, denoted by the solid histograms in these ®gures, reproduce the experimental distribution quite well for all positions and all energies,
Fig. 15. Distribution of the 27 Al n; a24 Na reaction rates along the cylindrical surface of a mercury target bombarded with 1.6, 12 and 24 GeV protons. The solid histograms denote the results of NMTC/JAM.
Fig. 14. Distribution of 209 Bi(n,4n)206 Bi reaction rates along the cylindrical surface of a mercury target bombarded with 1.6, 12 and 24 GeV protons. The solid histograms denote the results of NMTC/JAM, while the dashed lines show the results of LCS2.7, respectively.
though the result at 1.6 GeV in Fig 14 slightly underestimates the data. In Fig. 14, we also plot the results of LCS2.7 by the dashed lines. The results of LCS2.7 at 1.6 GeV in Fig 14 is almost the same as that of NMTC/ JAM. This is reasonable, since NMTC/JAM also uses the Bertini model for the intra-nuclear cascade part as in LCS2.7 at this energy. As we increase the incident energy, however, the discrepancy between them becomes large. The results of NMTC/JAM still reproduce the experimental distributions quite well for all positions. The results of LCS2.7, however, overestimate the reaction rate particularly at deeper positions. This trend is very similar to the results shown in Fig. 13. Accordingly, the peak position is shifted to the deeper position in the LCS2.7 results. Therefore, it also might be due to the inadequacy of the scaling law used in LCS2.7 at 12 GeV. As discussed in Fig. 10, the high-energy neutrons produced in proton-
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induced reactions at the energies above 3.5 GeV by LCS2.7 are restricted in the very forward angle and backward angle. Then these high-energy neutrons stay in the target and collide with the other nuclei again and again. By these facts, it can be explained that the neutron yields by LCS2.7 overestimate the data particularly at deeper positions, at incident energies above 3.5 GeV. On the other hand, the results of NMTC/JAM can predict precisely the peak position of the reaction rate as well as the absolute values of various reaction rates for all incident energies. 5. Summary We have developed a high-energy nucleon± meson transport code NMTC/JAM, which is an upgraded version of NMTC/JAERI97. We have introduced two new physical models in NMTC/ JAM, the high-energy nuclear reaction code JAM for the intra-nuclear cascade part and the generalized evaporation model GEM for the evaporation and ®ssion process. The JAM code can extend the applicable energy range of NMTC/JAM in principle up to 200 GeV for nucleons and mesons. While the GEM code enables us to calculate the light nucleus production like Be isotopes from the excited residual nucleus. These nuclei as well as the ®ssion products are very important in view of the radiation safety for estimating induced radiation activities and dose rate in the spallation neutron source facility driven by high-intensity proton beam. For the validation of JAM, we have compared the elementary hadron±hadron cross-sections and the particle production cross-sections from thin targets with the experimental data. It is found that JAM can reproduce the experimental data for the energy range up to several tens of GeV. For the particle transport part of NMTC/JAM, we have upgraded the nucleon±nucleus non-elastic and elastic cross-sections by employing new systematics. We have compared the calculations by NMTC/JAM code with the experimental data of thick targets measured at KEK-PS and AGS for proton-induced reactions up to several tens of GeV. The results of the NMTC/JAM code show
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excellent agreement with the experimental data. From these new calculation functions and the code validation, NMTC/JAM enables us to carry out the radiation transport analysis of a large-scale target system with complex geometry more accurately and easily than before.
Acknowledgements The authors would like to thank Dr. S. Furihata of MRI for supplying the GEM code. They also thank Dr. Y. Nara for his useful comments on the JAM code. They are grateful to Dr. T. Fukahori and Dr. S. Chiba for their useful discussions about parameterization of the nucleon±nucleus cross-sections. References [1] B.R. Appleton, in: Proceedings of the 14th Meeting of the International Collaboration on Advanced Neutron Sources, Illinois, Vol. I, ANL-98-33, Argonne National Laboratory, 1998. [2] S. Nagamiya, in: Proceedings of Ninth International Conference on Radiat. Shielding, ICRS-9, Tsukuba, Japan, 17±22 October 1999, J. Nucl. Sci. Technol. (Suppl. 1) (2000) 40. [3] N. Watanabe, M. Teshigawara, T. Kai, M. Harada, H. Sakata, Y. Ikeda, M. Kaminaga, R. Hino, Y. Oyama, in: Proceedings of ICONE-8 8th International Conference on Nuclear Engineering, 2±6 April 2000 Baltimore, MD USA, ICONE-8457. [4] H. Takada, N. Yoshizawa, K. Kosako, K. Ishibashi, An Upgraded Version of the Nucleon Meson Transport Code; NMTC/JAERI97, JAERI-Data/Code 98-005, 1998. [5] J.F. Briesmeister (Ed.), MCNP General Monte Carlo NParticle Transport Code, Los Alamos National Laboratory, LA-12625-Mm, 1997. [6] For Example, F.C. Di®lippo, L.A. Charlton, J.M. Aragones (Eds.), in: Proceedings of International Conference M&C '99, Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, Madrid, Spain, 27±30 September 1999, Senda Editrial, S. A., Vol. 2, 1999, pp. 949±954. [7] For example, J.R. Alonso, in: AccApp'98, 2nd International Topical Mtg. on Nucl. Application of Accelerator Technology, American Nuclear Society, Gatlinburg, TN, 20±23 September 1998, pp.197±201. [8] H.W. Bertini, Monte Carlo calculation on intranuclear cascade, ORNL-3833, Oak Ridge National Laboratory, 1963.
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