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Countrate estimates

Countrate estimates. Particle production in heavy ion collisions. Particle multiplicities for central Au+Au collisions from UrQMD calculations. Example Ω production Direct production: NN   +  - NN (E thr = 12.7 GeV) Production via multiple collisions: NN  K+ Λ N,

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Countrate estimates

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  1. Countrate estimates

  2. Particle production in heavy ion collisions

  3. Particle multiplicities for central Au+Au collisionsfrom UrQMD calculations Example Ω production Direct production: NN + - NN (Ethr = 12.7 GeV) Production via multiple collisions: NN K+ΛN, NN  K+K-NN, ΛK- - 0, -K- - - Au+Au 6 AGeV central minimum bias 0.00072 0.00018

  4. Observables U+U 23 AGeV

  5. RHIC Pion multiplicities per participating nucleons

  6. meson-baryon interaction

  7. Production of K+ und K- mesons in central AuAu/PbPb collisions SIS: KaoS AGS: E802,E866 SPS: NA49 RHIC RHIC NN  K+LN: Elab  1.6 GeV NN  K+K-NN: Elab  2.5 GeV

  8. Meson production in central Au+Au collisions GSI W. Cassing, E. Bratkovskaya, A. Sibirtsev, Nucl. Phys. A 691 (2001) 745

  9. Rapidity distributions Central Pb+Pb collisions at SPS energies C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692 Rapidity: y(0) = y-ym with y =0.5 ln [(E+pz)/(E-pz)]

  10. Particle yields in midrapidity from central A+A collisions

  11. Central Au+Au collisions (midrapidity): statistical model results A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199 E = 4 AGeV E = 2 AGeV E = 8 AGeV E = 6 AGeV

  12. Central Au+Au collisions (midrapidity): statistical model results E = 10.7 AGeV E = 40 AGeV E = 80 AGeV

  13. Central Au+Au collisions (midrapidity): Statistical model results E = 158 AGeV

  14. Central Au+Au collisions (midrapidity): Statistical model results

  15. Central Au+Au collisions (midrapidity): Statistical model results

  16. Central Au+Au collisions (midrapidity): Statistical model results

  17. Central Au+Au collisions (midrapidity): Statistical model results

  18. Central Au+Au collisions (midrapidity): Statistical model results

  19. Strangeness/pion ratios C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692 Decrease of baryon-chemical potential: transition from baryon-dominated to meson-dominated matter ?

  20. Strangeness = 2 × (K+ + K−) + 1.54 × (Λ + Λ¯) Entropy = 1.5 × (π+ + π−) + 2 × p¯

  21. The freeze-out curve in the QCD phase diagram A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199

  22. J. Randrup and J. Cleymans, hep-ph/0607065

  23. Pion production in Au + Au collisions at 1.5 AGeV Data: T. Schuck, Dipl. Thesis 2003, GSI/Uni Frankfurt

  24. "Boltzmann" parameterisation: d3/dp3 = C1 exp(-E/T1) + C2 exp(-E/T2)

  25. The explosion of the fireball Kinetic energy of a particle: Ek = Eth + Eflow = 3/2 kT + m/2flow2 Blast wave model: isotropically expanding System with temperature T P.J. Siemens and J.O. Rasmussen, Phys. Rev. Lett. 42 (1979) 880 dotted line: f =const. bold line: Hubble expansion f = rH

  26. N. Xu, Int. J. Mod. Phys. E16 (2007) 715

  27. Determination of collision centrality Participants Spectators or Zero Degree Calorimeter: EZDC= Ebeam APro-Spec and Apart = 2 ( A - EZDC/Ebeam) Number of participating nucleons in A+A collisions : Apart = 2 x A/Z x (Z – Zspec)

  28. Determination of the reaction plane Transverse Momentum Method: P. Danielewicz & G. Odyniec, Phys. Lett. 157 B (1985) 146 Dispersion of the reaction plane: Sub-Event-Method:  = 1 - 2 Q = p  = 1 für y>ycm R= arctan(Qy/Qx)

  29. The pion clock: in-plane emission in Au+Au collisions at 1.0 AGeV Nπproj/Nπtarg High-energy pions freeze-out early A. Wagner et al., Phys. Rev. Lett. 85 (2000) 18

  30. The Flow Probe Expect Large Pressure Gradients  Hydro Flow

  31. Dense baryonic matter up to 3 ρ0: Probing the nuclear equation-of-state with heavy ions

  32. The equation-of-state of (symmetric) nuclear matter C. Fuchs, Prog. Part. Nucl. Phys. 56 (2006) 1 Equation of state: PV  T  E P  E/V  E/A • E/A(ro) = -16 MeV • d(E/A)(ro)/dr = 0 • Compressibility: k = 9r2 d2(E/A)/ dr2 k = 200 MeV: "soft" EOS k = 380 MeV: "stiff" EOS Observable in HI collisions: collective flow (driven by pressure)

  33. Definition of the potentials in transport codes 2 and 3 body interactions (no equilibrium required) Bethe Weizsaecker –mass formula: +symmetry term Volume term (with eos) +Surface term +Coulomb term (+pairing term not included)

  34. The eos in IQMD after the convolution of the Skyrme type potentials supplemented by momentum dependent interactions (mdi)for infinite nuclear matter at equilibrium soft hard

  35. Baryon and energy densities at FAIR energies Baryon/energy density in central cell (Au+Au, b=0 fm): Transport code HSD: mean field, hadrons + resonances + strings E. Bratkovskaya, W. Cassing

  36. Dynamics of a semi-central Au+Au collision at 2 AGeV (BUU calculation, P. Danielewicz, MSU)

  37. Azimuthal angular distribution of protons measured in Au+Au collisions at 1.15, 2, 4, 6, 8 AGeV AGeV C.Pinkenburg et al., (E895), Phys. Rev. Lett. 83 (1999) 1295 Rapidity: y(0) = y-ym with y = 0.5 ln [(E+pz)/(E-pz)] Azimuthal angle distribution: dN/dF  (1 + 2v1cosF + 2v2 cos2F)

  38. Probing the nuclear equation-of-state: proton collective flow P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 K = 170 – 210 MeV K = 170 – 380 MeV Transverse in-plane flow: Elliptic flow: F = d(px/A)/d(y/ycm) dN/dF  (1 + 2v1cosF + 2v2 cos2F)

  39. New data: Au + Au collisions at SIS energies A. Andronic et al. (FOPI Collaboration) Phys. Lett. B612 (2005) 173

  40. Pressure as function of density pressure P = ρ2· ( δ(ε/ρ) / δρ ) with nuclear density ρ and energy density ε Within microscopic transport models the collective flow is sensitive to:  The nuclear matter equation of state  In-medium nucleon-nucleon cross sections  Momentum dependent interactions Independent observable ? particle production P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592

  41. Probing the equation-of-state of symmetric nuclear matter: Kaon production in Au+Au collisions at 1 AGeV u d d u d s L n d u s u K+ p+ K+ mesons probe high densities pp → K+Λp (Ethres= 1.6 GeV) K+ reabsorption negligible

  42. Kaon production in Au+Au collisions at subthreshold beam energies MK+ (Apart)1.8 Mp+ Apart NN  K+LNreduced (Ebeam = 1.6 GeV) pN  K+L, DN  K+LN enhanced

  43. u d u u d s L p u d d u d d n K+ n s u s u K+ s u K- u d u u d u p d d u n p d d u n u d s u d u u d d u d s p S0 L n u u s u K- d u s u p0 K+ p+ K-absorption The creation of strange mesons

  44. Probing the nuclear equation-of-state (ρ = 1 – 3 ρ0) by K+ meson production in C+C and Au+Au collisions Idea: K+ yield  baryon density ρcompressibility κ Transport model (RBUU) Au+Au at 1 AGeV: κ = 200 MeVρmax 2.9 ρ0  K+ κ = 380 MeV ρmax 2.4 ρ0  K+ Reference system C+C: K+ yield not sensitive to EOS Experiment: C. Sturm et al., (KaoS Collaboration), Phys. Rev. Lett. 86 (2001) 39 Theory: Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

  45. The compressibility of nuclear matter Experiment: C. Sturm et al., (KaoS Collaboration) Phys. Rev. Lett. 86 (2001) 39 Theory: QMD Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974 IQMD Ch. Hartnack, J. Aichelin, J. Phys. G 28 (2002) 1649 soft equation-of-state: k ≤ 200 MeV Au/C ratio: cancellation of systematic errors both in experiment and theory

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