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Hadron-Nucleus Interactions HadronHadron--NucleusNucleus InteractionsInteractions Had interactions and options 7th Fluka Course, NEA Paris Sept. 29-Oct.3, 2008 The FLUKA hadronic Models Hadron-nucleus: PEANUT Sophisticated Elastic,exchange P<3-5GeV/c G-Intranuclear Phase shifts Resonance prod Cascade data, eikonal and decay Gradual onset of hadron Glauber-Gribov multiple hadron interactions low E Preequilibrium π,K High Energy Special DPM Coalescence hadronization Evaporation/Fission/Fermi break-up γ deexcitation 2 Hadron-nucleon interaction models Particle production interactions: p-p and p-n cross section two kinds of models FLUKA and data total Those based on “resonance” production and decays, cover the energy range up to 3–5 GeV Those based on quark/parton elastic string models, which provide reliable results up to several tens of TeV Elastic, charge exchange and strangeness exchange reactions: • Available phase-shift analysis and/or fits of experimental differential data • At high energies, standard eikonal approximations are used 7th Fluka Course, Paris Sept.29-Oct.3, 2008 3 Nonelastic hN interactions at intermediate energies ’‘ ’‘ •N1 + N2 → N 1 + N 2 + π threshold at 290 MeV, important above 700 MeV, • π + N → π ‘+ π” + N ‘ opens at 170 MeV. Anti-nucleon -nucleon open at rest ! Dominance of the ∆ resonance and π-nucleon cross section of the N∗ resonances → isobar model Isospin → all reactions proceed through an decomposition intermediate state containing at least one resonance. Resonance energies, widths, cross sections, branching ratios from data and conservation laws, whenever possible. Inferred from inclusive cross sections when needed ” ’ ’ N1 + N2 → N 1 + ∆(1232) → N1 + N2 + π π + N → ∆(1600) → π’+ ∆(1232) → π’ + π“+ N’ N’1+ N2 7th→Fluka∆1 Course,(1232) Paris + Sept.29-Oct.3,∆2(1232) 2008 → N1’+ π1 + N’2 + 4 π2 Inelastic hN at high energies: (DPM, QGSM, ...) z Problem: “soft” interactions → QCD perturbation theory cannot be applied. z Interacting strings (quarks held together by the gluon-gluon interaction into the form of a string) z Interactions treated in the Reggeon-Pomeron framework z each of the two hadrons splits into 2 colored partons → combination into 2 colourless chains → 2 back-to-back jets z each jet is then hadronized into physical hadrons 7th Fluka Course, Paris Sept.29-Oct.3, 2008 5 Hadron-hadron collisions: chain examples Leading two-chain diagram in DPM for p-p scattering. The color Leading two-chain diagram in π+ (red, blue, and green) and quark DPM for -p scattering. The combination shown color (red, blue, and green) and in the figure is just one of the quark combination shown allowed possibilities in the figure is just one of the allowed possibilities 7th Fluka Course, Paris Sept.29-Oct.3, 2008 6 DPM and hadronization from DPM: Chain hadronization z Number of chains z Assumes chain universality z Chain composition z Fragmentation functions z Chain energies and momenta from hard processes and e+e− scattering z Diffractive events z Transverse momentum from uncertainty considerations Almost No Freedom z Mass effects at low energies The same functions and (few) parameters for all reactions and energies 7th Fluka Course, Paris Sept.29-Oct.3, 2008 7 Inelastic hN interactions: examples π+ + p →π+ + X (6 & 22 GeV/c) π+ + p → Ch+/Ch- + X (250 GeV/c) Positive Negative hadrons X2 hadrons Connected points: FLUKA Symbols w. errors : DATA Dots: Exp. Data Histos : FLUKA 6 GeV M.E. Law et. Al, LBL80 (1972) 22GeV 7th Fluka Course, Paris Sept.29-Oct.3, 2008 8 Nuclear interactions in PEANUT: Target nucleus description (density, Fermi motion, etc) t (s) 10-23 Glauber-Gribov cascade with formation zone Generalized IntraNuclear cascade 10-22 Preequilibrium stage with current exciton configuration and excitation energy (all non-nucleons emitted/decayed + all nucleons below 30-100 MeV) 10-20 Evaporation/Fragmentation/Fission model 10-16 γ deexcitation 7th Fluka Course, Paris Sept.29-Oct.3, 2008 9 Nucleon Fermi Motion z Fermi gas model: Nucleons = Non-interacting Constrained Fermions 2 dN k Momentum distribution ∝ = dk 2π 2 for k up to a (local) Fermi momentum kF(r) given by 1 2 3 (kF ) r = [π 3 ρN r (] ) The Fermi energy (kF ≈ 1.36 fm, PF ≈ 260 MeV/c, EF ≈ 35 MeV, at nuclear max. density) is customarily nt Nuclear Potentialeused in building a self-consist Depth of the potential well ≡ Fermi Energy + Nuclear Binding Energy 7th Fluka Course, Paris Sept.9-O2ct.3, 2008 10 Positive kaons as a probe of Fermi motion 7th Fluka Course, Paris Sept.29-Oct.3, 2008 11 (Generalized) IntraNuclear Cascade z Primary and secondary particles moving in the nuclear medium z Target nucleons motion and nuclear well according to the Fermi gas model z Interaction probability σfree + Fermi motion × ρ(r) + exceptions (ex. π) z Glauber cascade at higher energies z Classical trajectories (+) nuclear mean potential (resonant for π) z Curvature from nuclear potential → refraction and reflection z Interactions are incoherent and uncorrelated z Interactions in projectile-target nucleon CMS → Lorentz boosts z Multibody absorption for π, μ-, K- z Quantum effects (Pauli, formation zone, correlations…) z Exact conservation of energy, momenta and all addititive quantum numbers, including nuclear recoil 7th Fluka Course, Paris Sept.29-Oct.3, 2008 12 hA at high energies: Glauber-Gribov cascade with formation zone z Glauber cascade Quantum mechanical method to compute Elastic, Quasi-elastic and Absorption hA cross sections from Free hadron-nucleon scattering + nuclear ground state Multiple Collision expansion of the scattering amplitude z Glauber-Gribov Field theory formulation of Glauber model Multiple collisions ↔ Feynman diagrams High energies: exchange of one or more Pomerons with one or more target nucleons (a closed string exchange) z Formation zone (=materialization time) 7th Fluka Course, Paris Sept.29-Oct.3, 2008 13 Glauber ascadeC Quantum mechanical method to compute all ctions adron-nucleus cross serelevant h from hadron-nucleon scattering: iχhN(,) b s 2iδ hN ( b , s ) ShN(,) b= s e =ηhN(,)b s e and nuclear ntio func waveground state Ψi 2 A 2 3 ⎡ ⎤ sσ = d2 b dΨ u1 u − S Re b− j r⊥ , s talTo hA() T ∫ ∫ i ( ) ⎢ ∏ hN ( )⎥ ⎣ j=1 2 ⎦ 2 A 2 3 ⎡ ⎤ sσ d= b dΨ u u1 − Sj −⊥ b, r s Elastic hA() el ∫ ∫ i ()⎢ ∏ hN ()⎥ ⎣ j=1 ⎦ 2 2 A 2 3 ⎡ ⎤ σ s ≡sσ d= b dΨ u u1 − Sj −⊥ b, r s Scattering hAΣ () f ∑ hA () fi ∫ ∫ i () ⎢ ∏ hN ()⎥ f ⎣ j=1 ⎦ Absorption (particle prod.) Absorption probability over a given b and nucleon configuration hAσ s abs( ) ≡ σhA( T s)−σhAΣ ( f ) s 2 ⎧ A 2 ⎫ 2 3 ⎪ ⎧ ⎡ ⎤⎫⎪ d= bΨ d u1 − u 1 −S 1 − bj r⊥ , − s ∫ ∫ i ()⎨ ⎨∏ ⎢ hN ()⎥⎬⎬ ⎩⎪ ⎩ j=1 ⎣ ⎦⎭⎭⎪ 7th Fluka Course, Paris Sept.9-O2ct.3, 2008 14 Gribov interpretation of Glauber multiple collisions Therefore the absorption cross section is just the integral in the impact parameter plane of the probability of getting at least one non-elastic hadron-nucleon collision and the overall average number of ZNσhp+ r σhn r collision is given by 〈ν 〉 = hAσ abs z Glauber-Gribov model = Field theory formulation of Glauber model z Multiple collision terms ⇒Feynman graphs z At high energies : exchange of one or more pomerons with one or more target nucleons z In the Dual Parton Model language: (neglecting higher order diagrams): Interaction with n target nucleons ⇒ 2n chains Two chains from projectile valence quarks + valence quarks of one target nucleon ⇒valence-valence chains 2(n-1) chains from sea quarks of the projectile + valence quarks of target nucleons ⇒2(n-1) sea-valence chains 7th Fluka Course, Paris Sept.29-Oct.3, 2008 15 Formation zone Naively: “materialization" time (originally proposed by Stodolski). ative estimate:Qualit t = Δt ≈ h = h In the frame where p|| =0 E 2 2 T pT + M M M τ=t = h Particle proper time 2 2 ET pT + M Going to the nucleus system plab plab hplab Δx for ≡ β c ⋅ tlab ≈ t ≈ τ = k for 2 2 ET M pT + M Condition for possible reinteraction inside a nucleus: 1 3 Δx for ≤ RA ≈ r0 A 7th Fluka Course, Paris Sept.9-O2ct.3, 2008 16 Effect of Glauber and Formation Zone Rapidity distribution of charged particles produced No Glau in 250 GeV π+ collisions on No FZ No Glau Gold Yes FZ Points: exp. data (Agababyan et al., ZPC50, 361 (1991)). Yes Glau Yes Glau No FZ Yes FZ 7th Fluka Course, Paris Sept.29-Oct.3, 2008 17 WARNING z PEANUT has been extended to cover the whole energy range in late 2006 z A less refined GINC model is available for projectile momenta above about 5 GeV/c, and was the only choice until recently z However: the extended peanut is NOT yet the default, mainly because of some ambiguity in the definition of quasi-elastic cross sections. z To activate PEANUT at all energies: PHYSICS 1000. 1000. 1000. 1000. 1000. 1000. PEATHRESH 7th Fluka Course, Paris Sept.29-Oct.3, 2008 18 Nonelastic hA interactions at high energies: examples Recent results from the HARP experiment 12.9 GeV/c p on Al π+ production Double differential π+ production at for p C interactions at 158 GeV/c, as different measured by NA49 (symbols) and angles predicted by FLUKA (histograms) 7th Fluka Course, Paris Sept.29-Oct.3, 2008 19 Pions in nuclear medium 7th Fluka Course, Paris Sept.29-Oct.3, 2008 20 Emitted proton spectra at Pion absorption different angles , 160 MeV π+ on 58Ni Phys. Rev. C41,2215 (1990) Pion absorption cross Phys. Rev. C24,211 (1981) section on Gold and Proton spectra extend up to Bismuth in the Δ resonance 300 MeV region (multibody absorption in PEANUT) 7th Fluka Course, Paris Sept.29-Oct.3, 2008 21 Preequilibrium emission For E > π production threshold → only (G)INC models At lower energies a variety of preequilibrium
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