Conseil Scientifique et Technique du SPhN

RESEARCH PROPOSAL

Title: Modeling of spallation reactions and applications

Experiment carried out at:

Spokes person(s): S. Leray

Contact person at SPhN:

Team at SPhN: A. Boudard, J.C. David and D. Mancusi

List of IRFU divisions and number of people involved:

List of the laboratories and/or universities in the collaboration and number of people involved:

J. Cugnon, University of Liège (Belgium)

1 SCHEDULE

Possible starting date of the project and preparation time [months]:

Total beam time requested:

Expected data analysis duration [months]:

2 REQUESTED BUDGET

Total investment costs for the collaboration:

Share of the total investment costs for SPhN:

Investment/year for SPhN: 10 k€

Total travel budget for SPhN:

Travel budget/year for SPhN: 20 k€

3 If already evaluated by another Scientific Committee:

If approved Allocated beam time: Possible starting date:

If Conditionally Approved, Differed or Rejected please provide detailed information:

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CSTS SPhN, June 26, 2013

Modeling of spallation reactions and applications

S. Leray, A. Boudard, J.C. David and D. Mancusi

1 Background

During the last fifteen years, the SPALLATION group of SPhN has been studying spallation reactions by combining experimental and theoretical approaches with the objectives of:

Performing constraining experiments in order to gain deep insight of the reaction mechanism;

Providing predictive reaction models, based on physics understanding and therefore with a minimum number of free parameters, validated on an extensive set of experimental data;

Implementing these models into high-energy transport codes, which are used for various applications of spallation reactions.

This was motivated by both a fundamental interest in reaction mechanism understanding and by the numerous possible applications of spallation reactions, such as spallation neutron sources, projects of accelerator-driven sub-critical reactors (ADS) that could be used to transmute long-lived radioactive waste, radioactive ion beam facilities, hadrontherapy, cosmic ray studies, radiation protection of astronauts and radiation damage to microelectronics circuits near accelerators or in space missions, and simulation of detector set-ups in nuclear and particle-physics experiments. On the experimental side, after the program carried out at the FRragment Separator of GSI using the reverse kinematics technique, which has allowed for the first time to measure the complete isotopic distributions of the residues produced in spallation reactions [Wla00, Arm04,Fer05, Vil07], the group initiated the SPALADIN project, again in GSI. These experiments were devoted to the measurement of the spallation residues in coincidence with neutrons and light charged particles with the goal of constraining the models. The first experiment, Fe+p at 1 GeV, has permitted studying the different de-excitation modes as a function of the excitation energy in a light system [Leg08]. The second experiment, Xe+p, was the subject of a PhD Thesis in the group [Gor12] and suggests that multifragmentation is not necessary to explain the intermediate mass fragment production, contrary to what was claimed in [Nap07]. The full results will be published soon. This program was originally meant to last several years with the study of different systems in order to bring constraints on the de-excitation models on the whole range of nuclear masses and a wide range of excitation energies. The initial experiments with the SPALADIN setup were expected to be supplemented at FAIR R3B by the construction of a Time Projection Chamber which, combined with the GLAD magnet, would have permitted full mass and charge identification of all the produced fragments up to uranium and therefore, a kinematically complete reconstruction of the reaction events. Unfortunately, in view of the insufficient available manpower and expected cost of the TPC, this project could not be pursued. More recently, the group became involved in the FIRST program, which uses part of the SPALADIN setup and aims at studying the fragmentation of carbon and other light nuclei for hadrontherapy and space applications. The first experiment for C+C and C+Au at 400 MeV/u was successfully performed

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in 2011 [Ple12, Abo12]. Preliminary results have been presented at the INPC conference [Pat13]. Further experiments, with lighter beams, Li and He, for hadrontherapy, and Fe for space applications, are foreseen but depend on the availability of the beam and experimental area at GSI. Regarding theoretical studies, the Spallation group has a long-standing collaboration with J. Cugnon from the University of Liège about the development of the intranuclear cascade code INCL. The intranuclear cascade approach has been shown to be equivalent to the resolution of transport equations of particles interacting by binary collisions inside a nuclear mean-field. Its theoretical foundation is not inferior to other models like Glauber, optical models or DWBA [Bun85] and it allows predicting all cross sections corresponding to incoherent processes, providing differential cross-sections, spectra of particles and nuclei and correlation functions, in a wide range of energies and target mass. The conditions of validity have been also extensively discussed and a lower limit around 100 MeV for a proton beam on targets of at least 10 nucleons is commonly accepted. The high energy limit arises in principle when other degrees of freedom come into play, i.e. at a few tens of GeVs, but in practice is lower due to the fact that only a limited amount of channels are taken into account in the nucleon-nucleon interaction. The basic model (INCL4.2) has no free parameter since it uses experiment-based elementary interactions and target densities and ingredients such as average nuclear potential, the way to implement the Pauli blocking, Coulomb barriers for outgoing particles and stopping time have been fixed once for all. This makes it a predictive tool in its domain of validity. Some phenomenology was however introduced with the coalescence process added to describe the high energy tail observed in the experimental data [Bou04]. The model is sometimes used in transport codes well below its strict limits of validity, which may be lower than commonly believed [Yar07]. Therefore, we have worked on its extension to low energies, adding an ad-hoc compound nucleus model with a smooth transition to the INC picture and a proper account of exact reaction Q values for all channels. For the full calculation of observables, the remnant nucleus generated by the cascade, characterized by its mass, charge, excitation energy and angular momentum has to be decayed by the so called de-excitation models. There is a wide choice of models but none of them is unambiguously established and all of them include a large part of phenomenology in their practical realization. Although ABLA [Jun98] is the model we most often use, we have also coupled INCL with the most well-known ones, GEM [Fur00], SMM [Bon95] and Gemini [Cha08], so that we could make extensive comparative studies of observables. We have collaborations with the authors of ABLA, Gemini and GEM in view of possible further improvements of these models. The INCL4.2 version [Bou02] coupled to the ABLA de-excitation model [Jun98] from the group of K.H. Schmidt at GSI brought significant improvements with respect to other existing models, in particular in the prediction of spallation residues. This version was implemented into the widely used transport codes, MCNPX [Hen05] and, after a transcription in C++, in GEANT4 [Hei08, Kai10]. Since then, the group has worked on numerous improvements and extensions of INCL4, such as the production of composite particles through a coalescence mechanism in phase space [Bou04], the introduction of an energy and isospin dependent average single-particle potential [Aou04], the improvement of pion production [Aou06]. This work led to the INCL4.5 version [Cug09], which, coupled to the new ABLA version (ABLA07) [Kel09], was proven to be one of the best models on the market during the Benchmark of Spallation Models [IAE08, Ler11] organized under the auspices of IAEA. This is illustrated in Figure 1, in the case of the prediction of cross sections for double-differential neutron-production and for residual nuclei.

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Fig. 1. Result of the IAEA benchmark of spallation models: average evaluation of the different models regarding the prediction of: (left) neutron double-differential cross-sections, (right) residual nuclei production rates as a function of their mass or charge. The model has since been further improved and adapted to lower energies. In parallel, the code has been totally re-written in C++: this version, INCL++, has been extended to light ion induced reactions [Man12], in view of applications to hadrontherapy. In consideration of its success, INCL4 has been implemented in three of the most used simulation codes in the world, PHITS [Iwa02], in which it is now the default option, GEANT4 [Ago03], and a β-version of MCNPX. This allows simulating devices or facilities using spallation reactions.

2 Recent achievements

2.1 New potentialities of the model

A new version, INCL4.6, very similar to INCL4.5 for nucleon-induced reactions above 100 MeV but significantly improved for composite projectiles and energies below 100 MeV, has recently been released and is the subject of a paper in Physical Review C [Bou13]. We present here some of the main features of INCL4.6. 2.1.1 Cluster emission In INCL4 a mechanism based on surface coalescence in phase space has been introduced in [Bou04]. It assumes that a cascade nucleon ready to escape at the nuclear surface can coalesce with other nucleons close enough in phase space and form a cluster that will be emitted if its energy is sufficient to overcome the Coulomb barrier. All possible clusters are formed and the priority is given to the one with the lowest excitation energy per nucleon. In the last version of the model, the mechanism, originally limited to helium, has been extended to clusters up to mass 8 and we have revisited the phenomenological parameters of the model, which include the size of the phase space cell in which nucleons should be to form a cluster and the distance from the surface at which the clusters are built. It should be stressed however that, like all the ingredients and parameters of INCL4, once chosen, the coalescence parameters are kept constant whatever the system studied.

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Fig. 2. Double-differential cross section for alpha (left panel), 6He (central panel ) and 6Li (right panel) cluster production in p + 197Au collisions at 1200 MeV. The predictions of INCL4.6+ABLA07 (red histograms) are compared with the experimental data of [Her06] (black points) at different angles, indicated in the panels. The green histograms indicate the cascade component. In Fig.2, experimental data from [Her06] for alpha, 6He and 6Li production double-differential cross sections, in the p+Au reaction at 1.2 GeV, are compared to the model predictions. A very good agreement can be observed all along the energy spectrum. In order to emphasize the importance of the coalescence mechanism the green curve shows its contribution to the total production cross-sections. For 6He, as already observed in [Ler10] for 3He, it represents the major part of the production cross section. 2.1.2 Low-energy composite-particle induced reactions Although the INCL4 model was originally designed to handle reactions with composite particles up to alpha, little attention had been paid to this topic up to recently. However, when the model is used in transport codes to simulate for instance a complex spallation target, secondary reactions induced by composite particles generated in primary collisions can be of importance. Since data libraries available in public transport codes do not consider reactions induced by complex particles yet, models are to be used. It is therefore necessary to ensure that INCL correctly predicts at least the gross features of these interactions, although this falls well beyond the alleged theoretical limit of validity of INC models. This is why the treatment of low-energy composite particle induced reactions has been improved in [Bou13]. Let us summarize the main modifications:

the composite projectile is described as a collection of off-shell nucleons with Fermi motion, ensuring full energy and momentum conservation;

geometrical spectators, i.e. nucleons not passing through the target volume, are put on-shell and the energy needed to preserve a correct balance is taken from the participant nucleons;

if one nucleon enters the target below the Fermi level, all geometrical participants are assumed to fuse with the target nucleus and produce a compound nucleus, which is subsequently passed over to the de-excitation model. Otherwise, participants initiate a usual cascade process;

the projectile Coulomb deviation is now explicitly taken into account;

experimental mass tables are used to ensure correct Q-values for all the reaction channels.

The model is now able to rather well predict helium-induced total reaction cross sections [Bou13]. It

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also reasonably reproduces the different reaction channels that open with increasing incident energy. This is illustrated in Fig.3 which shows experimental 209Bi(α, xn) cross sections as a function of the incident particle kinetic energy, from the EXFOR experimental nuclear reaction database, compared with the model.

Figure 3. Excitation functions for the 209Bi(α,xn) cross sections for x=1 to 6. The curves correspond to the predictions of the INCL4.6+ABLA07 model. The experimental data were compiled using the experimental nuclear reaction database EXFOR. From [Dav13]. 2.1.3 Light-ion (beyond A=4) induced reactions A first attempt to extend INCL to light-ion-induced reactions is described in [Bou09]. However, this was done very crudely by considering the projectile as a collection of free nucleons. Recently, the model has been revisited on the basis of the INCL4.6 version and implemented into the C++ version, which has been included in the last GEANT4 release [Man12]. Although the treatment of the projectile and target is still not symmetrical, some features related to the projectile spectators are better controlled. In this model, the projectile is described as a collection of nucleons whose positions and momenta are drawn from realistic distributions and satisfy the center-of-mass constraint of zero total momentum. For each configuration, the depth of a binding potential is determined so that the sum of the nucleon energies is equal to the mass of the projectile nucleus. The projectile is then boosted with the nominal beam velocity. The nucleons that do not interact with the calculation sphere are combined together in the "projectile spectator". Nucleons crossing the sphere without any NN interaction are also combined in the "projectile spectator" at the end of the cascade. A fusion mechanism, similar to the one described above for composite particle induced reaction, is also included. The excitation energy of the projectile spectator nucleus is obtained by an empirical particle-hole model. Four-momentum is globally conserved. This nucleus is then given to the de-excitation model. In this model, this "projectile spectator" has not received any explicit contribution from the zone of interaction which is entirely contained in the target. Therefore, the calculation is not projectile-target symmetrical and, while this is not very important for particle emission, it is problematic for residues, the residue of the target being a priori more realistically treated than the "projectile spectator". This means that to compare with experimental data, if emanating from projectile fragmentation, the results of the calculation should be done in "inverse kinematics" with the target fragments from the calculation Lorentz-boosted to become projectile fragments. Comparisons of 12C + 12C experimental data to both "direct" and "inverse kinematics" simulations confirmed that the latter provides a better agreement [Ler12].

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Fig.4: Neutron production double differential cross sections in the 12C + 12C system at 135 (left) and 290 (right) MeV/u [Sat01] compared to INCL++, INCL4.3, both in inverse kinematics, and BIC, all INC coupled to the GEANT4 de-excitation handler. Fig.4 shows double-differential neutron production cross-sections measured in the 12C + 12C system at 135 and 290 MeV by Sato et al. [Sat01] compared with the present model, the former version INCL4.3, both in inverse kinematics, and the binary cascade (BIC) [Fol04], all models being coupled to the GEANT4 de-excitation handler [Que11]. It can be observed that the present model better reproduces the data than the former version and that BIC is definitely less good.

2.2 Examples of applications

As above mentioned INCL4.6 is now implemented into PHITS [Nii10] and in a β-version of MCNPX [MCN07], coupled respectively to the GEM and ABLA07 de-excitation models. The C++ version, INCL++, extended to light-ion beams up to 18O, associated to the Geant4 de-excitation handler, is included into GEANT4 [Ago03]. This allows simulations of thick targets. A few examples of recent simulations for applications are presented below. 2.3.1 Radioactive inventory of the ESS target Simulations of the helium-cooled rotating tungsten target foreseen for the ESS facility have been done using INCL4.6-ABLA07 implemented into MCNPX. This work was carried out in the framework of the WP11 (Waste disposal, emissions, dismantling and decommissioning) of the ESS Target Station Design Update (TDSU). The goal was determining the radioactive inventory [Lep13] and identifying the major contributors to the radiotoxicity and their production channels. In order to estimate the reliability of the simulation, the model has been compared, when possible, with elementary experimental production cross-sections (excitation functions). Examples of such excitation functions are displayed in Fig.5 for two nuclides that pose issues for radiation protection: 148Gd, which is an alpha emitter, and tritium. In most of the cases where elementary experimental data are available, the model reproduces them generally within a factor smaller than 2, implying a similar degree of confidence for the estimation of the radioactive inventory.

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Fig. 5: Experimental production cross sections of 148Gd (left panel) in p+W reactions and tritium (right panel) in p+Pb reactions compared with INCL4.6-Abla07. From [Lep13]. The ESS target is composed by 11 tungsten layers of different thicknesses surrounded by 2 mm of helium. The detailed geometry of the target and surrounding materials has been simulated with MCNPX and CINDER’90 has been used to take into account the production by low energy neutrons and decay of the different isotopes. In Figure 6, the activity at the end of an irradiation time of 3.6 years (left) and after a cooling time of 156 days (right), due to the different spallation products generated in the tungsten is represented on a chart of nuclides.

Figure 6: Nuclide activity (in Bq, see color code on vertical scales) in the ESS tungsten target irradiated during 3.6 years, just after shut down (left), after 156 days off beam (right), obtained by INCL4.6-Abla07 in MCNPX+CINDER’90 on a chart of nuclides. From [Lep13]. The left panel illustrates the very large number of radioactive nuclei produced in spallation reactions and the high level of the induced radioactivity. Although most of the generated nuclides are short-lived and have disappeared after 6 months (right panel) the total activity has only been reduced by a factor 7, mainly because it is due to a small number of major contributors, among which tritium(half-life ~12 years). As stressed in the preceding section, the fact that elementary reactions have been shown to be well predicted by our model gives confidence in the full simulation. 2.3.2 Astatine production in the ISOLDE target Some time ago, the IS419 experiment at the ISOLDE facility at CERN measured the production of astatine isotopes from a liquid lead-bismuth eutectic (LBE) target irradiated by a proton beam of 1 and 1.4 GeV [Tal07]. These isotopes are produced through the following mechanisms: either 209Bi(p,π-xn)210-xAt, i.e. double charge-exchange in primary reactions, or secondary reactions induced by helium nuclei produced in primary collisions, 209Bi(3He,xn)212-xAt and 209Bi(4He,xn)213-xAt. The simulation of the ISOLDE experiment with MCNPX [Dav13] (Fig.7 left) has actually revealed that isotopes with mass larger than 209 are produced only through secondary helium-induced reactions,

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4He playing a larger role and leading to higher masses, while the lightest isotopes are mostly populated by double charge-exchange reactions.

Fig.7. Left: Number of nuclei produced per incident proton for the different astatine isotopes as predicted by INCL4.6-ABLA07 implemented in MCNPX for the ISOLDE LBE target irradiated by 1.4 GeV protons: black total production, green: production through (p, π-) reactions; red and blue: through secondary reactions induced by alphas and 3He respectively. Right: Astatine release rates from [] at 1.4 GeV compared to MCNPX simulations, assuming an average release time of 10 hours, with INCL4.6-ABLA07 (red line), INCL4.6-ABLA07 without cluster production by coalescence (green line) and CEM03 (blue line). From [Dav13].} Fig.7 shows the result of the MCNPX simulation with INCL4.6-ABLA07 compared to the ISOLDE data at 1.4 GeV for the total production yields of astatine isotopes. An average release time from the liquid metal of 10 hours has been assumed during which the radioactive decay of the different isotopes is taken into account. A remarkable agreement between the calculation and the experiment is observed, regarding not only the shape of the isotopic distribution but also the absolute release rates. Clearly all the new features discussed in the preceding sections, in particular the better handling of low energy helium-induced reactions, have considerably improved the predictive capability of our model compared to the version used in [Tal07]. In order to emphasize the importance of the secondary reactions induced by clusters produced during the cascade stage through our coalescence mechanism, a calculation has been performed switching off this mechanism. The result is presented as the green curve and exhibits a severe deficit of heavy isotopes. Obviously, a model unable to emit high energy helium nuclei cannot be expected to correctly predict astatine production in a LBE target, since only a small fraction of the heliums produced in the evaporation stage has enough energy to undergo a reaction before being stopped. This is the case of the MCNPX default model option, Bertini-Dresner. In the same figure, the results are also compared with CEM03 [Mas06] (blue line). It is interesting to note that this model is not able to account for the measured yield of the heavy astatine isotopes. In fact, CEM03 does have mechanisms to produce high-energy helium nuclei; however, helium-induced reactions are handled by the Isabel INC model, which apparently provides an incorrect description in the relevant energy range.

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2.3.3 Fragmentation of carbon in PMMA targets With the INCL++ model implemented into GEANT4, it is possible to perform simulations of beam fragmentation experiments in thick targets, which are generally done for hadrontherapy applications. An experimental set of data concerning nuclear charge distributions from the fragmentation of a 95 MeV/u 12C beam in different thicknesses of PMMA (material mimicking the human body) targets was measured at GANIL by Braunn et al. [Bra11]. Fig.8 presents the results for the 5 mm target, at two different angles. They are compared with our model, BIC and QMD from [Koi08], also available in GEANT4. All models are coupled to the GEANT4 de-excitation [Bra13a].

Fig.8: Charge distribution of fragments produced by a 95 MeV/u 12C beam in a 5 mm PMMA target, at 10° (left) and 20° (right), measured by [Bra11] (red triangles), compared with INCL++ (blue crosses), BIC (blue circles) and QMD (blue squares).From [Bra13a]. It can be observed that all models reproduce rather well the light ion cross-sections (up to Z=4) but ours tends to underestimate higher charges at 10° while BIC and QMD overestimate these elements. INCL++ and QMD are better at 20°. In general, QMD seems to provide only a slightly better agreement with the data, at the expense of a much longer CPU time.

2.3 Requests from users

Among the numerous requests that we have recently received, and which could lead to interesting developments, let us mention:

A collaboration with I. Leya from university of Bern lasts for several years around galactic cosmic rays (GCR) and their interaction with interstellar medium, and more precisely on meteorite studies. These bodies are bombarded mostly by protons and alphas from the GCRs whom spectra are peaked in the spallation energy regime. Our contribution has been mainly to provide the needed elementary isotope production for several types of targets in the whole energy range [Amm08]. Thanks to the new performances of INCL at low energies and with composite particles as projectiles, better determination of elementary neutron cross sections (necessary inside the meteorite) is in progress and the role of alpha particles will be studied.

In the same line, V. Tatischeff from the CSNSM has asked our model in view of calculating the production of light nuclei produced in the interaction of galactic cosmic rays in the atmosphere.

The results obtained within the astatine study [Dav13] has led D. Schumann and D. Kiselev from PSI to ask us the possibility to use the new INCL in MCNPX to simulate polonium isotope production in a lead target irradiated at SINQ for more than one year. Actually, they performed measurements and preliminary calculations didn't fit at all the experimental data. The same

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calculations using INCL gave much better results. More detailed simulations (geometry) are foreseen.

The PISA collaboration (Cracow, Jülich), which is presently analysing data about light charged particles and intermediate mass fragments produced in light targets on a wide bombarding energy range [Fid11]. These data will be very useful to further constrain our coalescence model.

A longstanding collaboration is established with Y. Titarenko from ITEP (Russia) who measures very valuable excitations functions on numerous targets [Tit11a, Tit11b]. He will be associated to the future European CHANDA project [CHA13] for which he will provide tritium production cross-sections.

2.4 Involvement in European projects

The group has been involved in various European projects, which provided us the funding for postdocs. In the FP5 HINDAS [HIN05], FP6 EUROTRANS/NUDATRA [EUR05] and FP7 ANDES [AND10], we have been coordinating the work-packages devoted to high-energy data in relation with studies for accelerator-driven sub-critical reactors (ADS). The goal was basically to provide reliable simulation tools for the optimization of the spallation target for such a facility and the assessment of the radiation protection and material damage problems related to high-energy reactions [Ler06, Ler08]. The new version of the model has for instance permitted a significant improvement of the prediction of gas production in spallation targets [Ler10, Ley08]. Calculations of spallation targets have also been performed in the framework of the EURISOL [Rap06] and MEGAPIE [Lem08, Zan11] projects. We have also participated in the PROUESSE ANR project [PRO09], led by the CEA/DRT, which aimed at developing a fast MonteCarlo code for treatment planning in protontherapy. In this project, we have provided a library specific for proton therapy, built in collaboration with A. Koning, author of the TALYS code [Bra13b]. Also, we are part of the JRA SiNuRSE (Simulations for Nuclear Reactions and Structure in Europe) in the European project ENSAR, in which we are responsible for the Task devoted to the development and benchmarking of physics based event generators and our duty is to provide improved event generator for light-ion induced reactions and for few nucleon removal channels [Lou11].

3 Future programme

The Spallation group is world-renowned as specialist of the field of high-energy (spallation) reactions. Thanks to the work realized during the last fifteen years, the INCL model is considered as one of the best models on the market, if not the best one, and is now available in three of the most used radiation transport codes for simulations of devices or systems implying spallation reactions. It is quite clear that this success comes from the fact that the group has been combining work on experimental measurements, development of theoretical models, benchmarking and validation against extensive sets of experimental data and simulations for applications, leading to a unique global expertise built along the years. After the group has been led to renounce to his experimental program at R3B, we decided to focus on model development, although a modest experimental activity is remaining with the involvement in FIRST project. This program is expected to continue taking data in the coming years. Regarding the development of INCL4, it is clear that we have reached a point where the historical core of the model, i.e. the part corresponding to nucleon and light-charged-particle induced reaction between 100 MeV and 3 GeV, is globally satisfactory although it can still be improved in specific

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regions. It is therefore the right time to think about our strategy for the future, which aims a,t simultaneously, exploiting the model in new domains, for instance exotic nuclei, and extending its scope towards several directions. This is what we present in the following. Let us say first that the program of work we propose is motivated by several considerations:

Our main goal is the understanding of the reaction mechanisms, which is fundamental per se but also for reaching information on nuclear structure. We want to extend in priority the scope of our model towards directions that correspond to emerging key questions in nuclear physics. This is why, to our feeling, the inclusion in the model of strangeness production channels, which should allow studies of hypernuclei seems to us a very promising direction and will be our priority.

Our second goal is to broaden the scope of applications of the model. Needs for hadrontherapy and space applications motivate the extension to light-ion induced reactions.

We have always tried to include as much known microscopic physics as possible and limit the number of phenomenological parameters, which for those remaining are kept constant whatever the studied reaction. This is certainly one of the reasons of the high predictability of our model. We want to continue on these bases for the extension towards higher energies and heavy ion collisions.

The utilization of our model by identified users, i.e. groups with whom we have established more or less tight collaboration, and by unidentified users through the use of the transport codes in which the model is implemented, engages our responsibility. It means that we have to settle possible problems but also respond to requests of improvements in specific regions and, at least, consider requests for extension of the model to types of reaction not taken into account. This sometimes leads to interesting physics questions, as shown by the example of one nucleon removal channel cross sections.

We would like to keep a strong link to experimental groups, if possible inside the SPhN, since we find this necessary to access to high-quality data and influence the choice of experiments that could be useful to enlarge our physics understanding.

Most of the application-oriented developments are being done in the framework of European projects. A recurrent question we have to face concerns the uncertainty of the predictions of our model. We would like to address this issue in the future.

3.1 Further improvements of the model

Although, as above said, the model has a high degree of predictability in its general domain of application, there remain some specific points, which need to be improved, and which sometimes can be important for a particular physics field. Also, sometimes, in its utilization inside transport codes, our model is used outside its strict range of validity, for instance at low energies or with very light targets. We have, at least, to guarantee that reasonable results are provided. Therefore, a continuous limited amount of work has to be devoted to this task. Let us here point out some of these points that we have already identified and for which often work has already begun.

Heavy clusters The extension to clusters of mass up to 8 of the phenomenological mechanism of coalescence in phase space that was introduced in the last version of the model reproduces data at high incident energies reasonably well [Cug10]. However, it seems too strong and less adapted at energies around 200 MeV. We have started revisiting the ingredients of the coalescence mechanism, with the help of M. Hagiwara from KEK who spent one year in Saclay and who has participated to experiments in Japan that will be useful to constraint our parameters. This work is continuing and will also benefit from the new data from PISA.

Nuclear structure effects, exotic nuclei Up to now, the reactions that were studied mostly involve stable target nuclei. Therefore, the scope

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of the nuclear model at the core of INCL is limited to global properties and does not contain nuclear structure effects that would possibly become important in exotic nuclei, such as different space and momentum distributions for neutrons and protons or deformation. It is clear that structure effects are also important in the de-excitation stage, but it is necessary to first well handle the entrance channels and dynamical effects. Recently, we have begun collaboration with A. Obertelli in view of applying our model to the prediction of one-nucleon removal channel cross sections. Encouraging results were found [Lou11], in particular compared to the Glauber approach often used in this domain of physics. Comparison of our model to experimental data taken at RIKEN, on the other hand, seems to indicate that INCL4 (and other INC models) fails to reproduce the removal of the most bound nucleon. This likely originates from a too low excitation energy associated with the removal of one single nucleon in the cascade stage. Work is in progress to understand the deep reason of this failure, which seems common to all intranuclear cascade models, and find a remedy.

3.2 High-energy extension

The present INCL model is assumed to be usable up to 2.5-3 GeV, for nucleon, light ion and pion induced reactions. Although already open at these energies, strangeness production channels are not taken into account. With the availability of INCL in high-energy transport codes, there is an increasing request of potential users for an extension above 3 GeV up to 10-15 GeV, since it seems that the models used in this energy range have not the same level of predictability and validation as INCL. For instance, N. Mokhov, developer of the MARS code at Fermilab has expressed a strong wish for a version able to predict kaon production in view of the kaon factory envisaged in the framework of Project X. In Europe, the future FAIR facility will provide beams of ions in this energy range, but also of antiprotons. Furthermore, the study of hypernuclei seems to become a key promising domain of research in nuclear structure. In view of all these potential applications, we see a rather clear scheme for the extension of INCL to cover a much broader range of reactions, with the objective of achieving a similar level of reliability and validation as in the lower energy range. This should involve inclusion of multi-pion production channels, of strange particle production, addition of anti-proton-induced reactions, the amount of work and the difficulty being different for each item. 3.2.1 Multi-pion channels The present limitation of the model to 2.5-3 GeV is mostly due to the fact that the only inelastic nucleon-nucleon channel taken into account is NN→NΔ1232. The Δ resonance then propagates as a quasi-particle and can decay into Nπ according to its width and helicity or be reabsorbed. Pions move in a specific potential and can interact through πN collisions. At energies above 2.5-3 GeV, it is clear that other inelastic channels become significant and have to be taken into account. Generally, this is done by introducing additional heavier resonances [Nii95]. These resonances have a larger and larger width and are more and more overlapping with increasing mass. This raises some doubt about the usefulness of considering these resonances as individual objects. Furthermore, the interaction of these objects with nucleons is not well known. Considering that these resonances are too short-lived and too much overlapping for their degrees of freedom to really show up in the collision process, we can adopt the other, somehow opposite, assumption that NN and πN collisions lead directly to the final products, which should essentially be nucleons, pions and strange particles. This approach has recently been explored by a PhD student of J. Cugnon who has introduced multi-pion channels in the INCL4.2 version. The multiple-pion-production cross sections were deduced from experimental data using the procedure given by Bystricky et al. [Bys87]. This procedure is based on isospin symmetry so the knowledge of all the particular cross sections is not necessary and allows

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limiting the use of cross sections fitted on scarce data. A simple model fitted on available experimental data has been adopted for the energy and momentum distribution of the emitted pions.

Fig.6: Double-differential cross sections for π− production in proton-induced reactions on Pb at 5 GeV/c (left), for π+ production on Cu at 12 GeV/c (right) incident momentum. Data (symbols) from HARP collaboration [HAR08] are compared with the standard version (red lines) and the multi-pion version (blue lines) of the INCL4 model (from S. Pedoux PhD Thesis). The agreement between the extended version INCL HE and the experimental data is fairly good, the order of magnitude of the cross sections is in agreement with the data, even though there are discrepancies for production of pions with momentum smaller than 250 MeV/c [25]. However, this work was done within the old version of the model, which has no pion potential, no energy and isospin dependent nuclear potential, no cluster emission. The implementation of the work performed by S. Pedoux in the INCL4.6 version is in progress.

3.2.2 Strange particle production Besides the expectation from users of our code, our main motivation for the inclusion of strange particle production into INCL++ is the possibility to use it in hypernuclei research, which could emerge as a future line of research in SPhN. Indeed, the study of hypernuclei, i.e. nuclei comprising strange baryons (hyperons, Y), is a promising subject, attracting a growing community, in particular in Japan and in Europe. This could bring new constraints on the strong interaction since the existence of hypernuclei depends as much on the YN as on the NN interaction. Their lifetime also is strongly determined by the YN interaction. Some« traditional » nuclei (with S=0), which are not bound by the strong interaction, may become bound by addition of a hyperon. Therefore, the knowledge of the hypernucleus driplines, by comparison with those of S=0 nuclei, may bring key information. The existence of hyperons in neutron stars is also a controversial subject [Gle85]. Other new possibilities and open questions concern [Cug98, Sch98]:

Λ and K+ as sensitive probes of the nucleus interior thanks to the no Pauli-blocking of Λ (compared to nucleon) and to the needed strangeness conservation in strong interaction which leads to a long K+ mean free path in the nucleus;

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the mesonic weak decay of the Λ being often Pauli blocked (Λ + N) the non-mesonic channel becomes the main channel and then can be studied [Gib95, Bot12b];

while it is generally admitted that the Λ potential is attractive, the situation is much less clear for the Σ potential, which could be either attractive, repulsive or both according to the place in the nucleus [Dab09];

same question about K- potential, less known than K+ potential, and what about the mass of K- in nucleus [Har12].

Our goal is to build a model able to correctly predict the cross section for formation of a hypernucleus, and all the particles and nuclei formed in the reaction, with their characteristics; besides, the model should be fast enough to be used in a transport code as GEANT4 for experiment simulation and analysis. This model could be used to make simulations for a possible future program at R3B at GSI, led by the Structure group of SPhN, using a hydrogen target and the large acceptance GLAD magnet that would lead to better characteristics in term of noise rejection than existing setups. This could be done in collaboration with T. Saito from GSI [Sai12]. INCL will only be able to deal with the intranuclear cascade stage, which will provide a « hyper-remnant » with a given excitation energy, that should eventually be handled by a suitably extended statistical de-excitation model. For the second stage of the reaction which involves the de-excitation, we intend, at first, to use the model developed by A. Botvina et al. [Bot07, Bot12a]. In a second stage, we could also work on the de-excitation model (see section 3.4). Extending INCL to the production of strange particles is certainly more complicated than what has been done for multi-pion channels. The half-lives of strange hadrons are so long that they are practically stable on the timescale of an intranuclear cascade; therefore, their dynamics cannot be handled by reduced methods such as those used for multiple-pion production. It will be necessary to parameterize the elementary production channels, among which we will probably have to choose the ones that are most important. A great deal of ingredients have to be known, like production and scattering cross sections, energy and angular distributions of the output particles, hyperon and kaon potentials. Some of them can be found in the literature and parameterizations already exist in other transport codes; some can be updated and others be also seen as more or less free parameters (a sensitivity analysis will then be required).The validation of the parameterization of elementary channels, and later of the results of the model concerning pion and strange particle production, will use available data among which data from ANKE [Bus02], KaoS [Sch06] and from the HADES collaboration. We have initiated a collaboration with the IPNO group in this direction. We could certainly learn from what has been done in other codes, such as FLUKA or LAQGSM. Since strange particles mostly decay towards pions, our multi-pion channels should be revisited to avoid double counting. The question of the potentials to be used for strange particles will have to be addressed. Finally, since we will have to deal with very small production cross-sections, it will be mandatory to implement biasing techniques in our Monte-Carlo code, in order to easily compare the results to experimental data. 3.2.3 Antiprotons An old version of INCL extended to treat anti-proton annihilation in nucleus was built in the 90’s by J. Cugnon [Cug90]. Although the model at that time was much simpler than it is now, redoing something similar should in principle be rather straightforward. However, our standards of predictability are now much more stringent. This implies an extensive comparison with available experimental data that could lead us to reconsider the assumptions made at that time. However, it is clear that the amount of work would be smaller than for strangeness production.

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3.2.4 Others In the longer term, an extension of the model to gamma-induced reactions could be envisaged.

3.3 Nucleus-nucleus model

The idea to extend our model to heavy-ion reactions has originally arisen from the need of predictive transport codes for applications such as hadrontherapy and protection against radiation in space or near accelerators. In addition, we have also received more and more demands from groups working at GSI or RIKEN for calculations with our model of heavy ion induced reactions, in order, mostly, to disentangle in their experiment the role played by the reaction mechanism and nuclear structure effects. Since the model was very successful in nucleon and composite particle induced reactions, it seemed natural to try to extend it to heavier projectiles. As shown in the previous section, our first attempt to extend the INCL model to nucleus-nucleus collisions [Bou09] has been rather successful and INCL++ often gives similar or even better agreement with experimental data than more sophisticated models such as QMD. However, the model does not treat the target and the projectile on the same footing: the target is described as a bound system, in which nucleons from the “participant” zone enters and are treated by the standard INC model, whereas the projectile spectator is simply considered as a collection of nucleons to which an ad-hoc prescription is added to define excitation energy. It is obvious that, even if the gross features of particles emitted from the projectile spectator seem correct, the fragmentation of the second nucleus cannot be properly described within this framework. The adopted trick of kinematically reversing the target and projectile depending on the experimental observables is clearly unsatisfactory from the theoretical point of view and can only assure moderate success. In the future, it is foreseen to adopt a radically different approach. The nucleus-nucleus collision will be conceived as a binary nucleon cascade in two moving, interpenetrating potential wells that will initially be populated by Fermi nucleon gases; the model will allow exchange of nucleons between spectator and participant matter and possibly some dynamical adjustment of the well depth to take into account the number of escaped particles. Furthermore, using the same prescription of the INCL4 model for average potentials [Bou02] will permit to propagate particles in a single step between individual collisions (without relying on infinitesimal time steps) and so to secure the high numerical speed of the code, compared to QMD models. All the other performing features of INCL4 (description of initial state, statistical Pauli blocking, dynamical production of composites, energy-dependent mean field, etc…) will be maintained. The strategy for the model extension will be to extract the physics behavior from available elementary experimental data, in particular the most recent ones and the ones from the most complete experiments (e.g. constraining experiments measuring the correlations between different types of particles and fragments). Once the reaction mechanism is understood, the different physical ingredients of the model can be fixed once and for all, leaving hopefully as few free parameters (like the depth of the potential in the overlapping zones) as possible to be adjusted. The model will finally be validated against a wide set of experimental data. This approach, already successful for nucleon-induced reaction models, is expected to provide a model with a high predictive power in the whole domain of applications. It is clear however that our model cannot aspire to describe collisions of two very heavy nuclei since the description of important collective effects is definitely beyond its scope. Also, the de-excitation model, which the INC model has to be coupled to, has to be well chosen or adapted (see section 3.4). Therefore, it is foreseen to do the extension step by step, beginning with projectiles up to oxygen,

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until we reach a limit of validity of our assumptions. The goal is to provide an event-generator for high-energy transport codes, able to calculate the characteristics of all particles and nuclei generated in a particular application, with a main focus on simulations of experiments from SPhN at RIKEN and GSI and applications to hadrontherapy. It should be stressed that, even if strangeness production is implemented first in the present version of the model, namely INCL++, it will be important in a later stage to merge the target-projectile symmetrical version and the strangeness version since experiments with hypernuclei are often done with heavy ion beams.

3.4 De-excitation models

Statistical de-excitation models typically contain a large number of phenomenological parameters that effectively capture some behavior of excited nuclei. They are often poorly and rather indirectly determined by the experimental data. We can exploit the high predictive power of the INCL4 model to put stringent constraints on these parameters, and on de-excitation models in general. This strategy has already been successfully applied to the fission [Man10] and intermediate-mass-fragment [Man11] sector of the GEMINI++ model, leading to a predictive set of parameters that can be applied to fusion and spallation reactions. Unequivocal signatures of multifragmentation in proton-nucleus reactions can also be searched for using these methods [Man13]. In parallel to our extension of the INCL model towards more exotic nuclei, we will work towards an improvement of the constraints on the de-excitation parameters for such systems. Extending the INCL4 model to light-ion collisions means also introducing appropriate de-excitation mechanisms. At low excitation energies per nucleon, such as those reached in spallation reactions on heavy targets, the main de-excitation mechanism is statistical evaporation or sometimes fission; light nuclei, however, will easily reach higher excitation energies per nucleon which will trigger different de-excitation modes. The traditional solution for the de-excitation of light nuclei is the Fermi break-up formalism; however, it must be checked whether this model can help describe appropriately the observables relevant for the applications mentioned above. Moreover, the transition between Fermi break-up (light nuclei) and evaporation (heavier nuclei) is a delicate point that deserves investigation.

3.5 Transport codes

As already said, INCL4 is now distributed with several radiation-transport codes. In addition to the mandatory maintenance of the model and answers to the users, this implies also some work on the transport code itself. In particular, it is necessary to handle the coupling with the de-excitation models, which are not necessarily those we use with our stand-alone version, and the relations with other models, for instance in GEANT4, because of it wide scope of application in energy and types of particles. In PHITS, INCL4 has been now adopted as the default model. This has been done in the framework of a collaboration agreement between JAEA and CEA (in fact included in the general CEA-JAEA agreement as the Specific Topic of Cooperation: Transport codes for nuclear applications). We have a fruitful collaboration with physicists from JAEA who, for instance, have developed a way of combining INCL4 and DWBA for the prediction of peripheral collisions at low energies and for light targets, where our model is not working very well [Has13]. The model has been implemented by J.C. David into our own version of MCNPX, which have been made available to several users at ESS and PSI, for instance. From now on MCNPX will be replaced by MCNP6. The work to include INCL4 into MCNP6 will have to be done. As regards GEANT4, the INCL++ version has been provided with the last release. Some process for automatic and systematic benchmarking, requested by the GEANT4 collaboration, have also to be developed and maintained. Two of us, A. Boudard and D. Mancusi, are members of the Geant4

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Hadronic Physics working group

3.6 Uncertainty assessment

In an ADS, parameters related to the high-energy reactions in the accelerator, spallation target, and surrounding materials are calculated using Monte Carlo transport codes in which the cross sections and characteristics of produced particles are provided by nuclear models. Examples of parameters important for the safety analysis are: the isotope inventory in the different parts in view of waste management and assessment of radioactive emissions and high-energy neutron fluxes for shielding around the accelerator, target and sub-critical core. In order to determine and minimize the uncertainties on the quantities given by the codes, a specific methodology, different from the one used at low energies with libraries, has to be developed. A first method is based on making calculations with different codes and estimating the uncertainty from the found differences. The drawback is obviously that there is no guarantee that the chosen codes are not similarly wrong for a given quantity. A second method relies on a careful validation of the physics models on relevant basic experimental data, which allows assessing the uncertainties on the elementary processes and identifying deficiencies that can be later cured. The resulting uncertainties in simulations of complex systems are not straightforward but can be roughly estimated and recommendations on the code/model choice can be issued. Finally, a third method would consist in estimating the uncertainties on the different ingredients of the models and propagate them in the transport codes. This is a rather challenging task, which has never been done before. In the CHANDA project [CHA13], it is foreseen to employ the first two methods to estimate the uncertainties on parameters related to high-energy reactions and identified as crucial for the safety analysis of MYRRHA operating in sub-critical mode. Simultaneously, a further minimization of the present uncertainties will be done by working on the models and providing more complete and accurate data that should be used for benchmarking. The possibility to develop the third method will be investigated. Finally, the drawbacks and potentialities of the respective methods will be evaluated and recommendations for simulations of future ADS systems (or other spallation-based devices) will be issued.

4 Conclusion

All along the years, we have built a world-renowned and unique global expertise on spallation reactions. Our INCL4 model, built as much as possible on solid physics bases, is able to predict all cross sections corresponding to incoherent processes and characteristics of produced fragments and particles with their correlations, in a wide range of energies and target mass. It is used by an increasing number of physicists or engineers, either in its standalone version or through its implementation in widely-used transport codes. The predictability of the model is globally satisfactory although it can still be improved in specific regions. In the future, we would like to apply the strategy that made our success, i.e. the combination of theoretical developments, extensive validation on elementary experimental data and work on applications, to extension of the models towards new directions. The first one is the inclusion of strangeness degrees of freedom, which, in addition to being requested by users of our model at high energies, would allow studies of hypernuclei, a promising subject and a possible experimental line of SPhN at FAIR. The second, more application-motivated, is the extension towards light-ion induced reactions, in particular for hadrontherapy and space applications. Simultaneously, a substantial amount of work will be necessary to further improve the model in specific regions, in particular in the domain of few nucleon removal channels and for exotic nuclei in view of the use of the model by other groups of SPhN, to respond as far as possible to requests from the different users and to ensure the maintenance/upgrading in the transport codes.

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Part of the foreseen work will be realized in the framework of European programs: the further improvements for ADS and assessment of uncertainties will be carried out in the CHANDA FP7 EURATOM project; the inclusion of strangeness channels and improvement of the light-ion induced version are part of the SiNuRSE2 JRA proposed in ENSAR2. The group is presently composed of 3 physicists and a postdoc. One of the physicists will retire in 2014 and another one will be working only half-time. The achievement of the proposed program, which cannot be done by simply hiring successive postdocs, is possible only if an experienced young physicist is soon recruited.

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