Transverse and elliptic flows and stopping WCI-I Principle observables What is the major experimental uncertainty? To what accuracy can they be calculated? What is the major theoretical uncertainty? Ancillary observables What constraints on EOS have been provided? How can constraints be improved? New observables

Pressure and collective flow dynamics pressure contours density contours The blocking by the spectator matter provides a clock with which to measure the expansion rate.

Transverse directed flow Pinkenburg et al Sensitive to EOS, in-medium cross sections and momentum dependence. Experimental uncertainties: impact parameter determination acceptance correction reaction plane determination: Problematic for low multiplicities and at energies near Ebal.

Status Pinkenburg et al Systematics on Au+Au exists for a wide range of incident energies. Results are consistent at the 10-15% level. Light systems, lower energies and asymmetric systems are less systematically studied.

Elliptical flow (E895) Sensitive to EOS, in-medium cross sections and momentum dependence. Experimental uncertainties: impact parameter determination acceptance correction reaction plane determination: Problematic for low multiplicities. Pinkenburg et al

Status Pinkenburg et al Systematics are available for Au+Au over a wide range of energies. New Indra data extends systematics to low energies. Systematics for lighter systems and asymmetric systems are less extensive. New data from FOPI.

Kaon production Sensitive to density achieved, and to Kaon potentials. Fuchs et al., PRL 86, 1975 (2001) Sensitive to density achieved, and to Kaon potentials. Major experimental uncertainty concerns the acceptance correction.

Stopping Observable: heavy residue velocities for central collisions. Colin et al. PRC57(98)R1032; Observable: heavy residue velocities for central collisions. Sensitive in-medium cross sections and to EOS. Experimental uncertainties: impact parameter distribution for the observed channel. channel dependence of the linear momentum transfer.

Stopping at high energies Vartl provides a measure of the isotropy of the central collision event. vart1=1 for an equilibrated single source. Sensitive to in-medium cross sections. Major experimental uncertainty: impact parameter determination. acceptance correction. Reisdorf et al., Phys. Rev. Lett. 92, 232301 (2004).

Stopping-transverse flow correlation There is a correlation between the maximum transverse flow and the observed stopping measured by Vartl Note: two quantities are not measured at the same impact parameter. Reisdorf, PRL. 92, 232301 (2004).

Theoretical problem: mass dependence of flow observables The measured transverse and elliptical flows are mass dependent: problem important at low energies Presents problem for models that do not explicitly predict cluster observables. Molecular dynamics does explicitly predict clusters BUU does not Coalescence invariant analyses. Huang, Phys. Rev. Lett. 77, 3739 (1996)

Theoretical problem: constraining the momentum dependence Huang, Phys. Rev. Lett. 77, 3739 (1996) Momentum dependence, e.g. from vector meson exchange or from the Foch term, tends to make the mean field potential appear “stiffer”. Ancillary measurements are needed to constrain the momentum dependence V2 measurement in peripheral collisions. Measurements of transverse flow in asymmetric systems. Danielewicz, Nucl. Phys. A 673, 375.

Constraining theoretical uncertainties: in-medium cross sections Gaitanos et al., nucl-th/0412055, (2005) Calculations indicate that Vartl can provide sensitive constraints on the in-medium cross sections. More study needed to achieve this goal.

Constraining the EOS Danielewicz, Science 298, 1592 (2002) Vary the density dependence of the mean fields to reproduce the observed transverse and elliptical flows. momentum dependence constrained by V2 measurements Cross sections constrained by rapidity distributions.

Present constraints Danielewicz, Science 298, 1592 (2002) Use constrained mean fields to predict the EOS for symmetric matter Width of pressure domain reflects uncertainties in comparison and of assumed momentum dependence. Corresponding EOS for neutron matter includes pressure from the asymmetry term. Two regions correspond to two different density dependencies

Reliabilities of transport codes Currently there are efforts to compare different transport codes: main thrust is to understand where there are differences and what are the origins of the differences. What are the sources of the discrepancies? Some of these models have not been used in flow analyses. Are the nuclear surfaces of all these models been handled with sufficient care? Problems also reported in kaon production. Kolomeitsev et al., nucl-th/0412037 (2005).

Equation of State, consensus?

Spectator response to the participant blast BUU calculations : 124Sn +124Sn Tlab= 800 MeV/u b = 5 fm L. Shi, P. Danielewicz, R. Lacey, PRC 64 (2001) Idea: elliptic flow of the paricipant matter can be affected by the presence of the cold spectator (squeeze-out) spectator properties are influenced by the participants expansion WCI3 Texas 2004 Vlad Henzl for CHARMS

Spectator response – experimental evidence (projectile frame) Ptot/A= 682 MeV/c Fission events excluded !!! V.Henzl PhD thesis T.Enqvist et al. NPA658(1999)47 M.V.Ricciardi et al. PRL 90(2003)212302 The Outlook: 197Au+197Au, 27Al @ 500 A MeV (analysis in progress) 112,124Sn+112,124Sn @ 1 A GeV (2005/2006) WCI3 Texas 2004 Vlad Henzl for CHARMS

Flow angle and transverse energy: comparison HIPSE / INDRA data Flow angle-complete events (c) Transverse energy of LCP Selection Xe+Sn (b) Complete events Pzot,Ztot>80% Data (c) Central events Pzot,Ztot>80% and flow angle>30 deg Figure from A. Van Lauwe, Ph.D, LPC Caen (2003) Corresponding Impact parameters: Flow angle and transverse energy in central collisions [c] are rather well reproduced For complete events (selection [b]), a deviation is observed when the beam energy increases, In HIPSE, We attribute the difference in the absence of some reaction mechanisms at intermediate impact parameters (deformation effects, complex alignment of fragments…) (b) (c)