The microscopic phasespace approach URQMD is used to investigate the stopping power and particle production in heavy systems at SPS and RHIC energies. We find no gap in the baryon rapidity distribution even at RHIC. For CERN energies URQMD shows a pile up of baryons and a supression of multi-nucleon clusters at midrapidity

Amelin, Nikolai

Bass, Steffen A.

Bleicher, Marcus

Brandstetter, Mathias

Dumitru, Adrian

Ernst, Christoph

Gerland, Lars

Greiner, Walter

Konopka, Jens

Spieles, Christian

Stöcker, Horst

Weber, Henning

Winckelmann, Luke Andreas

English

Dumitru, Adrian Bogdan

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:nucl-th/9605044 v1   31 May 1996Nucleus-Nucleus Collisions at Highest EnergiesM. Bleicher, N. Amelin, S. A. Bass, M. Brandstetter, A. Dumitru, C. Ernst,L. Gerland, J. Konopka, C. Spieles, H. Weber, L. A. Winckelmann, H. St¨ ocker andW. GreinerInstitut f¨ ur Theoretische PhysikJohann Wolfgang Goethe Universit¨ at60054 Frankfurt am Main, GermanyThe microscopic phasespace approach URQMD is used to investigate the stoppingpower and particle production in heavy systems at SPS and RHIC energies. Weﬁnd no gap in the baryon rapidity distribution even at RHIC. For CERN energiesURQMD shows a pile up of baryons and a supression of multi-nucleon clusters atmidrapidity.nucl-th/96050441 MotivationOne of the main aims of relativistic heavy ion collisions at collider energies is todiscover if the individual hadrons dissolve into a gas of free quarks and gluons(quark-gluon-plasma, QGP) in the extremely compressed and heated hadronicmatter. This may happen in line with a transition into the chiral symmet-ric phase which modiﬁcates most hadron masses drastically. The achievableenergy deposition depends on the amount of stopping of the colliding nuclei.2 The URQMD ModelThe Ultrarelativistic Quantum Molecular Dynamics (URQMD) 1, is used to an-alyze the physics of the excitation function of hadronic abundances, stoppingand ﬂow. This framework bridges with one model consistently the entire avail-able range of energies from below SIS to CERN, even for the heaviest systemPb+Pb. URQMD is a hadronic transport model including strings. Its collisionterm contains 50 diﬀerent baryon species (including nucleon, delta and hyperonresonances with masses up to 2 GeV) and 25 diﬀerent meson species (includ-ing strange meson resonances), which are supplemented by their correspondingantiparticle and all isospin-projected states.1Figure 1: Left:Rapidity distribution of protons and positively charged particles for the re-action He+He at√s = 31 AGeV compared to the data 2. Right: Rapidity distributionof protons and negatively charged pions for central S+S reactions at Elab = 200 AGeVcompared to the data 8.3 He-He Collisions at ISRIn general it appears to be an intricate problem to describe stopping behaviourof baryons and pion production within one theoretical frame at very highenergies. If one wants to do LHC calculations it may be necessary to includemulti-string-excitation as it is done in dual parton approach. To demonstratethe ability of URQMD to model a nucleus-nucleus collision even at the todayhighest available bombarding energies for heavy particles, we compare thecalculated He+He collision at ISR with data 2 as shown in Fig.1 (left).It is not surprising, that such a light system as helium is totally transpar-ent. A baryon free area of 3 units in rapidity is produced. URQMD and thedata agree well, the calculated produced particle yield may increase by 15% ifone also simulates gluon jet events 3, which is not included yet.4 SPS Energy RegimeThe dominant reaction mechanism in the early stage of a reaction is the excita-tion of collision partners to resonances or strings 1. Then secondary interactions,i. e. the annihilation of produced mesons on baryons, lead also to the formationof s channel resonances or strings, which may explain the strangeness enrich-2Figure 2: Left: Rapidity distribution of π−, protons, deuterons and 4He in central Pb+Pbreactions at Elab = 160 AGeV. Right: Directed ﬂow of baryons and antibaryons for the samesystem.ment 4 and (for masses larger than 3mN) allow for NN creation 5. The escapeprobability for ¯ p’s from the exploding nuclear matter enters via the free NNannihilation cross section. For central events of Pb+Pb at SPS approx. 85%of the produced anti-baryons are annihilated during the reaction.These two counter–acting eﬀects may be measured by the directed “anti-ﬂow” of antimatter. The observable asymmetry for bouncing antimatter canbe quantiﬁed by the mean px vs. rapidity (Fig.2, right). The anti–ﬂow of an-tibaryons appears to be strongest for semicentral collisions, while for baryonsthe maximum px is at considerably smaller b–values. The latter is due to thepressure (i. e. the EOS) the former one due to absorption and geometry.Comparisons of URQMD calculations to data from SIS to SPS is docu-mented elsewhere 6. Good agreement of baryon and meson production anddynamics has been achieved. An impression is given in Fig.1 (both) - protonsas well as pions and kaons are shown.Further insight into the collision geometry may be gained by looking atcomposite particle probes. Since URQMD does not include the production oflight nuclei dynamically, cluster formation is added after strong freeze-out.(Freeze-out means after the last strong interaction of the particle.) We calcu-late the deuteron (helium) formation probability by projecting the nucleon pairphasespace on the deuteron wave function via the Wigner-function method asdescribed in 7. Especially for high bombarding energies or exotic clusters itis necessary to use this sophisticated method, since the complex phasespace3Figure 3: The system Au+Au at an energy of√s = 200AGeV (RHIC), central collisions se-lected. Left:Rapidity distribution of baryons, antibaryons and net-baryons. Right: Rapiditydistribution of pions and kaonsdistribution of the cluster ingredients has to be taken into account 9. TheHulth´ en parametrization is used to describe the relative part of the deuteronwavefunction. The yield of deuterons is given bydNd =1234DXi,jρWd (∆  R,∆  P)Ed3(pip + pjn).The Wigner-transformed Hulth´ en wavefunction of the deuteron is denoted byρWd . The sum goes over all n and p pairs, whose relative distance (∆  R) andrelative momentum (∆  P) are calculated in their rest frame at the earliest timeafter both nucleons have ceased to interact. The factors 12 and 34 account forthe statistical spin and isospin projection on the deuteron state. The calcu-lation of the high mass clusters is straight forward, e.g. by exchanging theHulth´ en parametrization of the d wavefunction with a 4-body harmonic os-cillator wavefunction 7 to describe the 4He (See Fig. 2 (left), π−, protons, aswell as deuterons and 4He are depicted). In contrast to the pile up of pro-tons at midrapidity, cluster production is strongly supressed due to the hightemperatures in the center of the collisions.Calculations of H0 (ΛΛ-clusters) for AGS and SPS energies have also beperformed in this framework 10.45 RHIC EstimatesAs shown above URQMD seems to be well suited for an estimate of stoppingpower in Au+Au collisions at RHIC. However, we are well aware of the factthat for certain observables (e.g. high pt components of particle spectra) thecurrent framework is not suﬃcient, since it does not incorporate hard partonicscattering explicitely. Figure 3 (left) shows the results of our calculation forgold-gold at√s = 200 AGeV (RHIC). The nuclei suﬀer a mean rapidity shiftof more than 2 units of rapidity. The mid-rapidity region is apparently notbaryon free, in contrast to some earlier expectations. Our results are similiarto RQMD calculations 3.We ﬁnally put our interest on the produced mesons. In Fig.3 (right) weshow the rapidity distribution of kaons and pions. As mentioned above at thishigh energies modiﬁcations of the string fragmentation may be necessary. Theinclusion of gluon jets as a ﬁrst step will increase the meson multiplicities byabout 15% 3.6 ConclusionAt ﬁrst some remarks on the validity of our calculation: It is believed to bea fact that a quark-gluon-plasma is created at RHIC. While our calculationdoes not assume a QGP, it certainly goes beyond the purely hadronic scenario- strings are excited and quarks and diquarks are subject to further interac-tion. From our calculation we infer that the interaction of leading quarks anddiquarks dictate the stopping behaviour of heavy ion collisions even at SPSenergies.AcknowledgmentsThis work is supported by GSI, DFG and BMBF. M.B. wants to thank R.Mattiello for many inspiring ideas and fruitful discussions.References1. S. A. Bass, M. Bleicher, M. Brandstetter, A. Dumitru, C. Ernst, L. Ger-land, J. Konopka, S. Soﬀ, C. Spieles, H. Weber, L. A. Winckelmann,H. St¨ ocker and W. Greiner;source code and technical documentation, to be published in 19962. L. Otterlund, Nucl. Phys. A418(1983)98c53. T. Sch¨ onfeld et al., Mod. Phys. Lett. A8(1993)2631; T.Sch¨ onfeld, Ph.D.Thesis Universit¨ at Frankfurt 19934. R. Mattiello, et al., Phys. Rev. Lett. 63(1989)14595. A. Jahns et al., Phys. Rev. Lett. 72(1994)3464 and refs. therein6. S. A. Bass et al. contribution to this volume7. R. Mattiello et al., Phys. Rev. Lett. 74(1995)2180; M. Gyulassy, K.Frankel, E.A. Remler, Nucl. Phys. A402(1983)596; E.A. Remler andA.P.Sathe, Ann. Phys. 91(1975)2958. H. Str¨ obele et al., Nucl. Phys. A525(1991)59c9. M. Bleicher et al., Phys. Lett. B361(1995)1010. C. Spieles et al. contribution to this volume6

Nucleus-nucleus collisions at highest energies

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