Midrapidity Dynamics Update - Some facts and observations (milestones?) Different approaches, same conclusions Several calculations - STOCHASTIC MEAN-FIELD TRANSPORT APPROACH - Neck observables Update

136Xe + 209Bi at 28.2 MeV/nucleon, b = 7 fm Simulations of collisions between nuclei at intermediate energy using the Boltzmann-Uehling-Uhlenbeck equation with neutron skin producing potentials L.G. Sobotka, Phys. Rev. C 50 (1994) R1272 « The foundation of this work is Professor W. Bauer’s BUU code”

J. Tõke et al.

Direct Measurement of Dissipation in the 35Cl + 12C Reaction at 43 MeV/nucleon L. Beaulieu et al., Phys. Rev. Lett. 77 (1996) 463 FIG. 2. Galilean invariant perpendicular vs parallel velocity in the c.m. frame for Z = 3 fragments. Parallel velocities are along the beam axis [(a),(c),(e)] and the main axis of the momentum tensor [(b),(d),(f)]. Cuts on Θflow < 30° [(a),(b)], Θflow > 75° [(c),(d)], and on E┴ > 135 MeV (top 10% of the distribution: [(e), (f)]) are made.

Intermediate velocity source of intermediate-mass fragments in the 40Ca + 40Ca reaction at Elab = 35 MeV/nucleon P. Pawlowski et al., Phys. Rev. C 57 (1998) 1771 Standard BNV code: A. Bonasera et al., Phys. Lett. B 246 (1990) 337.

- Different approaches, same conclusions

Intermediate Mass Fragment Emission Pattern in Peripheral Heavy-Ion Collisions at Fermi Energies S. Piantelli el al., Phys. Rev. Lett. 88 (2002) 052701 116Sn + 93Nb at 29.5A MeV

« In conclusion, peripheral collisions are characterized by a sizable emission of IMF’s at midvelocity, successfully competing with LCP’s and greatly overcoming the IMF evaporative emission. The peculiar pattern of midvelocity IMF’s from peripheral collisions seems to require the emission from an “extended neck” which also includes a fast contribution of IMF’s emitted nearly at rest in the PLF or TLF reference frame. » The QMD code CHIMERA : J. ukasik and Z. Majka, Acta Phys. Pol. B 24, 1959 (1993).

Origins of intermediate velocity particle production in heavy ion reactions L. Gingras et al., Phys. Rev. C 65 (2002) 061604(R) QP : vertical hatches QT : horizontal hatches IV: shaded histograms FIG. 1. c.m. parallel velocity distributions for charged particles

Conclusion: « With help of time-based cluster recognition algorithm applied to molecular dynamics simulation , it has been possible to determine the time scales associated to two different phenomena. The first origin is related to prompt nucleon-nucleon collisions that occur in the overlap zone of the two colliding nuclei. These processes will eject light particles and excited clusters out of the overlap on a very short time scale of the order of the reseparation time. Excited clusters ejected at this stage will however emit particles on a longer time scale. The second origin of IV particle production is related to the collective motion of nucleons at the perturbed ends of the QP and QT. Larger deformations will be carried by the heavier partner of the collision and will lead it to a mass asymmetric breakup aligned along the reseparation axis. This is expected to happen after a delay of the order of 150–500 fm/c. »

- Several calculations

Within the framework of classical molecular dynamics Quasiclassical model of intermediate velocity particle production in asymmetric heavy ion reactions A. Chernomoretz et al. Phys. Rev. C 65 (2002) 054613 Within the framework of classical molecular dynamics Availability of microscopic correlations at all times allowed a detailed study of the fragment formation process The physical origin of fragments and emission timescales allow to disentangle the different processes involved in the midrapidity particle production. Consequently, A clear distinction between a prompt preequilibrium emission and a delayed aligned asymmetric breakup of the heavier partner of the reaction was achieved.

Energetics of Midvelocity Emissions in Peripheral Heavy Ion Collisions at Fermi Energies A. Mangiarotti el al.,, Phys. Rev. Lett. 93 (2004) 232701 “We present here, for the first time, a direct simultaneous determination of the energy involved in the midvelocity and in the evaporative emissions.”

(a) Experimental yield of α particles, at TKEL ≈ 600 MeV, in the (v┴ , v║) plane with respect to the PLF*-TLF* separation axis; the dot at v║ ≈ 32 mm/ns is the location of the PLF* source. (b) Corresponding angular distribution in the PLF frame (histogram) and results of simulations for an evaporating source with spin 0 h and 30 h (dashed and dotted lines, respectively, normalized in the range 0° ≤ θ ≤ 30°). Average total mass of (a) the PLF* evaporation,<Aevap>, and (b) the forward-going midvelocity emissions <Amidv>; average amount of energy involved in (c) the PLF* evaporation, <Eevap>, and (d) the forward-going midvelocity emissions, <Emidv>. The data are presented as a function of TKEL and the different curves correspond to different N=Z values for the midvelocity emissions.

Pre-equilibrium and Neck emission in HIPSE model Early Fragment Formation at the Contact (t=0 fm/c) Strong reorganisation Of the partition due to Final State Interaction Desexcitation Clusters are formed using a coalescence algorithm in the participant region that essentially mimics a random partition of nucleons in the two Fermi spheres distorted by nucleon-nucleon collisions. Here a possible fusion of fragments is tested two-by-two (t=50 fm/c). These two stage gives the specific properties of the pre-equilibrium emission

Neck emission: comparison INDRA data / HIPSE model Selection of complete events : Ztot >80%, Pztot>80% Parallel velocity Angular distribution Data Data HIPSE with n-n collisions HIPSE without collisions The interplay between pre- and post-equilibrium emission is well reproduced Leading to a proper account for the Neck emission.

Stochastic two-stage reaction model Z. Sosin, Eur. Phys. J. A 11 (2001) 311 A two-stage reaction scenario: first stage of mean field mechanism and a second stage of nucleon transfer i) First stage: a number of nucleons become reaction participants as a result of mean field-effects and/or two-nucleon (NN) interactions. ii) Participating nucleons are transferred to definite states, creating finally a PLF, a TLF, or clusters. They can also escape into continuum.

40Ca + 40Ca at 35 AMeV AMPHORA Data Red IVS Blue PLF Green TLF Pink CS : Compound System

STOCHASTIC MEAN-FIELD TRANSPORT APPROACH VLASOV + COLLISION and PAULI CORRELATIONS Nucl.Phys. A 642 (1998) 449 Stochastic Mean Field Approach gain loss FLUCTUATIONS Markov

Initial: STOCHASTIC MEAN-FIELD TRANSPORT APPROACH Equilibrium in a phase space cell OK if FLUCTUATION.-DISSIPATION THEOREM tot. number of collisions Stochastic Mean Field Approach Initial: any time

Neck Fragmentation Mechanism 124Sn+124Sn 50 AMeV, semi-central b=4fm b=6fm STOCHASTIC MEAN-FIELD Time-scale matching: Instability growth vs Interaction time Rise and Fall: with impact parameter with beam energy Freeze-out V.Baran et al. NPA 703 (2002)

b=6fm Central density evolution 124Sn+64Ni 35 AMeV K=200 MEV K=380 MEV NECK FRAGMENTATION: COMPRESSIBILITY EFFECTS the role of volume instabilities 124Sn+64Ni 35 AMeV b=6fm K=200 MEV K=380 MEV cube of 10 fm side Central density evolution stiff soft V.Baran et al. NPA 730 (2004)

NECK FRAGMENTATION EVENTS up-early stage of fragment formation 124Sn+64Ni ; 35AMeV; b=6fm down- configurations close to freeze-out Nucleon-nucleon cross sections dependence free cross sections half free cross sections 124Sn+64Ni P=Nternary/Ntotal 112Sn+58Ni

r - ratio of the observed PLF-IMF relative velocity to the DEVIATIONS FROM VIOLA SYSTEMATICS r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocity; r1- the same ratio for the pair TLF-IMF The Neck-IMF is weakly correlated with both PLF and TLF Wilczynski-2 plot ! V.Baran, M.Colonna, M.Di Toro NPA 730 (2004)

REDUCED VELOCITY PLOTS: Note: BNV model accounts only for the “prompt” component of IMF’s BNV V. Baran et al. Nucl. Phys A730 (2004) 329 Chimera 124Sn+64Ni 35AMeV data, same E_loss selections

Gating the reduced plot for light IMFs:

NECK FRAGMENTATION: CM Vz-Vx CORRELATIONS Large dispersion also along transversal, x, direction TLF 124Sn + 64Ni 35 AMeV <0 IMF PLF >0 Alignement + Centroid at Clear Dynamical Signatures !

Angular distributions: alignment characteristics Out-of-plane angular distributions for the “dynamical” (gate 1) and “statistical” (gate 2) components: these last are more concentrated in the reaction plane. plane is the angle, projected into the reaction plane, between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

Mean Field & Chemical Potentials symmetry part of the mean field neutron-proton chemical potentials neutron neutron proton proton bulk neck 124Sn “asymmetry” I = 0.2

ISOSPIN COMPOSITION OF THE IMF’S PRODUCED IN NECK FRAGMENTATION: ASY-EOS EFFECT 124Sn+64Ni 35AMeV asysoft asystiff superasystiff 64Ni 124Sn

asysoft asystiff superasystiff  0.69 0.95 1.10 NECK ISOSCALING N  = 0.95 Z=1 Z=3 Z=2 Z=5 Z=7 Z=6 Z=8 Z=4 Z=9 lnR21 at 35 MeV/n (b=6,7,8fm) asysoft asystiff superasystiff  0.69 0.95 1.10 V. Baran, M. Colonna, M. Di Toro : NPA 370 (2004) 329

asysoft asystiff superasystiff  -0.67 -1.07 -1.16 NECK ISOSCALING Z ln R21  = -1.07 N=2 N=3 N=8 N=7 N=6 N=5 N=4 at 35 MeV/n (b=6,7,8fm) asysoft asystiff superasystiff  -0.67 -1.07 -1.16

58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV:Freeze-out Asymmetry distributions Fe: fast neutron emission Ni: fast proton emission White circles: asy-stiff Black circles: asy-soft Asy-soft: small isospin migration R.Lionti et al., nucl-th/0501012

Neck Fragments: N/Z – angle correlation FeFe vs NiNi b=4fm 47AMeV: 40% ternary Isospin Migration for almost symmetric systems - Minimum N/Z around 90° : earlier formation? R.Lionti et al, nucl-th/0501012

FeFe b=4fm 47AMeV: density contour plots fm/c R.Lionti et al. nucl-th/0501012 PLF/TLF residues asymmetry (N-Z)/A System initial t=100fm/c(after pre-eq) freeze-out 58Fe+58Fe 1.23 1.22 1.23 binary 1.19 ternary 58Ni+58Ni 1.07 1.12 1.17 binary 1.12 ternary n-enrichment of Neck-Fragments even for symmetric systems!

a) the neck region – low density interface ISOSPIN DIFFUSION AT FERMI ENERGIES 124Sn + 112Sn at 50 AMeV b=8fm b=10fm a) the neck region – low density interface b) pre-equilibrium particle emission Stochastic BNV - transport model b=8fm b=9 fm b=10fm 120fm/c 100fm/c contact time 80fm/c

Neck Observables FUTURE: WCI UPDATE: M. Di Toro, A. Olmi, R. Roy Properties of Neck-Fragments Time-scale measurements Isospin Dynamics Isospin Diffusion “Pre-equilibrium” emissions FUTURE: From transport simulations we presently get some indications of "asy-stiff" behaviors, i.e. increasing repulsive density dependence of the symmetry term, but not more fundamental details. Moreover, all the available data are obtained with stable beams, i.e. within low asymmetries: more to come with accelerated unstable beams WCI UPDATE: M. Di Toro, A. Olmi, R. Roy

Properties of Neck-Fragments: Midrapidity IMF produced in semicentral collisions: correlations between N/Z, alignement and size. The alignement between PLF-IMF and PLF-TLF directions: a very convincing evidence of the dynamical origin of the mid-rapidity fragments produced on short time scales. The form of the Φ distributions (centroid and width) can give a direct information on the fragmentation mechanism.