Thermalization -up to lowest energies?

A view on this question with microscopic transport models

C. Hartnack, J. Aichelin, H. Oeschler

SUBATECH, Nantes

TU Darmstadt

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

Motivation

The description of particle ratios at low temperature and intermediate density – why should/can we use thermal models?

Ask a transport model …

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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...

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

What is governing the dynamics?Elastic and inelastic cross sections

Parametrisations according to experimental data

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.

Effect on the pion productionCounterbalancing effects

of the cross sectionsNN↔NΔ andπN→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)

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.

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

Comparison to experiment

IQMD uses free cross section+ Pauli blocking

Kaon production also in agreement to experimental data from KaoS

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 …

The kaon « feels » the Δ

NΔ→XK

πB→XK

.. But the decay time may change this

Kaon per participantKaoS, PRC 74 (2007) 024906

Since π/A is constant we get also effects on K/π:

But do not insist too much on absolute yields

• Effects of parametrizations, potentials, eos, …

Effect stronger for low energy

Place reserved for Spencer’s THERMUS calculation

Well above the threshold the effects may diminuish

RC=1.5 shurely too small: K-prod is « collective »

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…

Antikaons: dominance of Yπ↔NK-

The Y is produced with the K+

K-

π

K+

Main effect from kaons

Ratio K-/K+ insensitive to π,ΔAt least for large systems

Participant number dependency for Au+Au:

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

Excitation function of K-/K+

J.Cleymans et al;PLB603(2004)146

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).

Test of the Law of Mass Action by J. Cleymans

κ = ([π] [Y])/([K-] [N])J.Cleymans et al;PLB603(2004)146

… or by the crew of Jean

• Agreement without any correction factor

Thermus run by Spencer Wheaton with R=7fm

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

If we shadows have offended,Think but this, and all is mended,That you have but slumber'd hereWhile 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

System size: question of geometry

For smaller systems with smaller R you need a smaller λ thus higher σ System size A

R

A « formation time » could interfere with the Δ absorption

Visible effects but for the actual free cross sections the effects are quite moderate.

KaoS, PRC 74 (2007) 024906