Boudard, A

Cugnon, J

Leray, S

Volant, C

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Improvements of Intra-Nuclear Cascade model stimulated by recent spallation dataA. BOUDARD, J. CUGNON, S. LERAY and C. VOLANTDAPNIA/SPhN, CEA-Saclay, 91191 Gif-sur-Yvette Cedex,FranceUniversity of Lie`ge, 4000 Sart-Tilman Lie`ge 1, BelgiumIn high-energy transport codes used to design Accelerator Driven Systems or spallation neutron sources, elementaryinteractions are computed through nuclear physics models. Among these, Intra-Nuclear Cascade models play a majorrole since the excitation energy at the end of the INC stage determines the number of evaporated particles. Therefore,in simulation of spallation targets, INC influences the total number of emitted neutrons and the isotopic distributionof produced nuclei. Recent data regarding the production of neutrons and residual nuclei in proton induced reactionsmake it possible to test the reliability of INC models and to improve them. A new version (INCL4) of the Lie`ge INCmodel including especially a realistic nuclear density and a consistent treatment of the Pauli principle is presented.KEYWORDS: Intra Nuclear Cascade; spallationI. IntroductionTo design Accelerator Driven Systems, it is necessary topredict with precision the energy spectrum and angular distri-bution of neutrons produced in the spallation target. This isimportant for the optimization of the target geometry in termsof useful neutron production and spatial distribution of theneutron flux. The spallation residue production has also to bewell understood since these nuclei contribute to the radioac-tivity or/and to the possible structure material embrittlement.The spallation processes are generally described in twosteps: the incident light particle first interacts with the targetnucleus through successive nucleon-nucleon hard collisionsmodeled by the so called Intra Nuclear Cascade (INC), lead-ing to the emission of high energy nucleons which will inducesubsidiary spallation reactions in a thick target. At the end ofthis stage, the remaining nucleus is left with some excitationenergy and then de-excites either by evaporation or by fission.The reliability of the available numerical code systems is notyet sufficient to assess all the parameters required to designspallation targets. Moreover, the revival of interest in the spal-lation physics has allowed the availability of very precise newmeasurements1–6) which put strong constraints on the models.Details in the calculations which were considered so far as re-finements become now crucial to correctly describe the data.II. New ingredients in the Lie`ge INC modelThe Lie`ge INC model for proton-nucleus interactions 7)has been revisited8) especially with more realistic elementarycross-sections, when accurate neutron spallation data fromSATURNE became available1) . In this version called INCL2,applied in 1) , the interplay between the stochastic implemen-tation of the Pauli blocking and the fluctuations of the phasespace occupation in the initial state, inherent to its stochas-tic generation, introduces unphysical results for certain eventswith a negative excitation energy of the residual nuclei forwhich zero excitation energy was assumed. Latter in a morerecent version, INCL3, applied in ref3) , the cascade events Corresponding author, Tel. (33-1) 69 08 43 44, Fax. (33-1) 6908 75 84, E-mail: aboudard@cea.frwere considered as complete when the excitation energy wasvanishingly small.The nucleons were moving in a sharp spherical potentialwith a realistic radius. This had two consequences. First thetotal reaction cross section was too small (20% to 30%), andthe calculations had to be renormalized with the experimentalvalue. Second, large discrepancies were observed for periph-eral reactions very sensitive to the nuclear surface. This is thecase for the production of residual nuclei close to the targetmass and is disturbing since they are the most produced ones.The new ingredients of the version called INCL4 are thefollowing ones:- A smooth nuclear surface is introduced. The shape ofthe matter density is described with a two-parameter Fermimodel, the parameters being obtained from electron scatteringdata.- A consistent dynamical Pauli blocking is now used. Thestatistical procedure is still used but the final acceptance of acollision is submitted to the condition that this collision doesnot lead to a negative excitation energy.- The collision between spectator nucleons are now for-bidden, but spectators are still moving in the potential. Thisavoids the “spurious boiling” of the Fermi sea. Participantnucleons are particles having collided with at least one otherparticipant, the incident particles being the only participant atthe beginning of the reaction.- An energy dependence has been adopted for the -particle lifetime to take into account the phase space variationof the pion-nucleon system with energy.- A correction factor has been applied to the   cross-section which was formerly deduced from the detailedbalance. A factor of 3 has been adopted as justified in 9) todescribe correctly pion absorption in nuclei.- The intrinsic angular momentum of the residual nuclei isnow calculated from angular momentum conservation. Thisis of some importance for the evaporation-fission stage of thespallation.- The stopping time formulation of8) has been revisited nowtaking into account the diffusivity of the target nuclei. Due tothe extension of the nucleus, it is now about two times largerthan before, but the results are less sensitive to small variationsof this parameter.- The extension to incident light clusters has been realized,namely to incident deuterons, tritons, He and He. A gaus-sian shape for the spatial distribution is used with a widthdictated by the charge r.m.s. radius. The same is done forthe momentum distribution, with widths taken from literature,except for deuterons. For this loosely bound nucleus, the mo-mentum distribution is taken from the wave function in mo-mentum space as calculated with the Paris potential10) .III. Comparison with dataOne of the interesting consequences of the introductionof the smooth nuclear surface is that the calculated reactioncross-sections are now in good agreement with the measure-ments. This is illustrated in fig. 1, where the predictions (fulllines) are compared to a compilation of measurements 11, 12) forprotons on iron, lead and uranium.Fig. 1 Calculated reaction cross-sections (full lines) compared to thedata (points).A significative improvement is obtained on the cross sec-tion of residual nuclei close to the target mass as measuredat GSI in reverse kinematics. This is illustrated for proton-lead interaction at 1 GeV 3, 6) on fig. 2 where the measuredmass distribution (top) and the isotopic distributions of Pb, Tiand Hg (bottom) are compared with calculations performedwith INCL3 and INCL4 coupled with the evaporation-fissioncode developed at GSI13, 14) . The realistic density is here cru-cial for heavy residues produced in peripheral reactions. Notealso that the fission part is very well reproduced due to theGSI model using a delayed fission and to the intrinsic angularmomentum as computed at the end of the cascade. The meanvalue of this momentum is about a factor 2 larger than the onecomputed in abrasion-ablation codes developed for heavy ioncollisions17) .The same conclusions are also valid for the proton-gold in-teraction5) at 800 MeV (per nucleon) fig. 3. Note here that1GeV p+Pb, INCL4 (INCL3) + KHS_V3p, V=45MeV2001/08/07   16.1311010 260 80 100 120 140 160 180 200ACross Section (mb)10-210-111010 2180 200 180 200 180 200Fig. 2 Improvements mainly due to the realistic nuclear density com-pare to residual nucleus cross sections measured at GSI inproton-lead interaction at 1 GeV per nucleon (dots).800 MeV Au+p, INCL4 + KHS_V3p2001/08/07   17.2410-210-111010 20 25 50 75 100 125 150 175 200ACross Section (mb)10-210-1110140 160 180 20014 160 180 20014 160 180 20010-210-1110140 160 180 20014 160 180 20014 160 180 200Fig. 3 INCL4-KHSV3p calculation of residual nucleus cross sec-tions compare to data measured at GSI in proton-gold inter-action at 800 MeV per nucleon (dots).even the isotopes of Hg, one more charge than the target, areconvincingly reproduced in shape and magnitude. Anotherconclusion is that the light fragmentation residues are under-predicted by the model, but both cascade and evaporation playhere a role.The double differential cross-sections of produced neutronsas measured at SATURNE (LNS) provide disentangled ob-servables since the neutrons above 20 MeV are purely pro-duced at the cascade stage of the calculation. As an example,fig. 4 presents the cross-sections for Pb(p,xn)X at 1200 MeV 1)compared to the same calculations. The quasi-elastic peak and 1200 MeV p+Pb, INCL4 + KHSV3p10-1210-1110-1010-910-810-710-610-510-410-310-210-111010 21 10 1021032001/07/10   12.52neutron energy (MeV)d2σ/dΩdEn  (mb/sr.MeV), norme=1 for 00Fig. 4 Comparison of a INCL4-KHSV3p calculation with the doubledifferential cross sections of neutrons produced in a proton-lead interaction at 1.2 GeV and measured at LNS (dots).the region of the excitation are slightly improved (compareto INCL3). The overall agreement is satisfactory above andbellow 20 MeV, especially if we consider that the transport inthe target (2cm thick) is not evaluated here. It is known 18) thatit de-populates slightly the high energy part to the benefit ofthe low energy (30% increase bellow 3 MeV). The evapora-tive part (GSI) gives an agreement comparable to the previ-ous calculations presented in1) and done with the evaporationtreatment of Dresner19) . This last code was shown in3) unableto reproduce the isotopic distributions of residual nucleus andthe fission cross section. The coupling of INCL4 with Dresnerevaporation gives however a much better mass (A) or charge(Z) dependence of the fragmentation residues, showing theimportance of the evaporation-fission stage for the light frag-ments. However, we have now the possibility to propose withINCL4 coupled with the GSI model a more coherent descrip-tion of the full data base. 800 MeV p+Pb (p), INCL4 + KHSV3p10-910-810-710-610-510-410-310-210-11100 100 200 300 400 500 600 700 80001/07/18   17.46 energy (MeV)d2σ/dΩdEn  (mb/sr.MeV), norme=1 for 00110 (10-1)130 (10-2)150 (10-3)200 (10-4)250 (10-5)300 (10-6)Fig. 5 Comparison of a INCL4-KHSV3p calculation with the doubledifferential cross sections of protons produced in a proton-lead interaction at 800 MeV and measured at Los-Alamos(dots). 1600 MeV d+Pb, INCL4 + KHSV3p10-310-210-11200 400 600 800 1000 12002001/08/08   09.44neutron energy (MeV)d2σ/dΩdEn  (mb/sr.MeV), norme=1 for 00Fig. 6 Comparison of a INCL4-KHSV3p calculation with the doubledifferential cross sections of neutrons produced in a deuteron-lead interaction at 1600 MeV and measured at LNS (dots).The same quality of agreement is obtained for other tar-gets (Al, Fe, Zr, W and Th) and energies (800, 1200 and 1600MeV) measured at SATURNE 20) . Data at lower energies(597, 256 MeV)15) are also reasonably reproduced. The out-going protons measured at 800 MeV16) are shown in fig. 5 forthe lead target. The quasi-elastic peak is here especially wellaccounted for.The possibility to use light clusters as projectile has not yetbeen fully exploited. However neutrons produced by deuteroninduced reactions have been measured at SATURNE20–22) .The calculations agree reasonably well with the data (seefig. 6). In particular the high energy tail of the neutron spec-tra above the beam velocity is well accounted for when usingthe deuteron momentum distribution obtained with the Parispotential.Residual nuclei production from lead23) and uranium24)beams at 1 GeV/nucleon bombarding a liquid deuterium tar-get has been also measured at GSI. Comparison of these datawith the code predictions is encouraging (see fig. 7).1GeV/A Pb+d, INCL4 + KHSV3p2001/08/08   12.1711010 225 50 75 100 125 150 175 200 225ACross Section (mb)10-310-210-111010 210-310-210-111010 2150 175 200 225150 175 200 225150 175 200 225Fig. 7 INCL4-KHSV3p calculation of residual nucleus cross sec-tions compare to data measured at GSI in deuteron-lead inter-action at 1 GeV per nucleon (dots).IV. ConclusionThe Lie`ge INC model has been improved by the additionof necessary physics ingredients such as the smooth nuclearsurface and a consistent dynamical Pauli blocking. In con-junction with a suitable evaporation-fission code developed atGSI, it is able to reproduce reasonably well a large set of re-cent data (neutron and proton production, residual nuclei fora wide set of incident energies from 200 to 1.6 GeV) with-out any change of parameters. The possibility to include lightfragments as projectiles is being exploited and appears veryencouraging for deuterons. Some remaining failures of theINCL4 model are still the excess of pion production althoughreduced by a factor 2 compare to previous versions (crosssections are 70% larger than the one measured at 730 MeVin proton on lead25) ) and the quasi-elastic peak in neutron pro-duction computed at 20 to 50 MeV above the data (whereasthe proton one is correct). In an intricated interplay with theevaporation, the cross-section of light fragmentation residuesis also under-predicted. An extensive confrontation of thismodel with data should be fruitful in future.References1) X. Ledoux et al., Phys. Rev. Lett. 82 (1999) 4412.Collaboration DSM-SPhN, DAM-SPN, LNS, LPC and Caen-Univ, Univ Libre Bruxelles,IPN Orsay, IReS Strasbourg, Uppsala Univ.2) M. Enke et al., Nucl. Phys. A657(1999)317.3) W. Wlazło et al., Phys. Rev. Lett. 84 (2000) 5736.Collaboration FRS-S184: GSI, DAPNIA-SPhN, Univ. Santiagode Compostela, IPN Orsay, CEN Bordeaux-Gradignan.4) J. Benlliure et al., Nucl. Phys. A683(2001)513.5) F. 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Borne, PhD thesis, Bordeaux University, France 1998.F. Borne et al., Etude expe´rimentale de la spallation en ciblemince, Rapport CEA-R-5887 (2000).21) E. Martinez, PhD thesis, Caen University, France 1997.22) P. Pras et al., Internat. Meeting on Sub-Critical A.D.S., ITEPMoscow, Russia, oct 11-16 (1999).23) T. Enqvist et al., in preparation.24) E. Casajeros, PhD thesis, University of Santiago de Com-postela, Spain 2001.25) D.R.F. Cochran et al., Phys. Rev. D6 (1972) 3085

Improvements of Intra-Nuclear Cascade model stimulated by recent spallation data

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