1. Fragments: experiments
about sorting
which observables
what seems to be established
what is still ambiguous and needs further measurements or analysis

2. Event sorting
Many variables linked with the violence of the collision or the energy dissipation
- LCP multiplicity
- LCP transverse energy
- ERAT
- Flow angle
- Zbound
- Principal Component Analysis
Questions : what is the aim of the sorting?
what is the quality of the sorting?
to which extent is the selection efficient?
Separate various impact parameters : useful for comparisons with dynamical models Select a source: what is a source? It is a « piece of nuclear matter » which is localized in momentum space. It is not necessarily fully equilibrated
● A given sorting can be more or less suited according to the objective of the selection

3. MSU
Isis
Au+Au 80MeV/u

4. Conclusions:
sorting is meaningful and efficient but some limitations exist:
sorting on dissipation cannot be very precise (correlations within ±20%)
in any case, detection as complete as possible is necessary
one has to be cautious with trivial autocorrelation between sorting and observables
continuous evolutions make sense
it seems difficult to isolate a definite class of events (for instance a single fusion source) without falling in one drawback: ● either a mixing from other event classes, ● or a cut in the available phase space for the selected event class.
- a sorting from a combination of various variables does not improve strongly the situation.
Central collisions :
10% selection
Indra: MF Rivet
Indra : O. Lopez

5. Fragment observables They are numerous: Multiplicities
Mass (charge) distributions
Isotopic distributions
Velocity distributions
Angular distributions
They may have various meanings depending on the collision nature (peripheral versus central; a-A versus A-A collisions)
They can magnify different collision features.
Low bombarding energies deep inelastic collisions is a good illustration of this statement
● deep inelastic angular and energy distributions (Wilczinski plots) reflect dynamics
● mass transfer in DIC are described with Fokker Planck equation with a heat bath (fast degrees of freedom) and slow evolving variables (mass transfert)
● the final product decay is described by thermal models.

6. Fragment production : multiplicities
Question : does the fragment multiplicity depends on the projectile mass (light or HI) and on the reaction type (peripheral or central) ?
Remark : it is difficult to compare precisely various data: the reasons for that are:
- various published data are sorted in various ways
- in order to compare them one has to convert the sorting variable in a relevant physical variable like excitation energy
- this is performed with uncertainties or mistakes:
- subtraction or no subtraction of « preequilibrium »
- subtraction or not of expansion energy
- definition of a source : neck included or not included in a PLF source
- use of a model (backtracing)
In spite of all these difficulties, it is possible to evidence some general behaviours independant of the entrance channel

7. Fragment production : multiplicities
Beaulieu
Peripheral AA reactions various systems Cl+Au43MeV/u, Ge+Ti35MeV/u
Rise and fall
Aladin
Peripheral AA reactions various projectile masses
Peripheral AA reactions various incident energies
Peripheral AA reactions various projectile masses
EOS
Rivet compilation from Indra data
Central collisions various systems
● Rise and fall is a general (and trivial) feature
● Normalization with the size of the system and the violence of the collision is observed but some data disagree with this statement

8. Fragment production yields
Further comparisons between AA and aA reactions
System
meth
Zsour
E*/u (MeV)
MultIMF/Zsource
π + Au 8 GeV/c (Isis; PRC64 (2001) )
cal 67 4
0.036
Cl + Au 43 MeV/u; peripheral (Laval PRC54(1996)R973) 17
0.035
Ge+Ti 35 MeV/u; peripheral (Laval PRC54(1996)R973) 32
Nb + Mg 30 MeV/u, central (Indra, PhD Manduci) 45
Au + Cu ; peripheral (Multics, pers. com)
~75
0.043
Au + Au 600MeV/u (Aladin); peripheral
~79 59
7-8
0.074 8
0.071
Ni + Au 90 MeV/u; central (Indra Nuc. Phys. A709 (2002))
cal/smm 86
7.5
0.081
Xe + Sn 50 MeV/u; central (Indra Nuc. Phys. A709 (2002)) 85
0.086
Xe + Sn 80 MeV/u; (Indra at GSI); peripheral 48
0.098
Au + Au 80 MeV/u (Indra at GSI); peripheral 70 7
0.083
Au + Au 600MeV/u (Aladin, Bormio 1995); peripheral 55
0.073
Au + C 1000MeV/u (EOS) semi-peripheral
53-40
7,5
La + C 1000MeV/u (EOS) semi-peripheral
40-34
Kr + C 1000MeV/u (EOS) semi-peripheral
26-23
Au+Cu central et peripherique mail Dagostino du 14/1/04

9. Many fragment yields do not indicate a strong difference between
- aA and AA collisions
- central AA and peripheral dissipative AA collisions
However it is difficult to be precise on this point because:
- results depend on sorting conditions
- some data indicate differences mainly for limited deposited energies
It would be necessary:
to sort various data aA, central and peripheral AA in similar ways to induce better comparisons
- to get new data in reverse kinematics on Aa collisions
For small dissipated energies (periph. collisions), there is a specific role of neck emission

10. IMF production in peripheral collisions : the role of neck emission
Indra Xe+Sn
Indra - Xe50MeV/u+Sn alpha contour plots
Indra Ta+Au 33MeV/u
Chimera
Memory of the beam direction for the mid-rapidity fragments, mainly for symmetrical collisions
Mid-rapidity leads to some ambiguity in the measurement of the PLF excitation energy (calorimetry)
Mid-rapidity does not lead to major ambiguity for the PLF size

11. Fragment observables : main features
collisions
Main ingredient
Multiplicities
centr, deep perip. and aA
Deposited energy
Perip. with limited dissipation
Neck emission
Angular distr.
Periph.
Dynam. features (neck)
Central
Velocity distr.
Mass (Z) distr.
Central.
Isospin

12. Fragment angular distributions for central collisions
Main features
- The memory effect observed for peripheral collisions is reduced for fragments emitted in central collisions (it is different for particles), but some memory is still there at least for some symmetrical systems
Multics
Indra Xe+Sn 50MeV/u

13. Fragment observables : main features
collisions
Main ingredient
Multiplicities
centr, deep perip. and aA
Deposited energy
Perip. with limited dissipation
Neck emission
Angular distr.
Periph.
Dynam. features (neck)
Central
Memory not fully lost
Velocity distr.
Mass (Z) distr.
Central.
Isospin

14. Charge or mass distributions
Main features
- evolution from residue-like events to multifragment events
- bimodality exists
- statistical behaviour when multiframentation takes place

15. Zmax evolves strongly when the deposited energy increases
Texas Nimrod - Ar 47MeV/u
Strong Zmax evolution
EOS 1GeV/u
Multics : Au+Au35MeV/u
Zmax evolves strongly when the deposited energy increases
raw Indra QP data Au + Au 80 MeV/u
Aladin : Au 600MeV/u
Isis: π + Au
E* (MeV/u)

16. Zmax : scalings
Campi plots
Delta scaling
Multics: periph. Au+Au 35 MeV/u
Indra (Frankland)
The largest fragment plays a specific role when the dissipation is limited (below multifragmentation treshold)
Texas – Nimrod - Ar
Multics : Au+Au and Cu 35MeV/u

17. Bimodality Bimodality seems to be a general feature
Au + Au 1000MeV/u Aladin
Zbound = 53-57
Au + Au 35 MeV Multics
GSI Au + Au 80 MeV/u
Bimodality seems to be a general feature
The signal is however weaker for central collisions
Ni + Au central - Indra
It would be also important to look for it in proton or pion induced reactions
It would then be possible to understand better the origin of bimodality
● excitation energy and low density
● spin effect
● geometry and dynamics
Spaladin will be able to answer this question
(see O. Lopez contribution)
Texas: Nimrod - Ar MeV/u

18. Mass distributions in central collisions
Even if the angular distributions may not exhibit isotropy, the mass distributions do not depend significantly on the emission angle.
This is a first indication of a dominant statistical behaviour.
Indra

19. Mass distributions in central collisions
Multics: Nucl.Phys.A724(2003)455
Indra Lopez
Dayras
Indra Orsay
Statistical models are able to fit mass distributions
When the multiplicity is fixed, the mass distribution is randomly deduced from mass conservation
-----true only above the fragmentation threshold-----
Indra : Guiot

20. The largest fragment has a specific role at limited excitations
Mass distributions
Chimera (Geraci) Sn+Ni central
D’Agostino:
Dark-blue: central-multics green: Fasa light-blue: Indra Xe+Sn 32MeV/u red: Isis
It seems that a statistical behaviour in the fragment mass (charge) distribution is established.
The largest fragment has a specific role at limited excitations
Multics central vs peripher.
However, the model parameters have to be adjusted to the data
The nuclear physics is contained in the evolution of the necessary model parameters.

21. Charge or mass distributions
The statistical behaviour is also recognized in the reducibility

22. Charge or mass distributions
Arguments in favor of a thermal behaviour : Arrhenius plots and …..
8GeV π+Au
Figure Michela:
symboles ouverts:QP multics Au+Au 35 MeV/u charge %
Bleu foncé : collisions centrales : Au+C, Au+ Cu 25 MeV/u
Au+Cu, Au+Au 35 MeV/u Zsource<90%
Rouge Isis
Bleu turquoise: Xe+Sn 32 MeV collisions centrales
Vert:FASA

23. Charge or mass distributions
…Fisher scalings
Isis - Moretto
Indra (Le Neindre)
Multics
The scaling seems fine…
but what about the χ2; or what about the extracted parameters ?
Figure Michela:
symboles ouverts:QP multics Au+Au 35 MeV/u charge %
Bleu foncé : collisions centrales : Au+C, Au+ Cu 25 MeV/u
Au+Cu, Au+Au 35 MeV/u Zsource<90%
Rouge Isis
Bleu turquoise: Xe+Sn 32 MeV collisions centrales
Vert:FASA

24. Fisher scalings Figure Michela:
symboles ouverts:QP multics Au+Au 35 MeV/u charge %
Bleu foncé : collisions centrales : Au+C, Au+ Cu 25 MeV/u
Au+Cu, Au+Au 35 MeV/u Zsource<90%
Rouge Isis
Bleu turquoise: Xe+Sn 32 MeV collisions centrales
Vert:FASA

25. Isoscaling seems to be a general feature.
Isotopic distributions : a futher evidence of statistical behaviour : isoscaling
R21 = C exp(αN + βZ)
Dubna LCP 0.6 to 3 GeV
Texas Fe/Ni 30MeV/u
MSU:
Sn+Sn 50MeV/u
Isoscaling seems to be a general feature.
But what it means?
Here again, it is necessary
- to sort various data in the same way,
- to control the quality of the fits (χ2),
- and to compare the α and β parameters extracted from the fits and their meaning.
Texas
Fe/Ni 3047 MeV/ui
MSU :DIC  MF
S(N) = R21(N,Z) exp(- βZ)
R21 should be linked with the free neutron and proton densities
α and β should be linked with the symmetry energy term and the nucleon-nucleon interaction force

26. Isoscaling
Yenello : Ni+Fe, Sn+Ni, H+Sn
Tsang : 112,124Sn+124,112Sn
It seems however that it is, at this point, difficult to get a concensus because the results depend also on the temperature and that one has to control side feeding and secondary decay effects.
Systematics are still necessary with defined analysis methods.
An alternative to reduce the uncertainties of the analysis consists in using mirror nuclei as suggested by M. d’Agostino
Chimera – Geraci: 112,124Sn+64,58Ni
Lynch : 112,124Sn+124,112Sn

27. Fragment observables : main features
collisions
Main ingredient
Multiplicities
centr, deep perip. and aA
Deposited energy
Perip. with limited dissipation
Neck emission
Angular distr.
Periph.
Dynam. features (neck)
Central
Memory not fully lost
Velocity distr.
Mass (Z) distr.
Statistical behaviour
Central.
Isospin

28. Fragment velocities in central collisions
GSI Xe+Sn and Au+Au
Fopi
Statistical models are unable to reproduce the data : it is necessary to add something which can be a collective energy or a deformation or an uncomplete mixing

29. Fragment observables : main features
collisions
Main ingredient
concensus
Multiplicities
centr, deep perip. and aA
Deposited energy
to be confirmed 1
Perip. with limited dissip.
Neck emission
established
Angular distr.
Periph.
Dynam. features (neck)
Central
Memory not fully lost
to be confirmed
Velocity distr.
Dynam. features (exp.)
to be better quantified 2
Mass (Z) distr.
Statistical behaviour
yes; thermal : no 3
Central.
Isospin
yes but which meaning? 4
1- Is the multiplicity slightly higher for head-on AA collisions (compression effect)
2- systematics with the same sorting
3- extend comparisons between Aa, periph AA and central AA
4- promissing with medium energy radioactive beams in order to reduce the model dependance of the analysis.

30. Summary
● Multifragmention takes place for large energy sharing among many degrees of freedom.
● Mid-rapidity (neck) is responsible for most very light fragment emissions for limited energy deposition
● The correlation between the fragment multiplicity and large energy deposition is probable but not fully established. One could try to define a protocole to compare more efficiently various data: sorting with the multiplicity or the transverse energy.
● Depending on the observable, different collision features are evidenced: statistical behaviour is dominant for fragment size and isospin
- the dominant ingredient is the available phase space
- angular and energy distributions are the signatures of the dynamical constraints which govern the filled phase space
● The heavy fragment plays a specific role at limited dissipations
● Hence, for comparisons between data, it is necessary either to remove the heaviest fragment, either for any event, or for events of the second class of the bimodality picture
● Key open question: does multifragmentation takes place through a low density transient state?

31. Many fragment yields do not indicate a strong difference between
- aA and AA collisions
- central AA and peripheral dissipative AA collisions
However it is difficult to be precise on this point because:
- results depend on sorting conditions
- some data indicate differences mainly for limited deposited energies
reaction
Etherm
MIMF>4
Xe+Sn 50 MeV/u central
7 MeV/u
5.457.08
Xe+Sn 32 MeV/u central
5 MeV/u
4.465.53
Au+Au 35 MeV/u periph.
2.75
It would be necessary:
to sort various data aA, central and peripheral AA in similar ways to induce better comparisons
- to get new data in reverse kinematics on Aa collisions

32. Charge or mass distributions The heaviest fragment may blur a signal.
Indra (Lopez) : sorting with double PCA
PCA sorting
PCA sorting + E* sorting
The mass distribution may be strongly affected if events are mixed because of an « incomplete » sorting
Texas (Ma)
QP Ar47MeV/u

33. On the importance of the sorting…
Coherence between bimodality and delta scaling only if the sorting is properly achieved
The comparison between data has to be performed if similar sorting have been achieved