IPN Orsay, 20 September 2004

1. Experimental evidences of dense neutron-rich matter in heavy ion collision • - Heavy ion collisions at high bombarding energies (0.1 – 2 GeV/nucleon) • The nuclear Equation of State (EOS) • Experimental observables sensitive to fragment’s isospin • kinetic energy of 3H and 3He • squeeze-out signal of 3H and 3He • Possible scenario of hot compressed matter’s evolution • Hybrid theoretical model • radial flow model • clusterization model • Reconstruction of the locally equilibrated source from experimental data measured • at p/2 polar angle • Assumption on a non-uniform isospin distribution inside the fireball • Results and Conclusions Adriana R. Raduta IPN Orsay, 20 September 2004

2. Why study heavy ion collisions at high bombarding energies ? At bombarding energies 100 MeV/nucleon - 2 GeV/nucleon one populates nuclear matter at high temperatures and densities (r r0) Information on the nuclear equation of state Important for neutron star physics and supernova explosions How? At high bombarding energies the nuclear matter behaves as a fluid ---> collective energy contains information on the nuclear equation of state

3. What is the EOS ? • Definition: The equation relating the main thermodynamical observables which characterize the state of the system (E, r, T) • Expected answers: ☻ Liquid – Gas phase transition taking place in multifragmenting systems ☻ compressiblity of nuclear matter at r r0 ☻ quark-gluon phase transition • How does it look like? E/A = W(r,T) = W0(r=r0,T0=0) + WT(r0,T) + WC(r,T=0) Compressibility: k=9r2 (2(E/A) / r2)r=r0 ☻soft EOS: k=200 MeV ☻hard EOS: k=380 MeV • Experimental tools:☻side flow ☻out-of-plane flow (squeeze-out)

4. Experimental observables sensitive to fragment isospin Kinetic energies of 3H and 3He in central collisions 197Au+197Au [Poggi et al., NPA 586, 755 (1995)] -> full symbols: Exp. Data (60<qcm<90) -> open symbols: Transport Model 129Xe+119Sn @ 50 MeV/u K(3He)K(3H) [Lisa et al., PRL 75, 2662 (1995)] [INDRA collab.]

5. Experimental observables sensitive to fragment isospin Squeeze-out signals(peripheral collisions) Experimental azimuthal distribution of emitted particles: FOPI data a2 (3H) a2 (3He) Fourier expansion: dN/df=a0[1 + a1 cos(f) + a2 cos(2 f)] a2 squeeze-out parameter

6. Theoretical attempts to explain the 3He-3H kinetic energy difference • Dynamical model – BUU Au+Au @ 100, 150, 250 MeV/nucleon [Danielewicz & Pan, PRC46, 2002 (1992)] [Poggi et al., NPA 586, 755 (1995)] • Hybrid model (Hidrodynamical expansion - RFM + statistical fragment • Formation – FREESCO, break-up stage) • Au+Au @ 250 MeV/nucleon [Petrovici et al, PRL 74, 5001 (1995)] Good description of charge distribution and mean kinetic energy per nucleon (25 < qcm < 45) K (3He-3H)=7-15 MeV < 23 MeV experimental data

7. What is the physics behind the 3H-3He anomaly?? K(3He)  K(3H) --- preferential spatial cluster formation: 3He are formed in the outer shells with respect to 3H such as to benefit from a larger amount of flow energy abs(a2(3He))  abs(a2(3H)) --- 3He was born earlier than 3H (reaction image for peripheral collisions: spectator nuclei obturate the fireball expansion such as the azimuthal distributions allow to see the temporal evolution of the source) [Stoicea, PRL92, 072303 (2004)] ??? How can one relate the space and time evolution of an expanding fireball?

8. Hybrid theoretical model for fireball evolution the initially compressed nuclear matter suffers an radial isentropic expansion followed by clusterisation Step: 1 Radial Flow Model (RFM)[Bondorf et al., NPA296, 320 (1978)] The spherical compressed nuclear matter expands uniformly into vacuum. The break-up takes place when the relative velocity between 2 particles exceds their thermal velocity. tb=bA(1-(r/R)2)1/2+a/3 rb=a(1-(r/R)2)a/B3/(tb2+t02)3/2 ub=ABr/R(1-(r/R)2)1/2+a/3/(tb2+t02)1/2 Tb=C (1-(r/R)2) /(tb2+t02) Input parameters: surface diffusivity a, break-up time parameter b, maximum compression, source size, bombarding energy

9. RFM predictions Radial (temporal) distribution of nuclear matter density, thermal and collective energies Step: 2 Cluster formation: Microcanonical Multifragmentation Model [PRC55, 1344 (1997) and PRC65, 054610 (2002)]

10. Central collisionsSource reconstruction from experimental data Collective flow extracted from Kmed(A) show different values function of qcm Molecular dynamics simulations show that particles emitted at larger values of qcm suffer more collisions -> are more “thermalized” We shall use exp. data measured at p/2 to extract the «thermalized» source FOPI data

11. Charge yields for 800<q<1000 polar angles • Yields for Z=1,2,3 fragments at midrapidity detected at 800<q<1000 [G. Stoicea]: • Au+Au • Z 90 MeV/u 120MeV/u 150 MeV/u 250 MeV/u 400 MeV/u • 1 4.061 4.873 7.020 7.067 10.559 • 2 3.418 3.086 2.666 2.632 1.421 • 0.675 0.606 0.555 0.337 0.194 • To get yields for 4p: 11.52 • Results: for all considered reactions the reconstructed source is 92-99% (394,158) • Even if we don’t have an isotropic energy emission, the particle emission is isotropic with good approximation

12. Inferring source information from 800 < qcm < 1000 data Au+Au @ 250 MeV/u - using Y(Z) (Z=1, 2, 3) data ------> Zs=Ztot ( = 158) - assuming Is=Itot ---> As=394 - using Kmed (Amed) (Z=1, 2, 3) data -------> initial source parameters: (a = 1.7, n = 2.5, b = 0.2) -------> break-up average values: (nmed=2.55, Eth=38.77 MeV/u, Eflow=14.11 MeV/u) as obtained by RFM [Bondorf et al, NPA 296, 320 (1978)]

13. Theoretical results for Au+Au @ 250 MeV/u Fragment Formation: Microcanonical Multifragmentation Model [PRC87, 1344 (1997)] Asymptotic stage results: Full symbols – model predictions Open symbols – experimental data Good description of Y(Z), Kmed(A) and K(3He)-K(3H)=23 MeV

14. Peripheral collisions Experimental information FOPI data Azimuthal distribution of emitted particles Azimuthal distribution of average kinetic energy dN/df=a0[1 + a1 cos(f) + a2 cos(2 f)] <Ekin > (f)= E0 - D E cos(2 f) <Ekin > = ½ m0bflow2+ 3/2 T Ecoll (f)= Ecoll 0 - D Ecoll cos(2 f) T (f) =T0 (f) – D T cos(2 f)

15. What is the expected information? Dynamical calculations show that amplitude of the azimuthal distribution of Ekin is sensitive to the EOS hardness [Stoicea, PRL92, 072303 (2004)]]

16. Azimuthal distributions providing information on temporal evolution • shadowing of the fireball due to spectator objects can be used as internal clocks • particles emitted from the fireball are visible once spectators move apart from • the collision zone by a distance corresponding to half of the transition time • - if we assume that the colliding nuclei pass each other in the middle of expansion F = F (tb ,b, v)

17. Reconstruction of the hot source from experimental data Sharp cut-off (Ap, At) Impact parameterb Size of the fireball <Ekin > (f)= E0 - D E cos(2 f) Ecoll (f)= Ecoll 0 - D Ecoll cos(2 f) T (f) =T0 (f) – D T cos(2 f) RFM Ethermal, Eflow, a, b, n Cluster formation dN/df=a0[1 + a1 cos(f) + a2 cos(2 f)], for all emitted clusters

18. Results for Au+Au @ 400 MeV/u at different centralities

19. … Au+Au @ 400 MeV/u … Source characteristics Azimuthal distributions of Coulomb, thermal and collective energies

20. Results Only a non-uniform isospin distribution produces a2(3He) non eq. a2(3H)

21. a2(3He)-a2(3H) vs. isospin distributions The larger is the non-uniformity of the isospin distributions, the larger a2(3He)-a2(3H) Function of their isospin, different clustersare produced at different break-up moments

22. Conclusions and future • Good description of the available experimental data for Au+Au @ 250 MeV/nucleon central collision has been obtained assuming a radial isospin distribution inside the fireball • Estimations on the azimuthal distributions of 3He and 3H based on the correlation between break-up time and azimuthal angle indicate a radial isospin distribution inside the fireball • WHAT TO DO NEXT? • - Cross-check the recent theoretical results concerning the time dependent isospin distribution -> extract information about the symmetry energy -> • Information on EOS of neutron-rich matter