Countrate estimates

Particle production in heavy ion collisions

Particle multiplicities for central Au+Au collisionsfrom UrQMD calculations Au+Au 6 AGeV central minimum bias 0.00072 0.00018Example production

Direct production:NN + - NN (Ethr = 12.7 GeV)

Production via multiple collisions:

NN K+N, NN K+K-NN, K- - 0, -K- - -

R = reactions/secNB = beam particles/sec = cross section [barn = 10-24cm2]NT /F = target atoms/cm2 = NA d/A with Avogadros Number NA = 6.021023 mol-1, material density [g/cm3], target thickness d [cm] atomic number A Reaction rate: R = NB NT/F

Reaction cross section and target thicknessReaction cross section: R = (2 R)2 = 4 (r0A1/3)2 with r0=1.2 fmAu+Au collisions: A=197 R = 6.1 barn, 1 barn = 10-24 cm2Reaction probability for Au+Au collisions: R/NB = R NT/F = 6.1 b 6.021023d/A = 6.1 10-24 cm2 6.02102319.3 g/cm3d/197 = 1%

target thickness d = 0.027 cm

Production cross sections for min. bias Au+Au collisions at 6 AGeV:

() = M() x R = 1.810-4 x 6.1 b = 1.110-3 bParticle production probabilities for min. bias Au+Au at 6 AGeV:R()/NB =()NAd/A = () [b]1.610-3 = 1.810-6recorded particles: R()/NB = ?Experimental efficiencies?

Acceptances and Efficiencies

= p Det Trigg DAQ analysiswith = angular acceptance p = momentum acceptanceDet = detector efficienciesTrigg = trigger efficienciesDAQ = deadtime correction of DAQanalysis = efficiency of analysis (track finding, cuts for background suppression , ...)Typical values: 0.5, p 0.8, Det 0.9, Trigg 0.9, DAQ 0.5, analysis 0.3,

0.05

Typical detection probabilities in Au+Au at 5 AGeV:R()/NB = 1.810-60.05 = 910-8

Recorded rates for a Au-beam intensity of 108/sec:R() = 108/sec x 910-8 = 9/sec

Recorded yield after 1 week beam on target: Y = 9 x 3600 x 24 x 7 = 5.4106

These numbers refers to one collision system and one beam energy only. Systematic studies require excitation functions (several beam energies) with different collision systems !

Observables

U+U 23 AGeV

Pion multiplicities per participating nucleons

meson-baryon interaction

SIS: KaoS AGS: E802,E866 SPS: NA49Production of K+ und K- mesons in central AuAu/PbPb collisionsNN K+LN: Elab 1.6 GeVNN K+K-NN: Elab 2.5 GeV RHICRHIC

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

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

Particle yields in midrapidity from central A+A collisions

Partition functionParticle densitygi = (2Ji+1) spin degeneracy factor, temperature T, and Ei = (p2 + m2)i the total energy. net baryon density: B 4 ( mT/2)3/2 x [exp((B-m)/T) - exp((-B-m)/T)] baryons - antibaryons

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

E = 10.7 AGeVE = 40 AGeVE = 80 AGeVCentral Au+Au collisions (midrapidity): statistical model results

E = 158 AGeVCentral Au+Au collisions (midrapidity): Statistical model results

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

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

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

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

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

Strangeness/pion ratios Decrease of baryon-chemicalpotential: transition frombaryon-dominatedto meson-dominatedmatter ?C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692

Strangeness = 2 (K+ + K) + 1.54 ( + )Entropy = 1.5 (+ + ) + 2 p

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

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

Particle yields

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

"Boltzmann" parameterisation:

d3/dp3 = C1 exp(-E/T1) + C2 exp(-E/T2)

Kinetic energy of a particle:Ek = Eth + Eflow = 3/2 kT + m/2flow2The explosion of the fireball 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. solid line: Hubble expansion f = rH

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

Determination of collision centralityNumber of participating nucleons in A+A collisions : Apart = 2 x A/Z x (Z Zspec) or Zero Degree Calorimeter: EZDC= Ebeam APro-Spec and Apart = 2 ( A - EZDC/Ebeam)

Determination of the reaction planeTransverse Momentum Method: P. Danielewicz & G. Odyniec, Phys. Lett. 157 B (1985) 146Q = p = 1 fr y>ycmR = arctan(Qy/Qx)

Dispersion of the reaction plane:Sub-Event-Method: = 1 - 2

The pion clock: in-plane emission in Au+Au collisions at 1.0 AGeVA. Wagner et al., Phys. Rev. Lett. 85 (2000) 18

Expect Large Pressure Gradients Hydro FlowThe Flow Probe

Dense baryonic matter up to 3 0:

Probing the nuclear equation-of-state with heavy ions

Observable in HI collisions: collective flow (driven by pressure)The equation-of-state of (symmetric) nuclear matter

E/A(ro) = -16 MeV d(E/A)(ro)/dr = 0 Compressibility:k = 9r2 d2 (E/A)/ dr2 k = 200 MeV: "soft" EOSk = 380 MeV: "stiff" EOSC. Fuchs, Prog. Part. Nucl. Phys. 56 (2006) 1Equation of state:

PV T E P E/V E/A

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

The eos in IQMDafter the convolution of the Skyrme type potentials supplemented by momentum dependent interactions (mdi) for infinite nuclear matter at equilibriumhardsoft

Energy per nucleon in nuclear matter (Skyrme potential):E/A = 3kF2/(10M) + ra/2 + brg /(1 + g) The nuclear matter equation of state Conditions: E/A(ro) = -16 MeV d(E/A)(ro)/dr = 0 Compressibility:k = 9r2 d2 (E/A)/ dr2 = 200 - 400 MeV

Baryon/energy density in central cell (Au+Au, b=0 fm):Transport code HSD: mean field, hadrons + resonances + strings

E. Bratkovskaya, W. Cassing Baryon and energy densities at FAIR energies

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

Azimuthal angle distribution:dN/dF (1 + 2v1 cosF + 2v2 cos2F)C.Pinkenburg et al., (E895), Phys. Rev. Lett. 83 (1999) 1295Azimuthal angular distribution of protons measured in Au+Au collisions at 1.15, 2, 4, 6, 8 AGeVRapidity: y(0) = y-ym with y = 0.5 ln [(E+pz)/(E-pz)] AGeV

dN/dF (1 + 2v1 cosF + 2v2 cos2F)P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 Probing the nuclear equation-of-state: proton collective flow Transverse in-plane flow: Elliptic flow: F = d(px/A)/d(y/ycm) K = 170 210 MeV K = 170 380 MeV

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

P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 pressure P = 2 ( (/) / )with nuclear density and energy density Pressure as function of density

Independent observable ? particle production

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

Probing the equation-of-state of symmetric nuclear matter:Kaon production in Au+Au collisions at 1 AGeV pp K+p (Ethres= 1.6 GeV)K+ reabsorption negligible

NN K+LN reduced (Ebeam = 1.6 GeV)pN K+L, DN K+LN enhanced MK+ (Apart) 1.8

Mp+ Apart

Kaon production in Au+Au collisions at subthreshold beam energies

The creation of strange mesons

Probing the nuclear equation-of-state ( = 1 3 0) by K+ meson production in C+C and Au+Au collisionsTransport model (RBUU)Au+Au at 1 AGeV: = 200 MeV max 2.9 0 K+ = 380 MeV max 2.4 0 K+Reference system C+C: K+ yield not sensitive to EOSIdea: K+ yield baryon density compressibility Experiment: C. Sturm et al., (KaoS Collaboration), Phys. Rev. Lett. 86 (2001) 39Theory: Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

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

Exploring the "nuclear" EOS at 30 < < 70

Measure excitation function of (multi-strange) hyperon production in heavy-ion collisions from 2 - 15 AGeV (no data yet):

Direct produc