On the role of secondary pions in spallation targets

EPJ manuscript No. (will be inserted by the editor) On the role of secondary pions in spallation targets Davide Mancusi1a, Sergio Lo Meo23, Nicola Colonna4, Alain Boudard5, Miguel Antonio Cortés-Giraldo6, Joseph Cugnon7, Jean-Christophe David5, Sylvie Leray5, Jorge Lerendegui-Marco6, Cristian Massimi38, and Vasilis Vlachoudis9 1Den-Service d’étude des réacteurs et de mathématiques appliquées (SERMA), CEA, Université Paris-Saclay, F-91191, Gifsur-Yvette, France 2ENEA, Research Centre “Ezio Clementel”, I-40129 Bologna, Italy 3INFN, Section of Bologna, I-40127 Bologna, Italy 4INFN, Section of Bari, I-70125 Bari, Italy 5IRFU, CEA, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France 6Universidad de Sevilla, Facultad de Fisica, 41012 Sevilla, Spain 7AGO department, University of Liège, allée du 6 août 17, bât. B5, B-4000 Liège 1, Belgium 8Physics and Astronomy Dept. “Alma Mater Studiorum” - University of Bologna, I-40126 Bologna, Italy 9European Organization for Nuclear Research (CERN), CH-1211 Geneva, Switzerland Received: December 19, 2016 Abstract We use particle-transport simulations to show that secondary pions play a crucial role for the development of the hadronic cascade and therefore for the production of neutrons and photons from thick spallation targets. In particular, for the n_TOF lead spallation target, irradiated with 20 GeV/c protons, neutral pions are involved in the production of ∼90% of the high-energy photons; charged pions participate in ∼40% of the integral neutron yield. Nevertheless, photon and neutron yields are shown to be relatively insensitive to large changes of the average pion multiplicity in the individual spallation reactions. We characterize this robustness as a peculiar property of hadronic cascades in thick targets. PACS. 25.40.Sc Spallation reactions – 24.10.Lx Monte-Carlo simulations – 28.20.Gd Neutron transport: diffusion and moderation 1 Introduction In spallation reactions, a high-energy ( >150 MeV) light projectile collides with a nucleus and on average leads to the emission of a large number of particles, mostly neutrons. The spectrum of spallation neutrons extends to large energies, up to the energy of the incoming projectile. For this reason, spallation reactions are often used for the purpose of generating intense high-energy neutron fluxes [1], as it is the case for instance in Accelerator-Driven Systems (ADS), subcritical reactor cores that are kept in a steady state by neutrons produced by a spallation source [2]. Neutrons are not the only particles that are emitted during spallation reactions. Protons and light charged particles (LCPs, A≤4) are also present, as are pions if the projectile energy is high enough. Spallation is actually capable of producing (with varying yields) all nuclei lighter than the target nucleus and close to the stability valley, as well as a handful of nuclei heavier than the target nucleus (as amply demonstrated by several experiaCorresponding author. E-mail address: da- [email protected] mental campaigns [see e.g. 3, Fig. 12]). All these particles, especially the lightest ones (neutrons, protons, pions and LCPs), are capable of inducing secondary nuclear reactions in a thick spallation target, and may thus contribute to the development of the hadronic cascade, to particle emission and to the production of residual nuclei [see e.g. 4]. The standard theoretical tool for the description of spallation reactions is a hybrid nuclear-reaction model where an intranuclear-cascade (INC) stage is followed by an optional pre-equilibrium stage and by a statistical de-excitation stage [1]. For the reasons evoked in the previous paragraph, these models must be validated not only for the primary reactions (typically reaction between fast protons and heavy nuclei such as tungsten, lead or bismuth), but also for all secondary reactions that may sizably contribute to the production of neutrons or to any other observable one may be interested in. It is generally acknowledged that secondary protonand neutron-nucleus reactions are important, as suggested by the selection of validation data for international nuclear-reaction-model intercomparisons [5–7]; however, the same intercomparisons devoted little attention to the production of secondary pions and to the arXiv:1603.05453v3 [nucl-th] 16 Dec 2016 2 Davide Mancusi et al.: On the role of secondary pions in spallation targets validation of models on pion-induced reactions. This is at least partly due to the fact that inclusive data for pionnucleus reactions are scarce, and partly to the fact that ADSs are expected to operate at energies of the order of 1GeV [2], where pion multiplicities are relatively low. Several spallation neutron sources are currently operational around the world and more are under construction or planned for the near future. Predictions of the neutronsource characteristics can typically be obtained by means of Monte Carlo (MC) simulations. Reliable results require detailed and accurate knowledge of the physical processes at the basis of the spallation reactions. Among the currently operating spallation neutron sources, the n_TOF (neutron Time-Of-Flight) facility [8] is an intense pulsed neutron source located at CERN. Neutrons are produced by spallation of lead nuclei caused by an incident 20 GeV/c proton beam, and subsequently moderated and collimated towards two experimental areas, where their energy can be measured using the time-of-flight technique. One of the foremost advantages of the detection capability of n_TOF is that the produced neutrons extend over more than twelve orders of magnitude, from thermal energies to the GeV range, allowing highly accurate measurements for a wide range of applications. Precise characterization of the neutron source is crucial for these purposes, and some features of the neutron beam must be inevitably determined via numerical simulations [9]. In recent publications [10, 11], the Geant4 toolkit for particle transport [12, 13] was used to characterize the neutron and photon fluxes directed towards the n_TOF experimental areas. Calculations of neutron and photon fluences performed with different Geant4 physics lists exhibited large relative differences. The authors suggested at the time that this difference could be related to different treatments of pion production and pion-induced reactions. In this work, we study the role of pion production and its influence on the spallation yields. In particular, it will be shown that secondary pions play a crucial role for particle production in thick spallation targets, such as the n_TOF neutron source. We shall demonstrate that the production of high-energy prompt photons is essentially dominated by π0decay; this phenomenon is well known in the context of the phenomenology of calorimetric measurements for high-energy physics [14]. At the same time, the production of neutrons is affected by both secondary π±- nucleus reactions and π0production. These facts notwithstanding, particle yields are less sensitive to the detail of the specific nuclear-reaction model used for the particletransport simulation. This is explained in terms of an intrinsic “resilience” of hadronic cascades in thick targets. The paper is structured as follows. In Sec. 2 we provide a brief description of the salient features of the Liège Intranuclear-Cascade model (INCL), which is pivotal for our numerical simulations of the n_TOF spallation target. Thin-target model calculations related to the pion sector are presented and discussed in Sec. 3, along with comparisons against experimental data. Section 4 shifts the focus towards the thick-target transport calculations of the n_TOF spallation target. The most important features of the MC simulations, described in detail in recent papers [10, 11], are recalled in Secs. 4.1 and 4.2. The role played by pions in the emission of neutrons and photons is highlighted in Secs. 4.3–4.5. Section 4.7 illustrates the tendency of the hadronic cascade to mitigate the sensitivity of the particle yields to the details of the description of the nuclear reactions. Conclusions are drawn in Sec. 5. 2 Model description: the Liège Intranuclear Cascade model The Liège Intranuclear Cascade model (INCL) [15, 16] is one of the most refined existing tools for the description of spallation reactions. The model is currently maintained and developed jointly by the University of Liège (Belgium) and CEA (Saclay, France). The model assumes that the first stage of the reaction can be described as an avalanche of independent binary collisions. The INCL model is essentially classical, with the addition of a few suitable ingredients that mimic genuine quantum-mechanical features of the initial conditions and of the dynamics: for instance, target nucleons are endowed with Fermi motion, realistic space densities are used, the output of binary collisions is random and elementary nucleon-nucleon collisions are subject to Pauli blocking. The model can describe the emission of nucleons and pions; light clusters (up to Z= 5, A= 8 by default) can also be produced through a dynamical phase-space coalescence algorithm. Intranuclear-cascade models in general (and INCL in particular) only describe the fast, dynamical stage of a spallation reaction, leading to the formation of excited nuclei which subsequently de-excite by emitting particles and/or fissioning. It is therefore necessary to follow the de-excitation of this cascade remnant if one requires a complete description of the nuclear reaction. Since the time scale for de-excitation is much longer than for cascade, a different physical description is usually employed. This may include an optional pre-equilibrium stage, which then handles the thermalization of the remnant; if preequilibrium is used, the intranuclear-cascade stage is stopped earlier. Either way, thermalization is attained and subsequent de-excitation of the remnant is described by statistical de-excitation models. Within Geant4, INCL can be directly coupled with two different de-excitation codes, namely: G4ExcitationHandler, the native statistical deexcitation model of Geant4 and the default choice [17], and ABLA V3, a de-excitation model developed at GSI (Darmstadt, Germany) [18, 19]. We stress here that this is not the code that is usually coupled to INCL (which is ABLA07 [20]), but rather an older version. A detailed comparison of the capabilities of the two versions can be found in Ref. 20. Different particles are produced in different stages of the spallation reactions. In particular, while neutrons and γ-rays are mostly generated in de-excitation processes, pion production, in particular, occurs entirely in the first reaction stage. The pion dynamics in INCL has been recently upgraded to push the upper energy limit of the Davide Mancusi et al.: On the role of secondary pions in spallation targets 3 model up to 15–20 GeV. Older versions of INCL considered only one mechanism for pion production, namely excitation and subsequent decay of the ∆(1232) resonance. For nucleon-induced reactions, this is a good approximation up to energies of about 2–3GeV. This is proven by the results of the IAEA benchmark [5–7], as well by the previous studies on the INCL pion dynamics [21, 22]. Additionally, one should not forget that, as soon as multiple collisions are involved, any particle correlation due to the action of an intermediate resonance will be washed out. For the purpose of correctly describing multiple-collision reactions, it is sufficient to capture the first-order behavior, and correlations may be neglected. Of course, selective or exclusive observables (such as two-particle correlations), especially if related to oneor few-collision reactions will generally be incorrectly described. Above 2–3GeV, excitation of heavier baryonic and mesonic resonances becomes likely1. A straightforward extension of INC would in principle entail the description of all the energy-angle-differential cross sections for the formation, scattering and absorption of the resonances in the nuclear medium, as well as their mean-field potentials, decay modes, etc. The amount of information that must be fed into the model is ponderous; besides, most of the time, the available experimental information on these elementary processes is direly scarce, or partial at best. One possible approach would be to rely on an independent event generator for the elementary hadron-nucleus collisions, in the spirit of Ref. 23. In this paper, however, we explore a different solution. It should be noted that baryonic resonances above ∆(1232) are largely overlapping. This raises the question of whether it is meaningful to consider them as having separate identities in the framework of INC. Additionally, their lifetime (in vacuum) is much smaller than the typical time between subsequent collisions during INC (a few fm/c), so that a heavy resonance is unlikely to undergo any collision before decaying in the nucleus. This is already marginally the case for ∆(1232), whose lifetime in vacuum is ∼1.6fm/c, and indeed most of the observables calculated in INC are rather insensitive to variations of the ∆(1232) lifetime. It should also be considered that the final (on the time scale of INC) decay products of baryonic resonances are often pions. Strictly speaking, the arguments above do not apply to most of the lightest unflavored mesonic resonances (η, ω,η0. . . ), whose lifetimes are comparable to or longer than the duration of the INC stage; nor do they apply to strange baryons and mesons (Λ,Σ,K. . . ), which undergo weak decay. However, the available experimental elementary cross sections associated with the production of these particles [24, 25] and order-of-magnitude estimates suggest that their global influence on the INC dynamics 1The excitation of the Roper N∗(1440) resonance is a special exception, because it may be excited at lower energy in the T= 0 channel. INCL4.6 assumes that the kinematics of pion production in this channel is governed by the ∆(1232) resonance. The extended version of INCL does not make this approximation. is weak. Therefore, it should be possible to treat them as corrections, at least in the energy range up to 10–15 GeV. In view of the discussion above, it is appropriate to use a more pragmatic approach to the description of highenergy reactions. In the latest version of the INCL model, the production and decay of individual resonances (except for ∆(1232)) is bypassed and replaced by multipion collisions, i.e. effective two-body collisions leading to the production of one or more pions in the final state, of the following form: N+N→N+N+xπ, (1a) π+N→N+xπ. (1b) In the current model, the number xof pions in the final state of the collision takes all values from 1to 4inclusive. The rest of the pion dynamics in the new version of INCL is the same as in the older one. The formation, absorption and decay of the ∆(1232) resonance is explicitly treated. Pion absorption is possible only via the formation of ∆(1232). No one-step mechanism for pion absorption on nucleon pairs is included. Further details on the latest version of INCL can be found in Refs. 26, 27. Relative to the published version, the current implementation of the model has slightly evolved, with the most notable difference concerning the biasing of nucleons towards the forward direction in the center-of-mass system2. The effect of the multipion extension can be studied by comparing some global quantities calculated with the old (INCL4.6) and the new extended model (INCL++). Figure 1 shows the average pion multiplicity (i.e. the average number of pions produced per inelastic reaction) in p+208Pb as a function of the proton energy. While the two models yield similar predictions at low projectile energy, in the older model the multiplicity saturates around 5GeV, never exceeding ∼1pion per reaction, while the extended model yields an almost linear increase up to 20 GeV. Figure 2 shows how the produced pions are distributed over the three charge states, according to the calculations of the extended model. The fraction of neutral pions is roughly energy-independent. On the contrary, the lines for positive and negative pions cross between 4and 5GeV. The suppression of negative pions at low energy can be explained by considering that the projectile (a proton) carries positive isospin, and that pions can only be produced in the first few collisions. As the energy and the number of collisions increase, pion production becomes increasingly dominated by the total isospin of the system, which is 2In the current model, the final-state particle momenta are generated according to a flat, unbiased phase-space sampling algorithm. Let Ebe the generated CM energy of the first nucleon; the value of Edetermines the minimum (tmin) and maximum (tmax) values of the Mandelstam four-momentum transfer t. The value of tis then sampled from a distribution of the form exp (Bt)and all the generated momenta are rotated to match the sampled four-momentum transfer for the first nucleon. Clearly this algorithm does not modify the singleparticle energy distributions in the CM system, which are therefore still given by the phase-space model. On the other hand, the distributions in the laboratory system are different. 4 Davide Mancusi et al.: On the role of secondary pions in spallation targets 0 5 10 15 20 proton energy (GeV) 0 2 4 6 8 10 12 average multiplicity neutrons ×0.25 protons pions INCL++ INCL4.6 Figure 1. Excitation function for the total average neutron, proton and pion multiplicities (from intranuclear cascade and de-excitation) in the final state of p+208Pb reactions, as calculated with (INCL++) and without (INCL4.6) multipion extension, coupled with ABLA07. Note that the neutron curve has been renormalized by a factor of 0.25. 0 5 10 15 20 proton energy (GeV) 0.0 0.1 0.2 0.3 0.4 fraction π+ π0 π− Figure 2. Excitation functions for the average fraction of produced pions for each of the three charge states, in p+208Pb, as calculated by INCL++. negative because N > Z in lead. Therefore, negative pions are asymptotically more abundantly produced than positive pions. For completeness, we mention that the version of the INCL model that was used for the present work is INCL++ v5.2.9.2. 3 Thin target: pion-production cross sections As discussed in Sec. 1, Geant4 simulations performed with an INCL++-based physics list yield the best overall reproduction of the measured neutron production for the n_TOF spallation target, contrary to the physics lists using the Binary Cascade (BIC) [28] or Bertini models [29], which overestimate the experimentally evaluated neutron production by as much as 70% [10]. In Ref. 10 it was hinted that a possible explanation of this difference could be related to pion production. In particular, it was pointed out that both neutral and charged pions could play an important role in determining the production of neutrons as well as of the so-called prompt γ-ray component, i.e. those produced in the first nanoseconds of the spallation reactions (with the delayed γ-ray component produced later on from neutron capture reaction and de-excitation of excited residues). In the following, the role of secondary pions in spallation targets is investigated, starting from a comparison of theoretical differential cross sections with the available experimental data. We remark that the predictive capability of the INCL model for the production of other particles (in particular neutrons, protons and light charged particles) below 3GeV has already been established in an extensive benchmark of spallation models, organized under the auspices of the IAEA [5–7]. In order to assess the validity of the INCL++ and other models, it is very useful to compare with one of the most complete and comprehensive data set on pion production at high energy. Such data were collected by the HARP experiment at CERN [30, 31], where extensive measurements of double-differential cross sections for charged-pion production in protonand pion-induced reactions were performed. Incident momenta of 3,5,8and 12 GeV/c were considered. 3.1 Integral pion production Figures 3–5 show inclusive pion-production cross sections integrated over the acceptance of the HARP experiment. In addition to the INCL++ calculation, we show the results of three other models: Bertini [29] and Binary Cascade (BIC) [28] are popular intranuclear-cascade models available in Geant4, while INCL4.6 represents the Liège Intranuclear Cascade model without multipion extension [32]. The difference between INCL4.6 and INCL++ clearly highlights the importance of the extension, which is already sizable at the lowest incident momentum of the HARP data-set (3GeV/c). The INCL4.6 model is reported to illustrate certain surprising features of the hadronic shower in Sec. 4, namely the relative insensitiveness to the details of the treatment of the individual elementary interactions. The INCL++ and Bertini models provide comparably accurate predictions. Bertini is generally closer to the experimental data for light targets, while INCL++ performs better on heavy targets, such as lead, which is most interesting for the present work and in general for spallation neutron sources. Proton-nucleus data are generally better reproduced than pion-nucleus data, with all calculations anyway being within a factor of 2 from the experimental data, with the BIC model having greater difficulties in reproducing the experimental cross sections. Davide Mancusi et al.: On the role of secondary pions in spallation targets 5 101102 target mass number 10−3 10−2 10−1 100 101 102 103 cross section (mb) 3 GeV/c 5 GeV/c (×10−1) 8 GeV/c (×10−2) 12 GeV/c (×10−3) π+ INCL++ INCL4.6 Bertini BIC 101102 target mass number 3 GeV/c 5 GeV/c (×10−1) 8 GeV/c (×10−2) 12 GeV/c (×10−3) π− Figure 3. Cross sections for the production of π+(left) and π−(right) from proton-nucleus reactions, integrated over the HARP angle-momentum acceptance, for different incident proton momenta, as functions of the target mass number. The lines represent calculations by different models (see text for details). The experimental data are taken from Ref. 30. 101102 target mass number 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 cross section (mb) 3 GeV/c 5 GeV/c (×10−2) 8 GeV/c (×10−4) 12 GeV/c (×10−6) π+ INCL++ INCL4.6 Bertini BIC 101102 target mass number 3 GeV/c 5 GeV/c (×10−2) 8 GeV/c (×10−4) 12 GeV/c (×10−6) π− Figure 4. Same as Fig. 3, but for π+-nucleus reactions. 101102 target mass number 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 cross section (mb) 3 GeV/c 5 GeV/c (×10−2) 8 GeV/c (×10−4) 12 GeV/c (×10−6) π+ INCL++ INCL4.6 Bertini BIC 101102 target mass number 3 GeV/c 5 GeV/c (×10−2) 8 GeV/c (×10−4) 12 GeV/c (×10−6) π− Figure 5. Same as Fig. 3, but for π−-nucleus reactions. It is important to remark that very few inclusive experimental data exist for the production of neutral pions in proton-nucleus and pion-nucleus reactions. This is of course mainly due to the short lifetime of the neutral pion, which complicates its detection. It is therefore customary to benchmark reaction models only on charged-pion production. We will follow the same approach in the present work. The validity of the interpolation to neutral pions can often be directly related to the goodness of the isospinsymmetry approximation, which is commonly used for the computation of elementary cross sections in intranuclear cascade. 3.2 Double-differential pion-production cross sections Figures 6 and 7 show double-differential (momentum-angle) cross sections for inclusive pion production in protonand pion-induced reactions. For benchmarking we select two incident momenta - 3and 12 GeV/c - and we focus on the lead target, which is the most important for the study of the n_TOF spallation source. For simplicity, we limit our discussion to π+production in protonand π−-induced reactions; these results exhibit all the typical features of the general case. For the purpose of this work, the most interesting quantity to compare is the pion emission spectrum. The cross sections of Figs. 3–5 are determined by integration of the double-differential cross sections in Figs. 6 and 7 over the momentum and angle acceptance of the HARP data-set. It clearly appears that no model accurately reproduces the emission spectra for all angles and momenta. INCL++ 6 Davide Mancusi et al.: On the role of secondary pions in spallation targets 10−2 10−1 dσ/dΩdp [mb/(sr MeV/c)] (a) INCL++ Bertini Binary (b) (c) (d) 0 200 400 600 p[MeV/c] 10−2 10−1 100 dσ/dΩdp [mb/(sr MeV/c)] (e) 0 200 400 600 p[MeV/c] (f) 0 200 400 600 p[MeV/c] (g) 0 200 400 600 p[MeV/c] (h) Figure 6. Double-differential cross sections for the production of π+at 25◦(a, e), 48◦(b, f), 71◦(c, g) and 105◦(d, h), from 3 GeV/c (a–d) and 12 GeV/c (e–h) p+Pb. The lines represent calculations by different models (see text for details). The experimental data are taken from Ref. 30. and Bertini are generally more accurate at forward and backward angles, respectively, while BIC is, as already noted, rather far from the experimental data. The goodness of the model predictions for this observable is qualitatively consistent with the results for neutron production in Geant4 simulations of the n_TOF spallation target, providing further evidence of the fundamental role of pion-induced reactions in thick spallation targets. An interesting observation that can be made about Figs. 6 and 7 is that INCL++ and Bertini consistently show a dip in the spectra at forward angles (even up to roughly 90◦) and around 250 MeV/c, which is not seen in the experimental data. This defect was also noticed by the authors of Ref. 29, who tentatively attributed it to insufficient moderation by the nuclear medium. In our opinion, however, the dip is related to the formation and decay of the ∆(1232) resonance, which manifests itself as a strong peak in the pion-nucleon cross section. This intuition is triggered by the observation that the position of the dip coincides approximately with the position of the resonance in the π+N→∆cross section. Indeed, we have verified that the dip is insensitive to reasonable modifications of the recombination (∆+N→N+N) cross section. The mechanism leading to the formation of the dip in the model is rather simple, if one makes a few reasonable assumptions. First, we assume that pion production in INC proceeds in two stages. In the first stage, early elementary collisions generate a structureless (no dip) pion spectrum (it is reasonable to assume that pions are produced early in the reaction because the energy available for pion production quickly degrades after a few collisions). In the second stage, the generated pions traverse the nucleus, possibly undergoing scattering and absorption, and possibly emerging as free particles. In this picture, the early pions are attenuated by the nuclear medium, with the excitation of the ∆(1232) resonance playing a role in the distortion of the pristine pion spectrum, due to selective pion absorption at the corresponding resonance energy. Since Davide Mancusi et al.: On the role of secondary pions in spallation targets 7 10−2 10−1 dσ/dΩdp [mb/(sr MeV/c)] (a) INCL++ Bertini Binary (b) (c) (d) 0 200 400 600 p[MeV/c] 10−1 100 dσ/dΩdp [mb/(sr MeV/c)] (e) 0 200 400 600 p[MeV/c] (f) 0 200 400 600 p[MeV/c] (g) 0 200 400 600 p[MeV/c] (h) Figure 7. Same as Fig. 6, but for 3 GeV/c (a–d) and 12 GeV/c (e–h) π−+Pb reactions. the dip is insensitive to the recombination cross section and to the resonance lifetime, and since ∆resonances (in INCL) can only be absorbed by recombination, we conclude that the intermediate ∆resonances mostly decay back to pion-nucleon pairs. In principle, the momentum of the pion should fall back in the dip region. However, while the formation and decay of the intermediate ∆resonances does not modify the pion momentum distribution, it does act on the angular distribution. If one makes the reasonable assumption that the pristine pion spectrum is sensibly forward-peaked, then the decay of the intermediate ∆resonances will redistribute pions from the forward angles to all angles. This manifests itself as a dip at forward angles in the double-differential spectra. While this explanation might hold valid for the dip observed in the model calculations, it is not clear whether it also applies to the data. A hint of a dip may be seen in the very forward angles, but in general data seems to indicate that in reality the dip, if any, is less pronounced than what predicted by the models. We performed some tests and we verified that the dip disappears if the π+N→∆cross section is artificially reduced by about a factor of 2. One can also act on the width of the ∆resonance peak in the π+N→∆entrance channel: interestingly, either increasing or decreasing the width of the Breit-Wigner-like peak will suppress the dip in the calculations. Theoretical calculations [e.g. 33] indicate that in-medium ∆resonances should be broader than the corresponding free particles, although unambiguous quantitative indications are still missing [34]. INCL already generates part of this medium effect (on the resonance lifetime) through the application of Pauli blocking on the resonance decay and through ∆ absorption. For consistency one should also modify the cross section of the formation process to reflect this. It remains to be seen if a realistic modification of the ∆width (in the spirit of e.g. Refs. 35, 36) can reconcile the calculations with the experimental data. For the sake of completeness, we mention that there is disagreement about the scientific adequateness of the HARP data analysis. A group of former HARP collaborators (the HARP-CDP group) have published a revisited analysis of the raw HARP data, which has sparked a long 8 Davide Mancusi et al.: On the role of secondary pions in spallation targets 10−1 100 dσ/dΩdp [mb/(sr MeV/c)] (a) (b) (c) (d) INCL++ Bertini Binary 0 400 800 p[MeV/c] 10−1 100 dσ/dΩdp [mb/(sr MeV/c)] (e) 0 400 800 p[MeV/c] (f) 0 400 800 p[MeV/c] (g) 0 400 800 p[MeV/c] (h) Figure 8. Double-differential cross sections for the production of π+at 0◦–25.8◦(a, e), 25.8◦–41.0◦(b, f), 41.0◦–50.6◦(c, g) and 50.6◦–59.0◦(d, h), from 12.3 GeV/c (a–d) and 17.5 GeV/c (e–h) p+Au. The lines represent calculations by different models (see text for details). The experimental data are taken from Ref. 39. 10−1 100 dσ/dΩdp [mb/(sr MeV/c)] (a) (b) (c) (d) INCL++ Bertini Binary 0 400 800 p[MeV/c] 10−1 100 dσ/dΩdp [mb/(sr MeV/c)] (e) 0 400 800 p[MeV/c] (f) 0 400 800 p[MeV/c] (g) 0 400 800 p[MeV/c] (h) Figure 9. Same as Fig. 8, but for the production of π−. and well-documented controversy [37]. Ref. 38 contains direct comparisons of the double-differential momentumangle cross sections, but only for the smallest angle (25◦) and for 3and 8GeV/c beam momenta (Figs. 12 and 13 in their paper). On this limited basis, it is difficult to decide whether the HARP-CDP cross sections are compatible with the dip in the calculations, although the fact that the HARP-CDP data seem to be consistently smaller than the HARP data at low momentum is encouraging. Given this state of affairs, it is surely wise and instructive to consider other data-sets. Figures 8 and 9 show results for the calculation of double-differential pion-emission cross sections for 12.3and 17.5GeV/c protons on gold targets, compared to the data from Ref. 39. The energy and the target for the 12.3GeV/c data-set are close to 100101102103104 energy [MeV] 10−5 10−4 10−3 10−2 10−1 100 101 dNreac/dE[MeV−1source−1] neutrons protons pions INCL++ INCL4.6 Figure 10. Incident-energy distribution of nuclear reactions induced within the hadronic cascade by protons, neutrons and pions, normalized to one primary proton, as calculated by the INCL model with (INCL++, solid lines) and without (INCL4.6, dashed lines) multipion extension, within the Geant4 simulation of the n_TOF spallation target (beam momentum of 20 GeV/c). the HARP data, Figs. 6 and 7. However, when comparing the two data-sets, it is important to keep in mind that 1) the momentum acceptance is larger in Chemakin’s data, and 2) the measured angles are smaller: the largest measurement angle in Chemakin’s data-set falls between the second and the third HARP measurement angle. If one makes abstraction of these differences, the models appear to behave consistently over all the Figs. 6–9. Therefore, we do not see any clear indication that the HARP data should be rejected. In view of these difficulties, new, high-acceptance data focusing on the pion production in high-energy protoninduced reaction would be highly desirable. Together with charged pions, direct measurements of π0production would provide fundamental information that could contribute considerably to the optimization of the INC models. 4 Thick target: pions in the n_TOF spallation target While thin-target double-differential cross section can provide some indications on the ability of the models to correctly predict pion production, the structure of the hadronic showers that take place in the spallation target, and in particular the role played by secondary pions in the production of neutrons and photons, can only be studied by means of dedicated MC simulations of the spallation process and comparison with available experimental data. In this respect, we have chosen in this work to perform further simulations of the n_TOF spallation target with the Geant4 toolkit. Before analysing the results of the simulations, it is convenient to briefly describe the toolkit and Davide Mancusi et al.: On the role of secondary pions in spallation targets 9 the implementation of the MC simulations for the n_TOF case. 4.1 The Geant4 toolkit Geant4 (GEometry ANd Transport) is a toolkit for the simulation of particle transport and detector response [12, 13]. The Geant family of codes was originally developed for the needs of the high-energy-physics community. However, since the beginning the array of physics models has been constantly expanding to encompass applications at lower energy. In particular, Geant4 has been successfully used, since several years, to describe the transport of neutrons down to thermal energy, using point-wise cross-section from evaluated libraries [40]. These developments recently triggered new work on the use of Geant4 for the simulation of spallation neutron sources. Recently, Geant4 simulations performed for the n_TOF source were benchmarked against experimental results [10], such as the neutron fluence and resolution function, and yielded interesting results which will be shortly described in the following subsection. Physics models in Geant4 are organized and collected in “physics lists”, which are specifications of the physical processes (and the associated models) that should be used in the simulation. The names of the available Geant4 physics lists are often obtained by concatenating the names of the models used in the hadronic sector, in decreasing order of incident energy. Thus, for instance, the FTFP_INCLXX_HP physics list, around which much of the present work revolves, relies on the Fritiof + preequilibrium model (FTFP) at high energy, the INCL++ model at intermediate energies, and the NeutronHP model at low energy. This work is based on Geant4 v10.1; however, the INCL++ model within Geant4 was manually upgraded to v5.2.9.4, which is the version that has been distributed with Geant4 v10.2 (December 2015). 4.2 The n_TOF simulation The n_TOF spallation target is a water-cooled lead cylinder surrounded by an aluminum container and by a neutron moderator. Its structure is described in detail in Refs. 8, 10, 11. A 20 GeV/c proton beam impinges on the base of the lead cylinder at an angle of approximately 10◦. The lead target cylinder can be considered as thick, in the sense that its size (radius 30 cm, length 40 cm) is large compared to the proton mean free path for inelastic collisions at the beam energy (∼15 cm). Therefore, the primary proton often triggers a nuclear reaction inside the Pb target and initiates a hadronic shower which eventually leads to the production of a large number of particles. A note about our nomenclature: we refer to all “non-primary” particles as secondaries, regardless of the reaction generation they appear in, in opposition to the “primary” particle incident on the spallation target. Among the particles escaping from the spallation target, we are particularly interested in neutrons, which are moderated in water, that can be either normal or borated, and collimated towards the experimental areas. Simulations of the n_TOF spallation target have focused on the reproduction of the measured energy dependence, resolution function, and spatial distribution of the neutrons entering the first experimental area (EAR1) [8, 10]. The expected flux in the direction of the second, new experimental area (EAR2) was also studied in a recent paper [11]. As shown in Refs. 10, 11, these measured quantities are best reproduced by the simulations using the FTFP_INCLXX_HP and QGSP_INCLXX_HP physics lists. For proton-nucleus reactions, these physics lists use the Liège Intranuclear Cascade model (INCL++) from 1MeV to 20 GeV incident energy, and either the Fritiof + pre-equilibrium model (FTFP) or the Quark-GluonString + pre-equilibrium model from 15 GeV upwards. In the region where the two model overlap (15–20 GeV), the choice of the model is randomly sampled, with linearlyinterpolated probabilities between the interval endpoints (a standard procedure in Geant4). Since the primary proton beam energy is ∼19 GeV (20 GeV/c), it is clear that the FTFP or QGSP will typically be used at most for the simulation of the first inelastic proton-nucleus reaction3; the rest of the hadronic shower is dominated by the INCL++ model. For this reason, we limit our analysis on the FTFP_INCLXX_HP physics list. The following section introduces a global description of INCL++, with particular focus on its pion dynamics. 4.3 Analysis of secondary reactions We start by illustrating how nuclear reactions in the target are distributed with respect to the type of the incident particle and its energy. Figure 10 shows the distribution of the projectile energy for nuclear reactions induced by protons, neutrons and pions. Each distribution is normalized to the total number of reactions per primary proton induced by the indicated particle. Note that Fig. 10 includes the reactions induced by the primary protons, which appear as a small peak close to the beam energy, whose integral roughly amounts to 0.91 reactions per incident proton; this is consistent with the thickness of the spallation target, which is of the order of 2.5nuclear mean free paths at the beam energy. Note also that this plot does not include elastic collisions. This choice mainly follows from the consideration that elastic scattering on lead nuclei does not sensibly modify the projectile energy for nucleons and pions; in addition, at high energy, the elastic angular distribution is sensibly forward-peaked and is unlikely to affect the global flow of energy and momentum within the spallation target. Table 1 presents the integral reaction rates over selected ranges of incident energy, as calculated by Geant4 simulations using the INCL model with (INCL++) and 3Except of course for events of specific classes, involving small energy losses, like e.g. quasi-elastic scattering. 16 Davide Mancusi et al.: On the role of secondary pions in spallation targets References 1. D. Filges and F. Goldenbaum. Handbook of spallation research. Theory, experiments and applications. Wiley-VCH, Berlin, 2009. 2. H. Aït Abderrahim, P. Baeten, D. De Bruyn, J. Heyse, P. Schuurmans, and J. Wagemans. 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