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

2. 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”

3. J. Tõke et al.

4. 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.

5. 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) Standard BNV code: A. Bonasera et al., Phys. Lett. B 246 (1990) 337.

6. - Different approaches, same conclusions

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

8. « 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).

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

10. 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. »

11. - Several calculations

12. 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)
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.

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

14. (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.

15. 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

16. 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.

17. 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.

18. 40Ca + 40Ca at 35 AMeV AMPHORA Data Red IVS Blue PLF Green TLF
Pink CS :
Compound System

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

20. 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

21. 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)

22. 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)

23. 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

24. 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)

25. 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

26. Gating the reduced plot for light IMFs:

27. 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 !

28. 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

29. 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

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

31. 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 
V. Baran, M. Colonna, M. Di Toro : NPA 370 (2004) 329

32. 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 

33. 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/

34. 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/

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

36. a) the neck region – low density interface
ISOSPIN DIFFUSION AT FERMI ENERGIES
124Sn Sn 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

37. 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

38. 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.