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

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

MSU Indra@GSI Isis Indra@GSI Au+Au 80MeV/u

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

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.

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

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

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) 064604) 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 3.4-3.8 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 0.06-0.10 La + C 1000MeV/u (EOS) semi-peripheral 40-34 0.04-0.077 Kr + C 1000MeV/u (EOS) semi-peripheral 26-23 0.03-0.07 Au+Cu central et peripherique mail Dagostino du 14/1/04

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

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

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

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

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

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

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)

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 QP @47MeV/u Multics : Au+Au and Cu 35MeV/u

Bimodality Bimodality seems to be a general feature Au + Au 1000MeV/u Aladin Zbound = 53-57 Au + Au 35 MeV Multics Indra @ 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 PLF @47 MeV/u

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

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

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.

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

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 79+-10% 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

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 79+-10% 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

Fisher scalings Figure Michela: symboles ouverts:QP multics Au+Au 35 MeV/u charge 79+-10% 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

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

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

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

Fragment velocities in central collisions Indra @ 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

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.

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?

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

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

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