1. Thermalization - up to lowest energies? A view on this question with microscopic transport models C. Hartnack, J. Aichelin, H. Oeschler SUBATECH, Nantes TU Darmstadt

2. Outline Microscopic transport: IQMD The world of pions, nucleons and Deltas Subtreshold kaons and their relation to π and Δ Subthreshold antikaons – why they are coupled to the kaon production Conclusion

3. Motivation The description of particle ratios at low temperature and intermediate density – why should/can we use thermal models? Ask a transport model …

4. And now, the end is near And so I face the final curtain. My friend, I'll say it clear, I'll state my case, of which I'm certain. I've lived a life that's full. I travelled each and ev'ry highway And more, much more than this, I did it my way. Regrets, I've had a few But then again, too few to mention. I did what I had to do And saw it through without exemption. I planned each charted course Each careful step along the byway, And more, much more than this, I did it my way. Yes, there were times, I'm sure you knew When I bit off more than I could chew. But through it all, when there was doubt, I ate it up and spit it out I faced it all and I stood tall And did it my way. I've loved, I've laughed and cried. I've had my fill, my share of losing. And now, as tears subside, I find it all so amusing. To think I did all that And may I say - not in a shy way,"Oh no, oh no not me, I did it my way". For what is a man, what has he got? If not himself, then he has naught To say the things he truly feels And not the words of one who kneels. The record shows I took the blows And did it my way IQMD - some lyrics - semiclassical model with quantum features - microscopic N-body description - calculation of heavy ion collisions on an event-by-event-basis -includes N,  with isospin d.o.f. - - strange particles treated virtually - 2 and 3 body potentials including nuclear equation of state, Coulomb...

5. Time-evolution π,Δ, K-production K + : early, multistep induced product. when baryon density is highest K - : prod. later when pion density is highest, strangeness exchange 0fm/c 4fm/c 8fm/c 12fm/c 16fm/c 20fm/c Highest density reached: first N then Δ then π

6. What is governing the dynamics? Elastic and inelastic cross sections Parametrisations according to experimental data

7. One sign for global thermalization would be the isotropy We should blow up our cross sections quite well. And this is already one of the heaviest systems.

8. Effect on the pion production Counterbalancing effects of the cross sections NN↔NΔ and πN→Δ (Δ→πN governed by the Δ-decay width) Thus changing all cross sections will only effect the yields moderately (and drop them, we are on the maximum)

9. The Δ- decay defines a time scale Pion yield remains constant for reasonable changes of the decay width. For very large values the absorption of the Δ is blocked.

10. Geometry? π/A A happy coincidence for the use of thermal models? The constant ratio of π/A can only be achieved with the actual free cross sections. KaoS, PRC 74 (2007) 024906

11. Comparison to experiment IQMD uses free cross section+ Pauli blocking

12. Kaon production also in agreement to experimental data from KaoS

13. Kaon production is more sensitive… Subthreshold K production needs multiple collisions. Strong sensitivity to density and Δ population. However, one should not forget the large dependencies of absolute kaon yields on cross sections, potentials, eos …

14. The kaon « feels » the Δ NΔ→XK πB→XK

15. .. But the decay time may change this

16. Kaon per participant KaoS, PRC 74 (2007) 024906 Since π/A is constant we get also effects on K/π:

17. But do not insist too much on absolute yields Effects of parametrizations, potentials, eos, …

18. Effect stronger for low energy Place reserved for Spencer’s THERMUS calculation Well above the threshold the effects may diminuish R C =1.5 shurely too small: K-prod is « collective »

19. If you didn’t see Spencer during lunch … The truth may be with some other R in between R=1.5 and R=7fm but the coffee breaks are lacking…

20. Antikaons: dominance of Yπ↔NK -

21. The Y is produced with the K+ K-K- π K+K+ Main effect from kaons

22. Ratio K - /K + insensitive to π,Δ At least for large systems Participant number dependency for Au+Au:

23. Insensitivity of K - /K + to Yπ↔NK - The antikaon production follows the law of mass action: The yield becomes insensitive to the cross section. For small cross section other channels take over the dominance. NΔ and Nπ→Δ do not show any influence

24. Excitation function of K - /K + J.Cleymans et al;PLB603(2004)146

25. Test on law of mass action If A is sufficiently high, the ratio K-/K+ is directly related to the pion multiplicity (while K+ dominated by BB-BYK).

26. Test of the Law of Mass Action by J. Cleymans κ = ([π] [Y])/([K - ] [N]) J.Cleymans et al;PLB603(2004)146

27. … or by the crew of Jean Agreement without any correction factor Thermus run by Spencer Wheaton with R=7fm

28. Assumption confirmed by experiment Analysis of the data of pions, kaons and antikaons at AGS confirms this behaviour: Application of the law of mass action H. Oeschler, SQM 01 and J. Phys. G: Nucl. Part. Phys. 27 (2001) 257

29. If we shadows have offended, Think but this, and all is mended, That you have but slumber'd here While these visions did appear. And this weak and idle theme, No more yielding but a dream Gentles, do not reprehend: if you pardon, we will mend. W. Shakespeare: A midsummer night’s dream Conclusions Systems far away from isotropy Pion yields quite insensitive to cross sections –Good starting point for applying thermo Pion/A constant: balance or happy coincidence? –At least for thermo this is nice … Kaons related to pions and deltas cross sections, but for small energies also sensitive to densities –Visible effects of cross sections - may disappear at higher energies –May be problematic for thermo –However huge incertainties on absolute yields from cross section, potential, eos etc … be very careful when concluding from yields Antikaons strongly related to the kaon production –K - /K + related to the pion yield due to the law of mass action –Ideal starting point for thermo

31. System size: question of geometry For smaller systems with smaller R you need a smaller λ thus higher σ System size A R

32. A « formation time » could interfere with the Δ absorption Visible effects but for the actual free cross sections the effects are quite moderate.

33. KaoS, PRC 74 (2007) 024906