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Properties of nuclear matter from subtheshold strangeness production

Properties of nuclear matter from subtheshold strangeness production. Christoph Hartnack, Helmut Oeschler, J ö rg Aichelin Subatech Nantes and TH Darmstadt Outline: Subthreshold production, optical potential Spectra, temperatures and KN rescattering

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Properties of nuclear matter from subtheshold strangeness production

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  1. Properties of nuclear matter from subtheshold strangeness production Christoph Hartnack, Helmut Oeschler, Jörg Aichelin Subatech Nantes and TH Darmstadt Outline: • Subthreshold production, optical potential • Spectra, temperatures and KN rescattering • Azimuthal distribution and the KN potential • Scaling laws and the nuclear equation of state • Conclusion Calculations performed with IQMD, a semiclassical, microscopic N-body model with quantum features for the description of HICs on an event-by-event basis

  2. Subthreshold kaon production • Production of kaons at energies below the kinetic threshold for K production in elementary pp collisions • Fermi momenta may contribute in energy • Multistep processes can cumulate the energy needed for kaon production • Importance of resonances (especially the D) for storing energy • Short livetime of resonance favors early production at high densities • Sensitivity to in-medium effects and nuclear equation of state

  3. Time-evolution & kaon production 0fm/c 4fm/c 8fm/c 12fm/c 16fm/c 20fm/c K+: early, multistep induced product. when baryon density is highestK-: prod. later when pion density is highest, strangeness exchange

  4. In medium effects on kaons • KN-Rescattering, absorption for K- • Optical potential: repulsive for K+, attractive for K- • Penalizes K+ production at high densities but favors K- production at high densities • Effects yields but also dynamics Parametrization from Schaffner-Bielich RMF results

  5. Can we reveal the KN potential from K+ yields? No Pot Au-data: Foerster et al, KaoS Ni-data: Uhlig et al., KaoS KN pot Visible difference between calculations with and without KN potential on a log-scale. KN-pot yields less kaons, but incertainties on D induced cross sections discourage a preliminary conclusion.

  6. K- production dominated by strangeness exchange +BY +pY BB+pB+pY+BY +pB BB Direct channels BB, pB enhanced by K- potential, similar for exchange channels pY+BY. The K+ potential penalizes hyperon production and compensates in the dominant channels pY+BY.

  7. Spectra: slopes dominated by KN-rescattering Rescatteringpotential Collision number K+ K- K+ rescatter Strong enhancement of the slope from initial to final mom. Slight effects: enhancement (K+) or reduction (K-) High K+ rescattering less K- rescattering

  8. Temperatures of K+ IQMD results with KN-rescattering are in good agreement with KaoS data K+ heated up by coll. with expanding nucl.medium KaoS A.Förster et al. PRC75(2007) 024906 K- show systematically lower temperatures. Reason: less rescattering, diff. potentials?

  9. Azimuthal distributions Azimuthal distributions are effected by rescattering and by the optical potential. While the rescattering acts in the same direction for K+ and K- the optical potential gives opposite effects for K+ and K- Azimuthal distribution fitted with a (1+v1 cos(f) + 2 v2cos(2f)) KaoS and FOPI see opposite signs of v2 for K+ and K- Ni+Ni 1.93 GeV, F. Uhlig et al, KaoS

  10. Excitation function of v2 for K+ Rescattering and optical potential are needed to describe the v2 of kaons. The effects of the optical potential become dominant with respect to the effect of rescattering when going down in beam energy. This is in agreement with calculations of Li&Ko who found a strong potential effect for Au+Au 1 GeV/A.

  11. Comparison of v1(y0) to FOPI data Preliminary data from FOPI (Kim et al. ) favor an optical potential less strong than implemented by us

  12. The original idea of measuring the eos • Eos describes the energy needed to compress nuclear matter • A hard eos requires more energy for a given densitythan a soft one • For a given density and a given available energy a soft eos leaves more thermal energy to the systemthan a hard eos • R.Stock: This thermal energy could be measured by regarding pion production

  13. At which density can we measure the eos? Different densities are reached for hard and soft eos. A soft eos yields higher densities than a hard eos. The differences in compressional energy and thus in thermal energy become less. The pion number is not sensitive enough. Pions come out late due to reabsorption in dense matter Kaons might be an interesting probe. However the effects of the optical potential and incertainties of the cross section do not allow a direct measure of the eos from kaon yields.

  14. The solution: ratios Au/C KaoS data support soft eos Symbols: KaoS data Lines IQMD Data: Ch.Sturm et al. RQMD: Ch. Fuchs IQMD supports this Robust against changes of cross sections, optical potential, Delta lifetimes, etc.

  15. Au: central versus peripheral Different cross sections and potential parameters may change the global yield. However, the parameter a for the increase of the kaon yield N with the number A of participating nucleons (raising with centrality) N(K)=N0 Aa depends on the eos. central peripheral A soft eos yields higher values than a hard eos.

  16. Determination of the eos from a The relation between the compression modulus and a is monotonously falling. KaoS data (Förster et al.)favor a value below 200 MeV, i.e. a soft eos. KaoS:Förster et al. soft hard Same for Au/C ratio C.H. et al. PRL 96 (2006) 012302

  17. Another scaling systematics: system size Scaling with system size in inclusive A+A events System size, Kaos Data Apart in Au+Au from KaoS agrees with that 2 independent observables ( centrality scaling and system size scaling) confirm soft eos

  18. Kaons and density isomers • Could reveal density isomers by a sudden rise in the excitation function of kaons - KaoS might measure it A 2ndminimum would yield a sudden factor of 10 in the kaon yield Density isomers yield up to factors of 10 in K+ production 800MeV 600 Effect related to subthreshold prod. C.H. et al. PRL 72 (1994) 3767

  19. KaoS DATA: no isomer up to 3r0 A density isomer would have needed the strong raise indicated by the arrows. IQMD calculations using a KN optical potential and a soft eos are consistent with KaoS data on Au+Au and C+C of Sturm et al. For higher densities/beam energies we need other particles produced below threshold

  20. Conclusions • Kaon spectra reveal strong rescattering of kaons with the surrounding nuclear matter • Comparison of flow variables supports the existence of KN optical potential • Scaling laws of the kaon production claim strongly for a soft equation of state • The KaoS measurements (which can be continued by eos data) contradict the existence of density isomers at moderate densities

  21. Effect of the potential: penalty reimbursed • Initial distributions show a difference of calculations with KN-pot and without pot at all energies. This is due to the penalty paid at the production. • In the final state the kaons regain the paid penalty and the curves of both calculations become rather close Only at small energies a lack remains stemming from those kaons which failed to be produced due to the penalty. Kaons with did not undergo collisions: No KN potential : final=initial

  22. KN collisions change the spectra Most kaons underwent many collisions before leaving. They show a significant enhancement of the slope. At the time before the freeze out of the kaons (about 12-20 fm/c) the nucleonic system is still hot and expanding. The kaons carry the temperature of that expansion phase. initial

  23. Comparison to data for K- Less rescattering for the K- yield smaller temperature than for K+

  24. Comparison of spectra for K+

  25. Temperature: centrality dependence

  26. Temperature and collisions

  27. Maxwellian Demon

  28. Au+Au 1.5 GeV azimuthal distribution For Au+Au at 1.5 GeV we needed both potential and rescattering to reproduce the results of Foerster et al.

  29. Influence on v2(pT) at midrapidity Again opposite effect on K+ an K- useful for balancing the effect of rescattering FOPI and KaoS see opposite signs of v2 for K+ and K-

  30. V2:pT dependence

  31. Polar distributions

  32. Polar distribution: rescattering and potential

  33. Excitation function of K+

  34. A observation which is robust sNDTsushima sND=.75 sNN versus effects of production cross sections, KN-potential, D-lifetime

  35. Going down in beam energy A soft eos yields a1.4 at E=0.8 AGeV, a hard eos yields a1.2 Limits for lower E: no asymptotic yield for peripheral collisions

  36. Einc System size dependence A soft eos obtains higher kaon yields for heavy systems 1.8 1.5 KaoS: PRC in preparation 1.2 1.0 0.8 0.6

  37. A mixture of both NC=0 has a visible fraction to the yield, shows a taller rapidity distribution and strongly negative flow. For NC>2 a positive flow and a wider y-distribution is observed

  38. The potential shifts to negative flow Initial vs final Pot vs. NoPot NC=0: initial shadowing boosted by potential to strong neg. flow NC>2: initial bias, enhanced by scattering, reduced by potential

  39. Final flow a superposition of different flows Initial flow: bias for having collisions or not Final flow: visible shift from the potential

  40. Rescattering enhances potential effect For NC=0 the initial flow is inverted Rescattering adds up more positive flow

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