Benchmarking GEANT4 nuclear models for hadron therapy with 95 MeV/nucleon carbon ions
BBenchmarking GEANT4 nuclear models for hadron therapy with95 MeV/nucleon carbon ions
J. Dudouet, D. Cussol, D. Durand, and M. Labalme LPC Caen, ENSICAEN, Universit´e de Caen, CNRS/IN2P3, Caen, France (Dated: June 2, 2014)
Abstract
In carbon-therapy, the interaction of the incoming beam with human tissues may lead to theproduction of a large amount of nuclear fragments and secondary light particles. An accurateestimation of the biological dose on the tumor and the surrounding healthy tissues thus requiressophisticated simulation tools based on nuclear reaction models. The validity of such modelsrequires intensive comparisons with as many sets of experimental data as possible. Up to now, arather limited set of double differential carbon fragmentation cross sections have been measured inthe energy range used in hadrontherapy (up to 400 MeV/nucleon). However, new data have beenrecently obtained at intermediate energy (95 MeV/nucleon). The aim of this work is to comparethe reaction models embedded in the GEANT4 Monte Carlo toolkit with these new data. Thestrengths and weaknesses of each tested model, i.e. G4BinaryLightIonReaction, G4QMDReactionand INCL++, coupled to two different de-excitation models, i.e. the generalized evaporation modeland the Fermi break-up are discussed.
PACS numbers: 25.70.Mn, 25.70.-z,24.10.Lx,Keywords: Fragmentation, Cross-sections, Hadrontherapy, Geant4 simulations a r X i v : . [ nu c l - e x ] M a y . INTRODUCTION The use of carbon ions in oncology is motivated by some balistic and biological advantages.Carbon ions allow to better target the tumor while preserving the surrounding healthytissues. However, the physical dose deposition is affected by the inelastic processes of theions along the penetration path in human tissues [1, 2]. For instance, the number of incidentions reaching the tumor (at the Bragg peak depth) is reduced up to 70% for 400 MeV/nucleon C in tissue equivalent material [3]. Carbon beam fragmentation in human body leads to theproduction of secondary lighter fragments with larger ranges and larger angular spreadings.Such fragments have also a different biological efficiency, which is strongly correlated tothe linear energy transfer (LET). These effects, due to carbon fragmentation, result in acomplex spatial dose distribution, particularly on healthy tissues. The influence of thesecondary particles production is the highest beyond the Bragg peak where only secondaryparticles contribute to the dose.In view of the previous remarks, to keep the benefits of carbon ions in hadrontherapyrequires a very high accuracy on the dose deposition pattern ( ±
3% on the dose value and ± et al. [11] studied the pre-diction capability of FLUKA [12] and GEANT4 [13] for the fragmentation of primary400 MeV/nucleon C in a thick water target. This work has shown disagreement up to100% for the models provided by the GEANT4 toolkit (namely G4BinaryLightIonReactionand G4QMDReaction). Another comparison has been done using the GEANT4 toolkit fora 95 MeV/nucleon C on thick PMMA targets [14]. This study has shown discrepancies upto one order of magnitude as compared to experimental data, especially at forward angles.In view of this difficulty of the GEANT4 nuclear models to reproduce the fragmentationprocesses on the energy range useful in carbon-therapy using thick targets, it appeared nec-2ssary to constrain these nuclear models with double differential fragmentation cross sectionson thin targets. A first set of experimental data has been obtained for a 62 MeV/nucleon C on thin carbon target [10]. GEANT4 simulations results have shown discrepancies upto one order of magnitude for both angular and energy distributions.A new set of double differential cross section data have been recently obtained by ourcollaboration (LPC Caen, IPHC Strasbourg, SPhN Saclay, IPN Lyon and GANIL). Thesedata, described in Dudouet et al. [15] provide good quality measurements (within a 5to 15% accuracy) of 95 MeV/nucleon C differential cross sections on thin targets (C,CH , Al, Al O , Ti and PMMA). These experimental data are used in this work to testthe different nuclear models embedded in the GEANT4 framework. These nuclear modelsare: G4BinaryLightIonReaction (BIC), G4QMDReaction (QMD) and INCL++. They arecoupled to two de-excitation models: the generalized evaporation model (GEM) and theFermi break-up (FBU). Strengths and weaknesses of these different models in reproducingthe fragment production yields, the angular and energy distributions, as well as the targetmass dependence will be discussed. II. MONTE CARLO SIMULATIONS
GEANT4 is a Monte Carlo particle transport code used to simulate the propagationof particles through matter by taking into account both electromagnetic and nuclear pro-cesses. It is widely used in a variety of application domains, including medical physics.The 9.6 version of GEANT4 has been used in this work. Electromagnetic interactions arethose developed in the “electromagnetic standard package option 3”. Particle transport cutshave been set to 700 µ m. Total nucleus-nucleus reaction cross sections have been deter-mined, as recommended, using the recently implemented Glauber-Gribov model [16]. Thismodel provides the full set of nucleus-nucleus cross-sections needed for the GEANT4 track-ing (inelastic, elastic, particle production and quasi-elastic) for all incident energies above100 keV/A.Nuclear reactions are usually described by a two-step process: a first dynamical step called“entrance channel” followed by a de-excitation step called “exit channel”. The entrancechannel model describes the collision and the production of excited nuclear species untilthermal equilibrium is achieved. The decay of such hot species is thus considered in a3econd step by means of statistical de-excitation models. All nuclear models implementedin GEANT4 follow this scheme. In this work, three different entrance channel models arecoupled with two exit channel models leading to six different combinations. We stress thatthe aim of this article is to provide a benchmark of nucleus-nucleus collision models as theyare implemented in the GEANT4 toolkit, rather than to test the physical relevance of thesemodels. A. The GEANT4 entrance channel models
Two nuclear models are currently recommended to perform simulations for hadrontherapy.The first one is a binary intra-nuclear cascade (BIC) called G4BinaryLightIonReaction [17].This is an extension of the Binary Cascade model [18] for light ion reactions. This modelcan be characterized as an hybrid model between a classical cascade code and a quantummolecular dynamics (QMD) description because the ’participating’ particles are described bymeans of gaussian wave functions. By ’participating’ particles, it is meant those particles thatare either primary particles from the projectile or particles generated and/or scattered duringthe cascade process. The Hamiltonian is built with a time-independent optical potential.This potential is acting on participants only. Note that in this model, scattering betweenparticipants is not taken into account. Participants are tracked until escaping from thenucleus or until the end of the cascade. The cascade stops if the mean kinetic energyof participants in the system is below 15 MeV or if all the participant kinetic energiesare below 75 MeV. If such conditions are fulfilled, the system is assumed to have reachedthermal equilibrium. The nuclear system is left in an excited state, which evolution towardequilibrium is described by the native pre-compound model of GEANT4.Another model used in hadron therapy is a QMD-like model called G4QMDReaction [19]adapted from the JAERI QMD (JQMD) code [20, 21]. As for the BIC model, the basicassumption of a QMD model is that each nucleon is decribed by a gaussian wave functionwhich is propagated inside the nuclear medium. Differently from the previous model, in theQMD model, all nucleons of the target and of the projectile are taken into account. Eachnucleon is thus considered as ’participant’. The particles are propagated and interact bymeans of a phenomenological nucleon-nucleon potential. The time evolution of the systemis stopped at 100 fm/c where it is assumed that equilibrium has been achieved. The QMD4odel does not include pre-compound model.A third model has been used in this work: the Li`ege Intranuclear Cascade model INCL++[17, 22, 23]. The last version implemented in GEANT4 is labeled as INCL++ v5.1.8. Thismodel has recently shown promising results [14] comparable with the BIC or QMD models.Nucleons are modeled as a free Fermi gas in a static potential well. To treat the collision,a target volume is first calculated. Nucleons from the projectile entering this volume arelabeled as participants. The quasi-projectile is built from projectile spectators and from non-cascading projectile participants. In contrast, the quasi-target is included in the calculationvolume, which also encompasses the participant zone. The final state of the quasi-target isdetermined by the full collision dynamics of the cascade. Its physical description is there-fore much more reliable. The nucleus-nucleus collision is thus not treated symmetrically.Results have shown that INCL better reproduces the target fragmentation than the pro-jectile fragmentation [14]. In view of this, INCL treats by default the collision in inversekinematics (target impinging on projectile), in order to obtain the best reproduction of theprojectile fragmentation. However, INCL is not able to use projectile heavier than A=18. Ifthe target is heavier than A=18, the collision will then be performed in direct kinematics.If both target and projectile are heavier than A=18, the description of the collision uses theG4BinaryLightIonReaction model. The effects of this asymmetry in the treatment of theprojectile and the target and the discontinuity at mass 18 will be discussed later. The cas-cade is stopped when no participants are left in the nucleus or when a stopping time definedas : t stop = 70 × ( A target / . fm/c is reached. As for the G4QMDReaction model, theINCL model does not include pre-compound model.For the QMD and INCL++ models, a clustering procedure is applied to nucleons. For theQMD model, this clustering procedure is made in phase-space. For the INCL++ model, thisclustering procedure is based on a coalescence model. The clustering procedure producesexcited species at the end of the cascade. For the BIC model, no clustering procedure isapplied and the excitation energies are determined for the projectile and the target remnants.The excitation energy of each species is then estimated and is the input for the de-excitationprocess considered in the statistical de-excitation codes.5 . The GEANT4 exit channel models GEANT4 provides several de-excitation models which have been recently improved [24].These models describe particle evaporation from excited nuclear species produced in theentrance channel. Two models have been considered in this work.The first one is the generalized evaporation model (GEM) [17, 25]. Based on theWeisskopf-Ewing evaporation model [26], it considers sequential particle emission up to Mg as well as fission and gamma decay.The second model is the Fermi Break-up model (FBU) [17]. This model considers thedecay of an excited nucleus into n stable fragments produced in their ground state or in low-lying discrete states. The break-up probabilities for each decay channel are first calculatedby considering the n-body phase space distribution. Such probabilities are then used tosample the decay channels by a Monte-Carlo procedure. This model is only used for lightnuclei (Z ≤ ≤ III. EXPERIMENTAL DATA
The models described above will be compared with data obtained during the E600 exper-iment performed in May 2011 at the GANIL facility (Grand Acc´el´erateur National d’IonsLourds). The experiment has allowed to measure the double differential cross sections ofvarious species in 95 MeV/nucleon C reactions on H, C, O, Al and nat
Ti targets [15]. Thedescription of the experimental set-up and the experimental energy thresholds are describedin Dudouet et al. [15].The particles have been detected using three stages telescopes, locatedat angles ranging from 4 ◦ to 43 ◦ . They have been identified using a ∆E-E method. Theanalysis method has been described in Dudouet et al. [27]. The errors bars of the presentedexperimental data are including systematics and statistical errors. These data are availablewith free access on the following web-site http://hadrontherapy-data.in2p3.fr .In the presented simulations, only the energy thresholds of the telescopes have beentaken into account. As a reminder, these thresholds are shown in table I for all the detectedisotopes. The main effects of these thresholds is to lower the contribution of the particlescoming from the target fragmentation. It has been verified that the presented simulations6 sotope H H H He He He Li LiE th (MeV) 4.0 5.2 6.1 14.2 16.0 18.6 29.9 31.7isotope Be Be Be B B B C C CE th (MeV) 44.3 48.6 50.5 60.6 65.8 68.1 81.3 84.2 86.9TABLE I: Energy threshold used in the simulations. and the simulations in which the whole set-up is taken into account give the sames results.The main drawback of these latter simulations is their lack of CPU efficiency since thefragmentation process in thin targets is rare and the solid angles of detectors are small. Thetarget thicknesses used in the simulations are the same than the experimental one in order toobtain the same angular and energy straggling. A number of 10 incident C has been usedin the simulations in order to minimize the statistical error on the simulated data (lowerthan 1% in most cases but up to 20% for the larger angles). The choice has been made tonot represent the statistical errors of the simulated data for clarity reasons.
IV. RESULTSA. The participant-spectator scheme
Some characteristics of the results will be discussed in the framework of the participant-spectator picture of the collision (see for instance Fig. 1 [28, 29]).This is a typical high energy process (in the GeV/A range) in which the internal velocitiesof the nucleons are (much) smaller than the relative velocity between the two partnersof the reactions. However, recent analysis have shown that it could still be valid around100 MeV/nucleon incident energy [15]. In such a picture, for a finite impact parameter,b, the nucleons located in real space in the overlapping region of the two nuclei constitutethe ’participants’. The projectile nucleons outside the overlapping region constitute themoderately excited quasi-projectile moving with a velocity close to the beam velocity. The7
Projectile Target
Before Collision QP After collision QT Mid-rapidity
ParticipantSpectator v P Spectator
Overlap region v T = 0 v QP ≃ v P v QT ≃ FIG. 1: (Color online) Schematic representation of the geometrical participant-spectator model inthe laboratory frame. same argument applies for the target nucleons leading to a quasi-target moving with avelocity close to 0. The participants constitute the so-called highly excited mid-rapiditysource. The decay products from this source show an energy distribution shifted towardslower values as compared to the beam energy. Therefore, in such a picture, three energycontributions in the laboratory frame are expected: a first one close to the beam energy, asecond one associated with the target at energies close to 0 and in between, a contributionassociated with the participants. This latter is thus to a large extent strongly coupled to thesizes of the projectile and of the target and should show up as the size of the target increases.We stress that this very simple picture is used here to define the terms that characterizethe origins of the detected fragments and not used as a realistic description of the reactionmechanisms.The results of the models considered above are now compared with experimental data.We first consider a comparison of simulated cross sections (production, angular and energydistributions) with the experimental data in the case of carbon target. Then, the targetmass dependence will be studied.
B. Production cross sections
Fig. 2 displays the production cross sections of the most abundant reaction productsin the case of a carbon target. They are compared with the GEANT4 results with thedifferent combinations between the entrance and exit channel models discussed previously.8ote that the production cross section of C fragments takes into account only inelasticinteractions, excluding elastic scattering. These production cross sections have been obtainedby fitting the angular distributions with a function resulting of the sum of a gaussian and anexponential function. These fitted function have then been integrated over the whole solidangle [15]. The errors bars represented on Fig. 2 have been obtained by propagating the fitparameters uncertainties, using the covariance matrix of the fit procedure.
FIG. 2: (Color online) Comparisons between data and the different combination of entranceand exit channel models (see text) for the production cross sections of various isotopes in95 MeV/nucleon C → C reactions.
The results of Fig. 2 clearly shows that none of the model combination is able to reproducethe production rates for all isotopes. Moreover, it is not easy to identify which modelcombination is the most suited for a comparison with experimental data. However, it maybe concluded that the influence of the entrance channel is larger than the influence of theexit channel model. Regarding the two exit channel models, the Fermi Break-up modelseems, for a given entrance channel model, to be, in most cases, more compatible with the9ata. This was already mentioned in B¨ohlen et al. [11] and Ivanchenko et al. [30]. Thisis due, to some extent, to the fact that the Fermi Break-up description allows to exploremore available phase space (especially at high excitation energies for which three (or more)body decay may play an increasing role) than the GEM model for which only sequentialevaporation is taken into account. In the following, we only consider calculations in whichthe Fermi Break-up model is used for the exit channel.
C. Angular distributions
The E600 experimental setup allowed to cover an angular range from 4 ◦ to 43 ◦ by stepsof two degrees. Fig. 3 displays the differential angular cross-sections for carbon target forboth experimental data and for simulations using QMD, BIC, and INCL models coupledwith the Fermi Break-up de-excitation model.Although QMD is the most achieved model as far as the dynamics of the collision isconcerned, it fails to reproduce the angular distributions. It strongly overestimates theproton production of about 50% (as also observed in Fig. 2), and poorly reproduces theangular distributions of the heavier isotopes considered here (up to one order of magnitude).The distibutions obtained with QMD show maximum values around 7 ◦ (apart for protons)with a fall off towards 0 ◦ . This is in disagreement with the experimental distributionsshowing an increase at very low angles.The distributions obtained with the BIC model are slightly closer to the data as comparedwith QMD, especially at forward angles and for heavier fragment distributions ( Li and Be).The lack of α at forward angles may possibly come from a failure of the model to take intoaccount the C three alpha cluster structure. The global shape is however not correct.The quasi-projectile contribution is too large and the large angles are poorly reproduced.The angular distributions obtained with the BIC model increases around 25 ◦ (except forprotons). This probably comes from the quasi-target contribution but is in disagreementwith experimental data.Finally, INCL is the model that seems to better reproduce the angular distributions,especially for light fragments. The shapes of protons and α distributions are nearly repro-duced over the whole angular range ( ∼ degrees) θ ) - ( b s r Ω / d σ d DataQMDBICINCL (a) (degrees) θ ) - ( b s r Ω / d σ d -1 DataQMDBICINCL (b) (degrees) θ ) - ( b s r Ω / d σ d -3 -2 -1
101 Li DataQMDBICINCL (c) (degrees) θ ) - ( b s r Ω / d σ d -3 -2 -1
101 Be DataQMDBICINCL (d) (degrees) θ ) - ( b s r Ω / d σ d -5 -4 -3 -2 -1
101 B DataQMDBICINCL (e) (degrees) θ ) - ( b s r Ω / d σ d -4 -3 -2 -1 DataQMDBICINCL (f)
FIG. 3: (Color online) Absolute differential angular cross-sections of protons, He, Li, Be, Band C obtained for the carbon target. Experimental data: black points. Histograms: GEANT4simulations with QMD, BIC and INCL models coupled to the Fermi Break-up de-excitation modelas indicated in the insert. model, only the forward angles are well described. At large angles the INCL model stronglyunderestimate the data (up to one order of magnitude).11e have shown in Dudouet et al. [15] that the experimental angular distributions ofparticles emitted in the 95 MeV/nucleon C reaction on H, C, O, Al and nat
Ti can berepresented as the sum of a gaussian and an exponential contribution. None of the modelsused here are able to reproduce this trend. The main problem is associated with the inabilityof such models to reproduce the magnitude of the exponential contribution which is dominantat large angles. Since this contribution is mostly resulting from the mid-rapidity sourcediscussed previously, it is tempting to conclude at this stage that the present models do notcontain the ingredients needed to describe the mid-rapidity processes. We now proceed withthe energy distributions.
D. Energy distributions
The agreement with the double differential cross sections constitutes the most severe testof the models. Fig. 4 shows few examples of energy distributions obtained for He, Li and Be at 4 and 17 ◦ .Here, we would like to focus on the shape of the distributions rather than on the abso-lute magnitude. The distributions may be interpreted as follows: the major contributionoriginates from the decay of the quasi-projectile and is thus located at an energy close tothe beam energy per nucleon. This peak close to the beam energy is clearly visible at smallangles (cf Fig. 4: distibutions at 4 ◦ ). At larger angles, this contribution tends to vanishbecause of the strong focusing of the quasi-projectile. The low energy part of the distribu-tion is associated with the species produced at mid-rapidity and also with the decay of thequasi-target although this last contribution becomes dominant only at very large angles andcan be poorly detected due to experimental energy thresholds. Therefore, the ability of themodels to reproduce the data can be appreciated on these two physical aspects: the decayof the projectile-like and the particle production mechanism at mid-rapidity.As shown in Fig. 4, among the three models, BIC shows the strongest disagreement withthe experimental data. In particular, the model is unable to account for the mid-rapiditycontribution (medium angles). This is due to the binary nature of the reaction mechanismassumed in the model. Indeed, composite fragments cannot be formed in this model and onlynucleons undergoing nucleon-nucleon collisions can be emitted. Moreover, the mean energyof the quasi-projectile contribution is too large as compared to data and its contribution12 (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -4 -3 -2 -1 ° He at 4 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -5 -4 -3 -2 ° He at 17 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -5 -4 -3 ° Li at 17 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -4 -3 -2 ° Li at 4 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -4 -3 -2 ° Be at 4 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -6 -5 -4 -3 ° Be at 17 DataQMDBICINCL (a)
FIG. 4: (Color online) Energy distributions of He, Li and Be fragments at 4 and 17 ◦ . Blackpoints: experimental data. Histograms are for simulations with QMD, BIC and INCL modelscoupled to the Fermi Break-up de-excitation model (see insert). (close to 95 MeV/u) remains too important at large angle. This leads for instance to thevery strong disagreement shown in Fig. 4 (d) for Be fragments at 17 ◦ .The INCL model better reproduces the quasi projectile contribution both for the mean13nd the width of the energy distribution. It also predicts more fragments at low energies(0 < E <
50 MeV/nucleon) as compared to the BIC model. However, the results still under-estimate the data. Moreover, the shape of the distributions at low energies (mid-rapiditycontribution) is not in agreement with the data.Contrary to angular distributions, the QMD model better reproduces the global shape ofthe energy distributions. Although the mean energy of the quasi-projectile peak is slightlytoo high, the shape of the mid-rapidity contribution is better reproduced than for the BIC orINCL models. However, as for other models, it underestimates the mid-rapidity contribution.The remarks mentioned above are valid for all fragments from protons to carbon isotopes.The main conclusion that can be drawn is that none of the tested models is able to reproducesimultaneously the quasi-projectile, the quasi-target and the mid-rapidity contributions.The INCL model better reproduces the quasi-projectile contribution: it is probably thebest model for the description of the quasi-projectile. In contrast, the QMD model betterdescribes the mid-rapidity emission, probably due to the fact that it is the only model totake into account the time propagation and the interaction of all the nucleons in the reaction.Similar conclusions have been drawn at lower energy in De Napoli et al. [10], where the BICand QMD models were tested in 62 MeV/nucleon C → C induced reactions.
E. Results with other targets
Our experiment allowed to gather data for a series of targets ranging from hydrogenup to titanium. The target dependence on the double differential cross sections is nowinvestigated. Fig. 5 displays the α energy distributions at 4 ◦ for the hydrogen, oxygen,aluminum and titanium targets for both data and simulations using QMD, BIC and INCLmodels coupled to the Fermi Break-up de-excitation model.The three models reproduce quite well the data for the hydrogen target, especially INCL.This result is not surprising in the sense that these models are mostly based on the conceptof nuclear cascade which was originally dedicated to nucleon-nucleus collisions. In suchreactions, the geometry of the collision is rather simple and the description of the quasi-projectile is easier than for nucleus-nucleus reactions. More, with the hydrogen target,the α particles are mainly produced by the quasi-projectile de-excitation. However, theexperimental data exhibits a small contribution at low energy (below 50 MeV/nucleon) and14 (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -4 -3 -2 -1 ° He at 4 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -3 -2 -1 ° He at 4 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -3 -2 -1 ° He at 4 DataQMDBICINCL (a)
E (MeV/nucleon)0 50 100 150 ) - ( M e V / nu c l e on ) - d E ( b s r Ω / d σ d -3 -2 -1 ° He at 4 DataQMDBICINCL (a)
FIG. 5: (Color online) Energy distributions of α particles at 4 ◦ for hydrogen (a), oxygen (b),aluminum (c) and titanium (d) targets. Black points: experimental data. Histograms: simulations(see insert). INCL is the only model to reproduce this contribution.Nevertheless, the heavier the target, the larger the disagreement between the simulationsand the experimental data. From carbon to titanium, the three models reproduce quitewell the quasi-target and the quasi-projectile contributions. The difficulty to produce mid-rapidity fragments is evidenced. The discrepancy is amplified as the target mass increasesemphasizing the increasing role of mid-rapidity in the data as a simple consequence of thegeometry of the reaction. The larger the mass of the target, the larger the size of themid-rapidity region. The BIC model does not produce mid-rapidity fragments (around E =40-50 MeV/nucleon). Although the situation is slightly better for INCL or QMD models,the mid-rapidity contribution is underestimated for both models.A particular attention needs to be paid to the INCL model. For the aluminum and15itanium targets, the shape of the energy distribution changes with respect to lighter targets.The projectile contribution is overestimated and the mean energy is too large. The reasonis due to the discontinuity in the treatment of the kinematics when the target is largerthan A=18 as mentioned in Sec. II A. Otherwise, for lighter targets, results concerning thequasi-projectile are promising while the production at mid-rapidity remains underestimated.In the participant-spectator reaction mechanism, the mid-rapidity contribution originatesfrom the overlap region as already mentioned previously. This is thus a geometrical contri-bution, which increases significantly with the target size, as it is observed experimentallywhen going from the hydrogen to the titanium target: more and more fragments are pro-duced in the low energy region. The three models that have been used here fail in accuratelyreproducing this region and the discrepancy increases with the mass of the target. This maybe due to the fact that none of them take accurately into account the possibility to producesizeable clusters in the overlapping region. This point should deserve additional studies.
V. CONCLUSIONS
In this work, comparisons have been performed between experimental data collected in95 MeV/nucleon C reactions on H, C, O, Al and nat
Ti targets and GEANT4 simula-tions in order to test the models embedded in the GEANT4 nuclear reaction package. TheG4BinaryLightIonReaction (BIC), the G4QMDReaction (QMD) and the INCL++ (INCL)entrance channel models have been coupled to the generalized evaporation model (GEM)and the Fermi break-up model (FBU) exit channel models.The main conclusion is that up to now, none of these six models combinations is able toaccurately reproduce the data, neither in term of production rates nor for angular or energydistributions.This study has shown that the entrance channel model characteristics have a larger ef-fect on particles and fragments production as compared to the choice of the exit channeldescription. However, the Fermi break-up de-excitation model seems to give better resultsthan the generalized evaporation model. This observation has also been done in B¨ohlen etal. [11] and Ivanchenko et al. [30].As for angular distributions, apart from INCL which reproduces quite well protons (witha small disagreement at forward angles) and α distributions for the carbon target, the models16re not able to reproduce the data. The QMD model is the worst, with a maximum valueof the distribution at around 7 ◦ and an unexpected fall off towards 0 ◦ .On the contrary, QMD is the one which better reproduces the energy distributions forall considered fragments. Apart from the hydrogen target, the BIC model fails to reproducethe data and in particular, it does not produce particles at low energy. The INCL modelreproduces very well the quasi-projectile contribution if the target is not larger than A=18.These results seems consistent with those observed at lower energy. Indeed, the GEANT4simulations that have been done in De Napoli et al. [10] have shown that the angular dis-tributions were better reproduced by the BIC model than the QMD model. Regarding theenergy distributions, it has been shown that the QMD model better reproduces the shape ofthe distribution than the BIC one. The conclusions on the GEANT4 nuclear models that wehave made at 95 MeV/nucleon are thus in agreement with the one made at lower energies.The better reproduction of carbon fragmentation processes for the QMD model than for theBIC one has also been observed on thick water target at higher energies in B¨ohlen et al. [11].However, no INCL simulations have been performed in these two studies.Finally, a study of the target mass dependence shows that the three models do not succeedin reproducing realistically the production of species at mid-rapidity. Comparisons with asimple phenomenological model that takes into account the geometrical overlap region isplanned in a near future. [1] D. Schardt et al. Nuclear fragmentation of high-energy heavy-ion beams in water. Adv. SpaceRes. , 17:87–94, 1996.[2] N. Matsufuji, A. Fukumura, M. Komori, T. Kanai, and T. Kohno. Influence of fragmentreaction of relativistic heavy charged particles on heavy-ion radiotherapy.
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