Laboratory for Nuclear Physics Division of Experimental Physics

1. Constancy of Energy Partition in Central Heavy-Ion Reactions at Intermediate Energies Zoran Basrak In collaboration with Philippe Eudes,MajaZorić, and François Sébille Laboratory for Nuclear PhysicsDivision of Experimental Physics RuđerBošković Institute, Zagreb, Croatia 11th International Conference on Nucleus-Nucleus Collisions May 28 – June 1st, 2011, San Antonio, TX–USA

2. Landau-Vlasov simulation Transport equation of theBoltzmann type H = T+U, U = Vnucl+VCoul , Vnucl – Gogny G1-D1 non-local potential K=228 MeV, m*/m=0.67 f = f(r,p;t) - distributionfunction Collision term Phenomenological, isotropic σ = σ(E, iso) [Chen et al.] An approach adequate for bulk (one-body) properties of nuclear dynamics, in particular for an early and compact reaction phase

3. Ar ( 65 MeV / u ) Al Ar ( 65 MeV / u ) Al Dynamical emission component Landau-Vlasov model simulation A similar two-stages process in 1A GeV range by EOS Coll J.A. Hauger et al. PRL 77 (1996) 235. P. Eudes, Z. Basrak and F. Sebille, Phys. Rev. C56 (1997) 2003. A similarconclusion valid for any reaction below 100A MeV

4. Early reaction phase • A HI collision is decisively governed by the early and compact reaction stage. • In violent collisions during this compactreaction phase an important mass andenergy is evacuated from system. • An early energy transformation should be studied in more detail.

5. Etot = Ecollect + Eintrin Eexcit  Ex/A Eintrin = Eexcit + Epotent Early energy transformation Asys = ~60 - ~400 nucl Aproj:Atarg = 1:1 – 1:5 Decompression followed by abundant emission and fast system cooling.

6. Evolution of excitation energy – Regular rise & fall with time at each EIN – Width & height regularlybehave as a f(EIN)

7. Evolution of excitation energy – Regular rise & fall with time at each EIN – Width & height regularlybehave as a f(EIN) – Maxima reflect the totalenergy deposited inthe reaction system

8. Eproj Atarg Aproj Eavail = Aproj (Atarg+Aproj)2 Excitation energy maxima

9. Ex as a fraction of EAVAIL –Fraction is almost constantover a wide energy range –Large variety of systems

10. Experimental excitation energy • In HIR excitation energy Ex is not directly accessible. • Calorimetry. Various corrections for issues which are not under control. Often one resorts to theoretical predictions. • To obtain Ex/A besides the total excitation energy also the mass of the primary emissionsource has to be estimated. • One must add a problem of selectingevents according to reaction centrality. • One cannot expect a most direct compa- rizon simulation – experiment

11. Experimental excitation energy All available data on Ex/A in central HI collisions in the last 20 years

12. Experimental excitation energy All available data on Ex/A in central HI collisions in the last 20 years – Strong spread of the data points – Connected data points of the same measurement – Close to linear dependence on EIN

13. Data for EIN> 100A MeV Radialflowdeduced by blast model. Remaining energy is taken as thermal. W. Reisdorf et al., Nucl. Phys. A612(1997) 493. – Radial flow of light reaction products deduced on two manners –Some correction relative to FOPI PHASE 1 but still a linear function of EIN W. Reisdorf et al., Nucl. Phys. A848(2010) 366.

14. Experimental excitation energy All available data on Ex/A in central HI collisions in the last 20 years – Strong spread of the data points – Connected data points of the same measurement – Close to linear dependence on EIN

15. Experimental excitation energy All available data on Ex/A in central HI collisions in the last 20 years – Strong spread of the data points – Connected data points of the same measurement – Close to linear dependence on EIN – Data within 35 % and 95 % of EAVAIL

16. Ex as a fraction of EAVAIL – The same system for the central collisions and the same EIN displays different features

17. Ex as a fraction of EAVAIL – The same system for the central collisions and the same EIN displays different features – Different leading assumption used in various analysis

18. Proton reduced rapidity distribution experiment 3 sources analyses QP mass QP excitation QP emission in BDCs Ar (95A MeV) + Ni INDRA experiment analyzed in the 3 sources assumption D. Dore et al. (INDRA Collaboration), Phys. Lett. B491 (2000) 15. Reaction dominantly of binary nature with a strong mid-rapidity contribution.

19. Ex as a fraction of EAVAIL – The same system for the central collisions and the same EIN displays different features – Different leading assumption used in various analysis –Group data by the approach used

20. Neglected dynamical emission (?)

21. Pure kinematical considerations

22. Accounted dynamical emission

23. Added FOPI thermal energy

24. Summary • “Hard” NN collisions play an important role in the dynamics of HIR already@EFermi • Maxima of excitationEx (heat) gene- rated in a collision display linearity with incident energy EIN • Ex represents a constant fraction ofavailable system energy EAVAIL • Some of experimental data (excluding the pre-equilibrium dynamical contribu- tion ?) display a tendency of similarconstancy with EIN

25. Constancy of Energy Partition in Central Heavy-Ion Reactions at Intermediate Energies Thank you Zoran Basrak In collaboration with Philippe Eudes,MajaZorić, and François Sébille Laboratory for Nuclear PhysicsDivision of Experimental Physics RuđerBošković Institute, Zagreb, Croatia 11th International Conference on Nucleus-Nucleus Collisions May 28 – June 1st, 2011, San Antonio, TX–USA

26. Backup slides

27. Ein= 10A MeV Ex≈EAVAILfull stopping Ein=35A MeV Ein=50A MeV At EFermi(≈35A MeV)“hard” NN collisions Ein= 125A MeV Central collisions 129Xe + 120Sn ≈5% σREAC sBDC>95% sREAC b=3 fm≈ 0.2 bmax 30 fm/c = 1∙10-21 s

28. pre-scission post-scission max. compression Configuration space local equilibration max. compression Impulse space local equilibration Mid-rapidityemission • pre-scissionemission Mid-rapidity emission in BDCs P. Eudes, Z. Basrak and F. Sebille, Phys. Rev. C56 (1997) 2003.

29. Central collisions • Above Coulomb barrier an adiabatic system rearrangement with full stopping and full E dissipation; fusion process EDISSIP = EAVAIL • Increasing E: incomplete fusion EDISSIP < EAVAIL • From about the Fermi energy EFermi BDCsBDC > 95 % sREAC irrespectively of • - event centrality - system size - system asymmetry • Increasing contribution of hard NN collisions

30. Z dynam emiss = 100 Z targ + Z proj Dynamical emission component Dem (%) = F. Haddad et al., Phys. Rev. C60 (1999) 031603.

31. Eproj Atarg Aproj Eavail = Aproj (Atarg+Aproj)2 Excitation energy maxima

32. Ex as a fraction of EAVAIL – Fraction almost constantover a wide energy range – For symmetric systemsbreak below EFermi – Large variety of systems

33. Fraction for experimental Ex

34. Binary Dissipative Collisions (BDC) – BDC opens around the Fermi energy –σBDC>95% σREAC Irrespectively of - event centrality - system size - system massasymmetry V.Metivier et al. (INDRA Collaboration), Nucl. Phys. A672 (2000) 357.

35. Ar (95 MeV/u) Ni QP emission in BDCs • Reconstructed primary QP massapproxim.. equal to the projectile mass • Thus obtained primary QP extremely hot Y.-G. Ma et al., Phys. Lett. B390 (1997) 41. J. Peter et al., Nucl. Phys.A593 (1995) 95.

36. Ar ( 65 MeV / u ) Al Ar (65 MeV/u) Al Statistical emission component Landau-Vlasov model simulation Thegeniune primary QP emission Ph. Eudes and Z. Basrak, Eur. Phys. J. A 9 (2000) 207. D. Cussol et al., Nucl. Phys. A561 (1993) 298. J. Peter et al., Nucl. Phys. A593 (1995) 95.

38. Heat & compression – Maximal compression at ~25 fm/c – In each volume cell a local equilibration at ~35 fm/c – System scission at ~55 fm/c I. Novosel et al., Phys. Lett. B625 (2005) 26. Despite of the establishment of a local equi-librium throughout the compact system the (Eth/A)sys and (Ath/A)proj differ substantially: Global equilibrium is far from being reached

39. c.m. E proj A targ A proj Eavail = A proj (A targ + A proj ) 2 Head-on collisions Dependence on available energy I. Novosel et al., Phys. Lett. B625 (2005) 26. A universal linear proportionality law proves the eminent role of “hard” NN collisions.

40. Ratio of thermal energy maxima Dependence of relative sub-systems Eth/A on incident energy for head-on collisions Projectile ratio = (Eth/A)proj (Eth/A)sys I. Novosel et al., Phys. Lett. B625 (2005) 26. Target ratio = (Eth/A)targ (Eth/A)sys

41. Ratio of thermal energy maxima Dependence of relative sub-systems Eth/A on incident energy for head-on collisions Projectile ratio = (Eth/A)proj (Eth/A)sys I. Novosel et al., Phys. Lett. B625 (2005) 26. Target ratio = (Eth/A)targ (Eth/A)sys A symmetric system

42. Ratio of thermal energy maxima Dependence of relative sub-systems Eth/A on incident energy for head-on collisions Projectile ratio = (Eth/A)proj (Eth/A)sys I. Novosel et al., Phys. Lett. B625 (2005) 26. Target ratio = (Eth/A)targ (Eth/A)sys An asymmetric system

43. Ratio of thermal energy maxima Dependence of relative sub-systems Eth/A on incident energy for head-on collisions Projectile ratio = (Eth/A)proj (Eth/A)sys I. Novosel et al., Phys. Lett. B625 (2005) 26. Target ratio = (Eth/A)targ (Eth/A)sys Increasingly asymmetric systems

44. Ratio of thermal energy maxima Dependence of relative sub-systems Eth/A on incident energy for head-on collisions Projectile ratio = (Eth/A)proj (Eth/A)sys I. Novosel et al., Phys. Lett. B625 (2005) 26. Target ratio = (Eth/A)targ (Eth/A)sys

45. Ratio of thermal energy maxima Dependence of relative sub-systems Eth/A on incident energy for head-on collisions • The reaction geo-metry is important in intermediate E HIC. • The Fermi energy is a transient region where the main reac-tion mechanism un-dergoes a fundamen- I. Novosel et al., Phys. Lett. B625 (2005) 26. tal change from the fusion-deep inelasticinto the BDC – partic.-spect,(fireball)-like behavior.