Hirschegg 98: List of Abstracts

Hirschegg workshop: Multifragmentation, Jan. 17 - 23, 1999

Date: Tue Dec 16 08:52:15 CET 1997

So far the following abstracts have been handed in:

News on Multifragmentation
Aichelin,J., Nebauer,R.,(SUBATECH)
Abstract: We present the recent results on multifragmentation obtained by simulating the haevy ion reaction with the QMD program. We discuss how close the system comes to equilibrium, which observables are sensitive to equilibration. We will discuss which information on the radial flow is contained in the fragment data and whether they support the recently conjectured universal curve of the radial flow from low to high beam energies.

News on Multifragmentation
Aichelin,J., Nebauer,R.,(SUBATECH)
Abstract: We present the recent results on multifragmentation obtained by simulating the haevy ion reaction with the QMD program. We discuss how close the system comes to equilibrium, which observables are sensitive to equilibration. We will discuss which information on the radial flow is contained in the fragment data and whether they support the recently conjectured universal curve of the radial flow from low to high beam energies.

Collective expansion and stopping in symmetric heavy ion collisions
Andronic, A., FOPI Collaboration
Abstract: Experimental information obtained with the FOPI detector in centrality selected collisions of Au+Au, Xe+CsI and Ni+Ni between 90 and 400 MeV/u, sheds light on the importance of the collective expansion, shadowing and rotation as well as on the degree of stopping as a function of the system size.

Collective expansion and stopping in symmetric heavy ion collisions
Andronic, A., FOPI Collaboration
Abstract: Experimental information obtained with the FOPI detector in centrality selected collisions of Au+Au, Xe+CsI and Ni+Ni between 90 and 400 MeV/u, sheds light on the importance of the collective expansion, shadowing and rotation as well as on the degree of stopping as a function of the system size.

Statistical and Dynamic Properties of Nuclear Multifragmentation
S.P. Avdeyev (Dubna), V.A. Karnaukhov (Dubna), L.A. Petorv (Dubna), V.K. Rodionov (Dubna), H. Oeschler (Darmstadt), O.V. Bochkarev (Moscow), L.V. Chulkov (Moscow), E.A. Kuzmin (Moscow), A.S. Botvina (Moscow), A. Budzanowski (Cracow), W. Karcz (Cracow), M. Janicki (Cracow), E. Norbeck (Iowa City)
Abstract: The experimental data on fragment multiplicities, their energy and charge distributions, the emission times are considered for the nuclear multifragmentation process induced by relativistic light projectiles (protons, helium) and heavy ions. With light projectiles, the multifragmentation is a pure "thermal" process, well described by the statistical models. Heavy-ion-induced multifragmentation is influenced by dynamic effects related first of all to the compression of the system in the collision. But statistical models can also be applied to rendering the partition of the system if the exitation energy is less than 10 MeV/nucleon and compression is modest.

Statistical and Dynamic Properties of Nuclear Multifragmentation
S.P. Avdeyev (Dubna), V.A. Karnaukhov (Dubna), L.A. Petorv (Dubna), V.K. Rodionov (Dubna), H. Oeschler (Darmstadt), O.V. Bochkarev (Moscow), L.V. Chulkov (Moscow), E.A. Kuzmin (Moscow), A.S. Botvina (Moscow), A. Budzanowski (Cracow), W. Karcz (Cracow), M. Janicki (Cracow), E. Norbeck (Iowa City)
Abstract: The experimental data on fragment multiplicities, their energy and charge distributions, the emission times are considered for the nuclear multifragmentation process induced by relativistic light projectiles (protons, helium) and heavy ions. With light projectiles, the multifragmentation is a pure "thermal" process, well described by the statistical models. Heavy-ion-induced multifragmentation is influenced by dynamic effects related first of all to the compression of the system in the collision. But statistical models can also be applied to rendering the partition of the system if the exitation energy is less than 10 MeV/nucleon and compression is modest.

Deuteron Formation in Heavy Ion Collisions at Intermediate Energies
Beyer, M., Kuhrts, C., Roepke, G. (U Rostock)
Abstract: We consider deuteron formation in heavy ion collisions at intermediate energies. The elementary reaction rates (Nd $\rightarrow$ NNN etc.) in this context is calculated using rigorous Faddeev methods. To this end an in-medium Faddeev equation that consistently includes the energy shift and Pauli blocking effects has been derived and solved numerically. As a first application we have calculated the life-time of deuteron fluctuations for nuclear densities and temperatures typical for the final stage of heavy ion collisions. We find substantial differences between using the isolated and the in-medium rates. We have extended the QMD (quantum molecular dynamics) approach to include deuteron distributions and exact reaction rates. We report on the latest results. Also we present the consequences of using exact three body equations to discuss the triton in-medium properties.
References: M. Beyer: to appear Few Body Syst Suppl. (nucl-th/9809002). M. Beyer, G. Roepke: Phys. Rev. C 56, 2636 (1997). M. Beyer, G. Roepke, A. Sedrakian: Phys. Lett. B376, 7 (1996).

Deuteron Formation in Heavy Ion Collisions at Intermediate Energies
Beyer, M., Kuhrts, C., Roepke, G. (U Rostock)
Abstract: We consider deuteron formation in heavy ion collisions at intermediate energies. The elementary reaction rates (Nd $\rightarrow$ NNN etc.) in this context is calculated using rigorous Faddeev methods. To this end an in-medium Faddeev equation that consistently includes the energy shift and Pauli blocking effects has been derived and solved numerically. As a first application we have calculated the life-time of deuteron fluctuations for nuclear densities and temperatures typical for the final stage of heavy ion collisions. We find substantial differences between using the isolated and the in-medium rates. We have extended the QMD (quantum molecular dynamics) approach to include deuteron distributions and exact reaction rates. We report on the latest results. Also we present the consequences of using exact three body equations to discuss the triton in-medium properties. References: M. Beyer: to appear Few Body Syst Suppl. (nucl-th/9809002). M. Beyer, G. Roepke: Phys. Rev. C 56, 2636 (1997). M. Beyer, G. Roepke, A. Sedrakian: Phys. Lett. B376, 7 (1996).

Influence of Coulomb interaction of projectile- and target-like sources on multifragmentation.
Botvina A.S. (INFN, Bologna), Bruno M. (INFN, Bologna), D'Agostino M. (INFN, Bologna), Gross D.H.E. (HMI, Berlin)
Abstract: We show that the fragment partitions and kinematic characteristics of fragments can change in the presence of an external Coulomb field at statistical multifragmentation of highly excited nuclei. There are indications that this effect takes place at intermediate energy peripheral nucleus-nucleus collisions. The phenomenon has general importance for understanding disintegration processes affected by long range forces.

Influence of Coulomb interaction of projectile- and target-like sources on multifragmentation.
Botvina A.S. (INFN, Bologna), Bruno M. (INFN, Bologna), D'Agostino M. (INFN, Bologna), Gross D.H.E. (HMI, Berlin)
Abstract: We show that the fragment partitions and kinematic characteristics of fragments can change in the presence of an external Coulomb field at statistical multifragmentation of highly excited nuclei. There are indications that this effect takes place at intermediate energy peripheral nucleus-nucleus collisions. The phenomenon has general importance for understanding disintegration processes affected by long range forces.

Mean Field Instabilities
Ph.Chomaz, D. Lacroix, B. Jacquot, M. Colonna, S. Ayik
Abstract: We present a general discussion of the mean field dynamics of finite nuclei prepared under extreme conditions of temperature and pressure Many features of the dynamics are carefully studied such as the collective expansion, the evaporation process, the different time-scale... We show that under the thermal presure and the effect of the compression the system may reach low density regions where it may become unstable. Early development of the instabilities in a dilute nuclear source is investigated using a finite temperature quantal RPA approach for different systems. The growth rates of the unstable collective modes are determined by solving a dispersion relation, which is obtained by parametrizing the transition density in terms of its multipole moments. Under typical conditions of a dilute finite system at moderate temperatures the dispersion relation exhibits an ultraviolet cut-off. As a result, only a finite number of multipole modes becomes unstable, and the number of the unstable collectivemodes increases with the size of the source. Calculations indicate that for an expanding source, unstable modes show a transition from surface to volume character.

Mean Field Instabilities
Ph.Chomaz, D. Lacroix, B. Jacquot, M. Colonna, S. Ayik
Abstract: We present a general discussion of the mean field dynamics of finite nuclei prepared under extreme conditions of temperature and pressure Many features of the dynamics are carefully studied such as the collective expansion, the evaporation process, the different time-scale... We show that under the thermal presure and the effect of the compression the system may reach low density regions where it may become unstable. Early development of the instabilities in a dilute nuclear source is investigated using a finite temperature quantal RPA approach for different systems. The growth rates of the unstable collective modes are determined by solving a dispersion relation, which is obtained by parametrizing the transition density in terms of its multipole moments. Under typical conditions of a dilute finite system at moderate temperatures the dispersion relation exhibits an ultraviolet cut-off. As a result, only a finite number of multipole modes becomes unstable, and the number of the unstable collectivemodes increases with the size of the source. Calculations indicate that for an expanding source, unstable modes show a transition from surface to volume character.

Isospin effects on the Spinodal Decomposition mechanism
Colonna M., Di Toro M. and Maccarone S. (LNS-INFN and Phys.Dept. Catania)
Abstract: We study dynamical properties of asymmetric nuclear matter at low density. The occurrence of new instabilities, of chemical plus mechanical nature, that lead to a dynamical fragment formation is illustrated. Realistic simulations are performed using a new consistent method to introduce fluctuations in a transport approach. Configurations with less asymmetric fragments surrounded by a more asymmetric gas are favoured. This is indeed expected also in a pure thermodynamical approach. However in our dynamical picture we get a larger proton fraction in the gas phase, depending on the freeze-out time. For a finite hot and dilute initial source a comparison is performed with yield and isotopic content of primary fragments obtained with a Statistical Multifragmentation code. The Spinodal Decomposition mechanism predicts a quite larger rate of neutron rich light ions. Simulations are performed for fragmentation reactions with different charge asymmetries, in particular to analyse the isotopic structure of mid-rapidity emissions. All these features are deeply related to the structure of the symmetry term in the nuclear Eq.of State and can be used to extract information on the low density part.

Isospin effects on the Spinodal Decomposition mechanism
Colonna M., Di Toro M. and Maccarone S. (LNS-INFN and Phys.Dept. Catania)
Abstract: We study dynamical properties of asymmetric nuclear matter at low density. The occurrence of new instabilities, of chemical plus mechanical nature, that lead to a dynamical fragment formation is illustrated. Realistic simulations are performed using a new consistent method to introduce fluctuations in a transport approach. Configurations with less asymmetric fragments surrounded by a more asymmetric gas are favoured. This is indeed expected also in a pure thermodynamical approach. However in our dynamical picture we get a larger proton fraction in the gas phase, depending on the freeze-out time. For a finite hot and dilute initial source a comparison is performed with yield and isotopic content of primary fragments obtained with a Statistical Multifragmentation code. The Spinodal Decomposition mechanism predicts a quite larger rate of neutron rich light ions. Simulations are performed for fragmentation reactions with different charge asymmetries, in particular to analyse the isotopic structure of mid-rapidity emissions. All these features are deeply related to the structure of the symmetry term in the nuclear Eq.of State and can be used to extract information on the low density part.

Multifragmentation of very heavy systems
D'Agostino,M., Botvina,A.S., Bruno,M. (Dip. Fis and INFN, Bologna), Bonasera,A. (INFN, LNS Catania), Bondorf,J.P., Mishustin,I.N. (NBI, Copenhagen), Gulminelli,F., Bougault,R., LeNeindre,N., (LPC, IN2P3-CNRS, Caen), Desesquelles,P. (GANIL, Caen), Geraci,E., Pagano,A. (Dip. Fis. and INFN, Catania), Iori,I., Moroni,A. (Dip. Fis, and INFN, Milano), Margagliotti,G.V., Vannini,G. (Dip. Fis. and INFN, Trieste)
Abstract: The multifragmentation of heavy systems formed in Au (35 A.MeV) induced reactions is studied. The decaying sources are characterized by a geometrical and a thermodynamical point of view, by looking for signal of critical behaviour. It is show that the Coulomb interaction, as well as the compression in the initial stage of the reaction influence the behaviour near the transition point.

Multifragmentation of very heavy systems
D'Agostino,M., Botvina,A.S., Bruno,M. (Dip. Fis and INFN, Bologna), Bonasera,A. (INFN, LNS Catania), Bondorf,J.P., Mishustin,I.N. (NBI, Copenhagen), Gulminelli,F., Bougault,R., LeNeindre,N., (LPC, IN2P3-CNRS, Caen), Desesquelles,P. (GANIL, Caen), Geraci,E., Pagano,A. (Dip. Fis. and INFN, Catania), Iori,I., Moroni,A. (Dip. Fis, and INFN, Milano), Margagliotti,G.V., Vannini,G. (Dip. Fis. and INFN, Trieste)
Abstract: The multifragmentation of heavy systems formed in Au (35 A.MeV) induced reactions is studied. The decaying sources are characterized by a geometrical and a thermodynamical point of view, by looking for signal of critical behaviour. It is show that the Coulomb interaction, as well as the compression in the initial stage of the reaction influence the behaviour near the transition point.

Nuclear phase transitions and transport theory
Pawel Danielewicz (NSCL-MSU)
Abstract: Challenges for the reaction theory represented by the nuclear phase transitions are discussed. Possible way above the quantum and fermion molecular dynamics involves the Zwanzig's equation. The issue of equilibration within the neck may be addressed by comparing data to the simple Boltzmann equation with light fragments only. Thermodynamics of the phase transition to the quark-gluon plasma may be implemented into a hadronic transport model through a mean field reducing hadron masses.

Nuclear phase transitions and transport theory
Pawel Danielewicz (NSCL-MSU)
Abstract: Challenges for the reaction theory represented by the nuclear phase transitions are discussed. Possible way above the quantum and fermion molecular dynamics involves the Zwanzig's equation. The issue of equilibration within the neck may be addressed by comparing data to the simple Boltzmann equation with light fragments only. Thermodynamics of the phase transition to the quark-gluon plasma may be implemented into a hadronic transport model through a mean field reducing hadron masses.

Possible signature for expansion in mid-peripheral collisions of 238U + lead at 1 AGeV
Enqvist, T., Benlliure, J., Farget, F., Schmidt, K.-H., Armbruster, P. (GSI), Bockstiegel, C., de Jong, M. (TH Darmstadt), Bernas, M., Tassan-Got, L. (IPN Orsay), Boudard, A., Legrain, R., Volant, C. (CEA Saclay), Dufour, J.P. (CENBG)
Abstract: Possible signature for expansion in mid-peripheral collisions of 238U + lead at 1 AGeV
Projectile fragmentation induced in collisions of 238U at 1 AGeV with lead have systematically been studied at the GSI fragment separator FRS. The mean momentum transfer and the momentum width could be deduced up to a relative mass loss of 60\%. The result on the mean velocity reduction for small mass losses is in agreement with the expectation that the projectile is slowed down in the nuclear interaction with the target nucleus. For large mass losses, however, the mean velocity of the fragments even exceed that of the beam. These light fragmentation products originate from similar impact parameters than intermediate-mass fragments studied in earlier experiments at ALADIN. The observed features of the velocity distributions may be an important signature of the dynamics of the nuclear collision.

Possible signature for expansion in mid-peripheral collisions of 238U + lead at 1 AGeV
Enqvist, T., Benlliure, J., Farget, F., Schmidt, K.-H., Armbruster, P. (GSI), Bockstiegel, C., de Jong, M. (TH Darmstadt), Bernas, M., Tassan-Got, L. (IPN Orsay), Boudard, A., Legrain, R., Volant, C. (CEA Saclay), Dufour, J.P. (CENBG)
Abstract: Possible signature for expansion in mid-peripheral collisions of 238U + lead at 1 AGeV Projectile fragmentation induced in collisions of 238U at 1 AGeV with lead have systematically been studied at the GSI fragment separator FRS. The mean momentum transfer and the momentum width could be deduced up to a relative mass loss of 60\%. The result on the mean velocity reduction for small mass losses is in agreement with the expectation that the projectile is slowed down in the nuclear interaction with the target nucleus. For large mass losses, however, the mean velocity of the fragments even exceed that of the beam. These light fragmentation products originate from similar impact parameters than intermediate-mass fragments studied in earlier experiments at ALADIN. The observed features of the velocity distributions may be an important signature of the dynamics of the nuclear collision.

Liquid-gas phase transition in Fermionic Molecular Dynamics
H. Feldmeier, T. Neff, J. Schnack, R. Roth
Abstract: The time evolution of excited nuclei, which are in equilibrium with surrounding vapour, is investigated. It is shown that finite nuclear systems undergo a first order phase transition. The caloric curve is presented for O, Mg, Al and Ca. A possible relation to fragmentation reactions is discussed.

Liquid-gas phase transition in Fermionic Molecular Dynamics
H. Feldmeier, T. Neff, J. Schnack, R. Roth
Abstract: The time evolution of excited nuclei, which are in equilibrium with surrounding vapour, is investigated. It is shown that finite nuclear systems undergo a first order phase transition. The caloric curve is presented for O, Mg, Al and Ca. A possible relation to fragmentation reactions is discussed.

Indications of equilibrium from measurements of isotope yields for nuclear
Friedman, W.A., (Univ. of Wisconsin)
Abstract: Measurements of isotope yields, motivated by attempts to determine nuclear temperatures, provide valuable information on the question of equilibrium and reaction dynamics. The general trends, that have been observed, are explored within the framework of the EES model.

Indications of equilibrium from measurements of isotope yields for nuclear
Friedman, W.A., (Univ. of Wisconsin)
Abstract: Measurements of isotope yields, motivated by attempts to determine nuclear temperatures, provide valuable information on the question of equilibrium and reaction dynamics. The general trends, that have been observed, are explored within the framework of the EES model.

Thermodynamical characterization of heavy Ion reactions
Gaitanos, T. (Uni Muenchen), Fuchs, C. (Uni Tuebingen), Wolter, H. (Uni Muenchen)
Abstract: We analyze the results of simulations of transport descriptions of heavy ion collisions with respect to the thermodynamical state of the system. We aim to obtain information on the degree of equilibration of the colliding system, the possibility of defining temperature, and the occurrance of instabilities, phase transitions, and, as a consequence, fragmentation. Since heavy ion collisions represent an extreme non-equilibrium situation, the thermodynamical states have to be analyzed locally in space-time. We perform two types of analyses: (a) We analyze locally the momentum distribution, determine the degree of anisotropy and the temperature by adjusting to it one or two Fermi distributions. We further determine density, currents, pressure, etc. Among others this allows to define locally conditions of instability and thus of fragmentation. (b) We generate final fragment spectra (using a coalescence algorithm) and compare to freeze-out models with radial flow and temperature.
The comparison of these pictures gives information about the reliability of the experimental extraction of temperatures and the locations of regions of fragmentation.

Thermodynamical characterization of heavy Ion reactions
Gaitanos, T. (Uni Muenchen), Fuchs, C. (Uni Tuebingen), Wolter, H. (Uni Muenchen)
Abstract: We analyze the results of simulations of transport descriptions of heavy ion collisions with respect to the thermodynamical state of the system. We aim to obtain information on the degree of equilibration of the colliding system, the possibility of defining temperature, and the occurrance of instabilities, phase transitions, and, as a consequence, fragmentation. Since heavy ion collisions represent an extreme non-equilibrium situation, the thermodynamical states have to be analyzed locally in space-time. We perform two types of analyses: (a) We analyze locally the momentum distribution, determine the degree of anisotropy and the temperature by adjusting to it one or two Fermi distributions. We further determine density, currents, pressure, etc. Among others this allows to define locally conditions of instability and thus of fragmentation. (b) We generate final fragment spectra (using a coalescence algorithm) and compare to freeze-out models with radial flow and temperature. The comparison of these pictures gives information about the reliability of the experimental extraction of temperatures and the locations of regions of fragmentation.

Neutron neutron interferometry in 45 A MeV 58Ni + 27Al collisions.
R. Ghetti, N. Colonna, B. Jakobsson, J. Helgesson, CHIC Collaboration
Abstract: Two-particle interferometry is used in intermediate energy heavy ion collisions to probe the space-time evolution of hot and possibly compressed nuclear systems. To this end, an experimental investigation of 45 MeV/nucleon $^{58}$Ni- induced reactions has been recently undertaken at the Superconducting Cyclotron of Laboratori Nazionali del Sud (Catania, Italy). A complex apparatus has been put together to simultaneously measure n-n, p-p and p-n correlation functions in coincidence with the fragment decay channel. Experimental single-particle energy spectra and two-neutron correlation functions from the 45 MeV/nucleon $^{58}$Ni + $^{27}$Al reaction will be shown and compared with theoretical calculations. The contributions from different mechanisms (pre-equilibrium, evaporation, etc. ) to the reaction dynamics will be discussed through their effects on the energy spectra and correlation functions.

Neutron neutron interferometry in 45 A MeV 58Ni + 27Al collisions.
R. Ghetti, N. Colonna, B. Jakobsson, J. Helgesson, CHIC Collaboration
Abstract: Two-particle interferometry is used in intermediate energy heavy ion collisions to probe the space-time evolution of hot and possibly compressed nuclear systems. To this end, an experimental investigation of 45 MeV/nucleon $^{58}$Ni- induced reactions has been recently undertaken at the Superconducting Cyclotron of Laboratori Nazionali del Sud (Catania, Italy). A complex apparatus has been put together to simultaneously measure n-n, p-p and p-n correlation functions in coincidence with the fragment decay channel. Experimental single-particle energy spectra and two-neutron correlation functions from the 45 MeV/nucleon $^{58}$Ni + $^{27}$Al reaction will be shown and compared with theoretical calculations. The contributions from different mechanisms (pre-equilibrium, evaporation, etc. ) to the reaction dynamics will be discussed through their effects on the energy spectra and correlation functions.

Decay modes induced by light particles (with special emphasis on antiprotons)
{F.~Goldenbaum$^0$, W.~Bohne$^1$, J.~Eades$^2$, T.v. Egidy$^3$, P.~Figuera$^1$, H.~Fuchs$^1$, J.~Galin$^4$, Ye.S.~Golubeva$^5$, K.~Gulda$^6$, D.~Hilscher$^1$, A.S.~Iljinov$^5$, U. Jahnke$^1$, J.~Jastrzebski$^6$, W.~Kurcewicz$^6$, B.~Lott$^4$, M.~Morjean$^4$, G.~Pausch$^7$, A.~P\'eghaire$^4$, L.~Pienkowski$^{1,6}$ , D.~Polster$^1$, S.~Proschitzki$^8$, B.~Quednau$^4$, H.~Rossner$^1$, S.~Schmid$^3$, W.~Schmid$^3$, P.~Ziem$^1$; \it $^0$Forschungszentrum-J\"ulich, D-52425 J\"ulich $^1$Hahn-Meitner-Institut Berlin, Glienickerstr. 100, D-14109 Berlin $^2$CERN-PPE, CH-1211-Geneva 21 $^3$TU-M\"unchen, D-85748 Garching $^4$GANIL (IN2P3-CNRS, DSM-CEA), BP 5027, F-14021 Caen-Cedex $^5$INR, Russian Academy of Science, 117312 Moscow $^6$University of Warsaw, 02-097 Warszawa $^7$FZ-Rossendorf, D-01314 Dresden $^8$IPN Orsay, BP 1, F-91406 Orsay-Cedex }
Abstract: The annihilation of energetic (1.2~GeV) antiprotons is exploited for the first time as a means to deposit very high thermal excitation (up to 1000 MeV) in massive nuclei (Cu, Ho, Au and U) while minimizing the contribution from collective excitation such as rotation, shape distortion and compression. Applying a novel technique, excitation energy distributions, $d\sigma/dE^*$, for antiproton induced reactions on nuclei at rest and in flight are deduced from event-wise observation of the whole nuclear evaporation chain with two $4\pi$ detectors one for neutrons, and one for charged particles. Excitation energy- and multiplicity-distributions of neutrons and charged particles are compared to a combined intra nuclear cascade/evaporation model which provides a reasonable description of the antiproton-annihilation-mechanism and good agreement has been obtained. The observed mean intermediate mass fragment {\small (IMF)} multiplicities for 1.22~GeV-$\overline{p}$ reactions on heavy nuclei ($A\ge 165$) which are found to decay predominantly statistically, are below 1.1 up to the highest excitation energies and can be fully explained by statistical evaporation.

Decay modes induced by light particles (with special emphasis on antiprotons)
{F.~Goldenbaum$^0$, W.~Bohne$^1$, J.~Eades$^2$, T.v. Egidy$^3$, P.~Figuera$^1$, H.~Fuchs$^1$, J.~Galin$^4$, Ye.S.~Golubeva$^5$, K.~Gulda$^6$, D.~Hilscher$^1$, A.S.~Iljinov$^5$, U. Jahnke$^1$, J.~Jastrzebski$^6$, W.~Kurcewicz$^6$, B.~Lott$^4$, M.~Morjean$^4$, G.~Pausch$^7$, A.~P\'eghaire$^4$, L.~Pienkowski$^{1,6}$ , D.~Polster$^1$, S.~Proschitzki$^8$, B.~Quednau$^4$, H.~Rossner$^1$, S.~Schmid$^3$, W.~Schmid$^3$, P.~Ziem$^1$; \it $^0$Forschungszentrum-J\"ulich, D-52425 J\"ulich $^1$Hahn-Meitner-Institut Berlin, Glienickerstr. 100, D-14109 Berlin $^2$CERN-PPE, CH-1211-Geneva 21 $^3$TU-M\"unchen, D-85748 Garching $^4$GANIL (IN2P3-CNRS, DSM-CEA), BP 5027, F-14021 Caen-Cedex $^5$INR, Russian Academy of Science, 117312 Moscow $^6$University of Warsaw, 02-097 Warszawa $^7$FZ-Rossendorf, D-01314 Dresden $^8$IPN Orsay, BP 1, F-91406 Orsay-Cedex }
Abstract: The annihilation of energetic (1.2~GeV) antiprotons is exploited for the first time as a means to deposit very high thermal excitation (up to 1000 MeV) in massive nuclei (Cu, Ho, Au and U) while minimizing the contribution from collective excitation such as rotation, shape distortion and compression. Applying a novel technique, excitation energy distributions, $d\sigma/dE^*$, for antiproton induced reactions on nuclei at rest and in flight are deduced from event-wise observation of the whole nuclear evaporation chain with two $4\pi$ detectors one for neutrons, and one for charged particles. Excitation energy- and multiplicity-distributions of neutrons and charged particles are compared to a combined intra nuclear cascade/evaporation model which provides a reasonable description of the antiproton-annihilation-mechanism and good agreement has been obtained. The observed mean intermediate mass fragment {\small (IMF)} multiplicities for 1.22~GeV-$\overline{p}$ reactions on heavy nuclei ($A\ge 165$) which are found to decay predominantly statistically, are below 1.1 up to the highest excitation energies and can be fully explained by statistical evaporation.

Energy correlations as a thermodynamical signal for phase transitions
F.Gulminelli, Ph.Chomaz (GANIL)
Abstract: A new method is proposed to extract information on the properties of the possible phase transition occurring in finite systems. The average energy of a subsystem is demonstrated to provide a thermometer when data are sorted in excitation energy bins, and the associated fluctuations are quantitatively related to the heat capacity. A coupled analysis with total energy fluctuations in bins of the partial energy allows to detect the presence of a phase transition and the associated order.

Energy correlations as a thermodynamical signal for phase transitions
F.Gulminelli, Ph.Chomaz (GANIL)
Abstract: A new method is proposed to extract information on the properties of the possible phase transition occurring in finite systems. The average energy of a subsystem is demonstrated to provide a thermometer when data are sorted in excitation energy bins, and the associated fluctuations are quantitatively related to the heat capacity. A coupled analysis with total energy fluctuations in bins of the partial energy allows to detect the presence of a phase transition and the associated order.

Spinodal and dynamical instabilities at the QCD phase transition
Y.-B. He, P. Bozek, J. Huefner, P. Zhuang
Abstract: The stability of an expanding parton plasma is analyzed within quasi-particle models. At thermal equilibrium the stability is studied within thermodynamics (mechanical stability) and via a linear response analysis of the Vlasov equation. The instabilities related to a first-order phase transition are found. For a plasma expanding in three and one dimensions far from equilibrium a new type of instability, called dynamical, appears. The relation to cluster formation is shown in a molecular dynamics calculation. The effect of hadronization on the instabilities have also been investigated.

Spinodal and dynamical instabilities at the QCD phase transition
Y.-B. He, P. Bozek, J. Huefner, P. Zhuang
Abstract: The stability of an expanding parton plasma is analyzed within quasi-particle models. At thermal equilibrium the stability is studied within thermodynamics (mechanical stability) and via a linear response analysis of the Vlasov equation. The instabilities related to a first-order phase transition are found. For a plasma expanding in three and one dimensions far from equilibrium a new type of instability, called dynamical, appears. The relation to cluster formation is shown in a molecular dynamics calculation. The effect of hadronization on the instabilities have also been investigated.

Multifragmentation of the Pb Projectile at 158 GeV/nucleon in Pb-Pb interactions.
Rman Holynski for KLM Collaboration
Abstract: We have investigated the process of fragmentation of the Pb nucleus at 158 GeV/nucleon in Pb-Pb interactions recorded in lead-emulsion chambers of the EMU13 CERN experiment. The number of Pb-Pb interactions found was larger then that expected from the nuclear charge changing cross section which indicates an important role of electromagnetic dissociation processes in Pb-Pb interactions at this high energy. Different modes of the Pb projectile break-up, including multifragmentation process, are discussed. The rates and properties of the fragmentation processes such as fission, multifragmentation and disintegration into singly charged fragments will be presented.

Multifragmentation of the Pb Projectile at 158 GeV/nucleon in Pb-Pb interactions.
Rman Holynski for KLM Collaboration
Abstract: We have investigated the process of fragmentation of the Pb nucleus at 158 GeV/nucleon in Pb-Pb interactions recorded in lead-emulsion chambers of the EMU13 CERN experiment. The number of Pb-Pb interactions found was larger then that expected from the nuclear charge changing cross section which indicates an important role of electromagnetic dissociation processes in Pb-Pb interactions at this high energy. Different modes of the Pb projectile break-up, including multifragmentation process, are discussed. The rates and properties of the fragmentation processes such as fission, multifragmentation and disintegration into singly charged fragments will be presented.

AMD study of multifragmentation
Horiuchi, H., Dept. of Phys., Kyoto Univ.; Ono, A., Dept. of Phys., Tohoku Univ.; Y. Sugawa, Dept. of Phys., Kyoto Univ.
Abstract: Au + Au collisions at 150 and 250 MeV/u are analysed with AMD-V model which takes into account the quantum branching due to wave packet splitting in addition to the two-nucleon collision process. The effect of coalescence is discussed. The reproduction of the data by the theory is good.

AMD study of multifragmentation
Horiuchi, H., Dept. of Phys., Kyoto Univ.; Ono, A., Dept. of Phys., Tohoku Univ.; Y. Sugawa, Dept. of Phys., Kyoto Univ.
Abstract: Au + Au collisions at 150 and 250 MeV/u are analysed with AMD-V model which takes into account the quantum branching due to wave packet splitting in addition to the two-nucleon collision process. The effect of coalescence is discussed. The reproduction of the data by the theory is good.

On the Time Sequence of Proton and Composite Particle Emission in Central Collisions of Ru(Zr)+Ru(Zr) at 400 AMeV
Kotte, R., FOPI collaboration
Abstract: Small-angle correlations of pairs of nonidentical light charged particles produced in central collisions of Ru(Zr)+Ru(Zr) at a beam energy of 400 AMeV are investigated with the FOPI detector system at GSI Darmstadt. The difference of longitudinal correlation functions with the relative velocity parallel and anti-parallel to the center-of-mass velocity of the pair in the source frame allows to extract the apparent emission-time sequence of the charged particles. The comparison of the correlations with the corresponding results of a final-state interaction and resonance decay model delivers quantitative estimates of these emission times. Time differences as short as 1 fm/c are resolved. The strong collective expansion of the participant zone found in central collisions introduces not only an apparent reduction of the source radius but also a modification of the emission time differences which i strongest for large differences of the particle masses. After correcting for both effects, for the first time a complete sequence of the emission times of p, d, t, 3He, and alpha particles is presented.

On the Time Sequence of Proton and Composite Particle Emission in Central Collisions of Ru(Zr)+Ru(Zr) at 400 AMeV
Kotte, R., FOPI collaboration
Abstract: Small-angle correlations of pairs of nonidentical light charged particles produced in central collisions of Ru(Zr)+Ru(Zr) at a beam energy of 400 AMeV are investigated with the FOPI detector system at GSI Darmstadt. The difference of longitudinal correlation functions with the relative velocity parallel and anti-parallel to the center-of-mass velocity of the pair in the source frame allows to extract the apparent emission-time sequence of the charged particles. The comparison of the correlations with the corresponding results of a final-state interaction and resonance decay model delivers quantitative estimates of these emission times. Time differences as short as 1 fm/c are resolved. The strong collective expansion of the participant zone found in central collisions introduces not only an apparent reduction of the source radius but also a modification of the emission time differences which i strongest for large differences of the particle masses. After correcting for both effects, for the first time a complete sequence of the emission times of p, d, t, 3He, and alpha particles is presented.

Multifragmentation of non-spherical hot nuclei
Le F\`evre, A. (GANIL) - Ploszajczak, M. (GANIL) - Toneev, V.A. (Dubna, GANIL) - Chbihi, A. (GANIL)
Abstract: The influence of nuclear shape on various characteristics of multifragmentattion is studied. The analysis is based on an extension of the statistical microcanonical multifragmentation model. Combined effects of the shape of decaying nuclei and high angular momentum as well as of a collective expansion velocity are discussed. Preliminary results for a hot source formed in central Xe+Sn (50 A.MeV) collisions will be presented and compared with experimental data.

Multifragmentation of non-spherical hot nuclei
Le F\`evre, A. (GANIL) - Ploszajczak, M. (GANIL) - Toneev, V.A. (Dubna, GANIL) - Chbihi, A. (GANIL)
Abstract: The influence of nuclear shape on various characteristics of multifragmentattion is studied. The analysis is based on an extension of the statistical microcanonical multifragmentation model. Combined effects of the shape of decaying nuclei and high angular momentum as well as of a collective expansion velocity are discussed. Preliminary results for a hot source formed in central Xe+Sn (50 A.MeV) collisions will be presented and compared with experimental data.

Virial corrections to simulations of heavy ion reactions
Klaus Morawetz (Fachbereich Physik, University Rostock,
Abstract: A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Enskog corrections is derived [1,3]. The space shifts parallel finite-diameter corrections to collisions of hard spheres. The time shift is similar to the collision delay [2]. This treatment unifies achievements of dense gases where nonlocal Enskog-like corrections had been worked out and the Landau theory of quasiparticle transport in metals, where wave function renormalizations are important.
Compared to the Boltzmann- equation, the presented form of virial corrections only slightly increases the numerical demands in implementations. Unlike in standard codes, the binary collisions are treated as non-local so that the contribution of the collision flux to the reaction dynamics is covered. A comparison with standard QMD simulations shows that the virial corrections lead to a broader proton distribution bringing theoretical spectra closer towards experimental values of current INDRA data. Complementary BUU simulations reveal that the non-locality enhances the collision rate in the early stage of the reaction. It suggests that the broader distribution appears due to an enhanced pre-equilibrium emission of particles.
Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. These balance equation are in agreement with the correlated observables found from the used extended quasiparticle ansatz, which in turn proves the consistency of the theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy [4].

[1] V. \v Spi\v cka, P. Lipavsk\'y, K. Morawetz, Phys. Rev. B. {\bf 55}, 5084 (1997); 5095 (1997).
[2] P. Danielewicz and S. Pratt, Phys. Rev.~C {\bf 53}, 249 (1996).
[3] P. Lipavsk\'y, K. Morawetz and V. \v{S}pi\v{c}ka, Rev. Mod. Phys., (1998), sub.
[4] V. \v{S}pi\v{c}ka, P. Lipavsk\'y, and K. Morawetz, Phys. Lett. {\bf A 240}, (1998), 160.
[5] K. Morawetz, V. \v{S}pi\v{c}ka, P. Lipavsk\'y, G. Kortemeyer, Ch. Kuhrts, R. Nebauer, Phys. Rev. Lett., sub.

Virial corrections to simulations of heavy ion reactions
Klaus Morawetz (Fachbereich Physik, University Rostock,
Abstract: A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Enskog corrections is derived [1,3]. The space shifts parallel finite-diameter corrections to collisions of hard spheres. The time shift is similar to the collision delay [2]. This treatment unifies achievements of dense gases where nonlocal Enskog-like corrections had been worked out and the Landau theory of quasiparticle transport in metals, where wave function renormalizations are important. Compared to the Boltzmann- equation, the presented form of virial corrections only slightly increases the numerical demands in implementations. Unlike in standard codes, the binary collisions are treated as non-local so that the contribution of the collision flux to the reaction dynamics is covered. A comparison with standard QMD simulations shows that the virial corrections lead to a broader proton distribution bringing theoretical spectra closer towards experimental values of current INDRA data. Complementary BUU simulations reveal that the non-locality enhances the collision rate in the early stage of the reaction. It suggests that the broader distribution appears due to an enhanced pre-equilibrium emission of particles. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. These balance equation are in agreement with the correlated observables found from the used extended quasiparticle ansatz, which in turn proves the consistency of the theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy [4]. [1] V. \v Spi\v cka, P. Lipavsk\'y, K. Morawetz, Phys. Rev. B. {\bf 55}, 5084 (1997); 5095 (1997). [2] P. Danielewicz and S. Pratt, Phys. Rev.~C {\bf 53}, 249 (1996). [3] P. Lipavsk\'y, K. Morawetz and V. \v{S}pi\v{c}ka, Rev. Mod. Phys., (1998), sub. [4] V. \v{S}pi\v{c}ka, P. Lipavsk\'y, and K. Morawetz, Phys. Lett. {\bf A 240}, (1998), 160. [5] K. Morawetz, V. \v{S}pi\v{c}ka, P. Lipavsk\'y, G. Kortemeyer, Ch. Kuhrts, R. Nebauer, Phys. Rev. Lett., sub.

Dynamic Evolution and Caloric Curves
Natowitz, J. B. et al,Cyclotron Institute, Texas A\&M University, College Station, Texas 77843-3366
Abstract: As participants in, and witnesses to, nearly every phase of the reaction, light particles carry detailed information on the reaction dynamics, the excitation energies reached and the degree of equilibration of any hot nuclei formed in these collisions . This is of particular interest in reactions leading to multifragment final states since these reactions are expected to yield information on the nuclear equation of state at non-normal densities.In this paper we report on the application of coalescence model analyses of light particle emission yields to follow the evolution of the temperatures and densities of A~125 nuclei produced in violent collisions induced by four different 47A MeV projectiles. With increasing projectile mass the temperatures increase and the densities decrease. The caloric curve derived for expanded A~120 nuclei is found to plateau near T=7 MeV. The plateau extends from 3 to 8 MeV/u excitation energy.

Dynamic Evolution and Caloric Curves
Natowitz, J. B. et al,Cyclotron Institute, Texas A\&M University, College Station, Texas 77843-3366
Abstract: As participants in, and witnesses to, nearly every phase of the reaction, light particles carry detailed information on the reaction dynamics, the excitation energies reached and the degree of equilibration of any hot nuclei formed in these collisions . This is of particular interest in reactions leading to multifragment final states since these reactions are expected to yield information on the nuclear equation of state at non-normal densities.In this paper we report on the application of coalescence model analyses of light particle emission yields to follow the evolution of the temperatures and densities of A~125 nuclei produced in violent collisions induced by four different 47A MeV projectiles. With increasing projectile mass the temperatures increase and the densities decrease. The caloric curve derived for expanded A~120 nuclei is found to plateau near T=7 MeV. The plateau extends from 3 to 8 MeV/u excitation energy.

Realistic Interactions and Multiconfiguration States in FMD
H. Feldmeier, T. Neff, R. Roth (GSI), J. Schnack (Uni Osnabrueck)
Abstract: Former studies of heavy ion reactions and the decay of excited nuclei proved to be very sensitive to the chosen nucleon-nucleon interaction. To include realistic interactions into the FMD model the unitary correlation operator method has been developed. In a first step short range correlations due to the core of the nucleon-nucleon interaction have been included. First results indicate that the FMD trial state does not provide enough freedom in both the static and the dynamical case. For groundstates multiconfiguration calculations show promise. In reaction dynamics a quantum branching process should allow a better description of multifragmentation.

Realistic Interactions and Multiconfiguration States in FMD
H. Feldmeier, T. Neff, R. Roth (GSI), J. Schnack (Uni Osnabrueck)
Abstract: Former studies of heavy ion reactions and the decay of excited nuclei proved to be very sensitive to the chosen nucleon-nucleon interaction. To include realistic interactions into the FMD model the unitary correlation operator method has been developed. In a first step short range correlations due to the core of the nucleon-nucleon interaction have been included. First results indicate that the FMD trial state does not provide enough freedom in both the static and the dynamical case. For groundstates multiconfiguration calculations show promise. In reaction dynamics a quantum branching process should allow a better description of multifragmentation.

Thermal Multifragmentation Induced with Light Relativistic Projectiles
Oeschler H., TU Darmstadt for the FASA Collaboration
Abstract: Multiple emission of intermediate mass fragments (IMF) has been studied in collisions of proton (up to 8 GeV) and $\alpha$ and $^{12}$C (both up to 3.65 AGeV) on Au using the 4$\pi$ setup FASA [1] installed at the Synchrophasotron, Dubna.
This data set gives a complete survey on multifragmentation studies using light projectiles at energies from the onset of this process up to highest IMF multiplicities [2]. The mean IMF multiplicity for events with at least one IMF depends mainly on the total energy and little on the mass of the projectile. An emission time scale of less than 100 fm/c is extracted from small angular correlations [3]. The charge distributions and kinetic energy spectra of IMF's differ little when comparing reactions with light projectiles but strongly when comparing those with heavy projectiles.
Our results are compared with model calculations using an intranuclear cascade followed by a statistical multifragmentation model [2]. Satisfactory agreement can only be obtained, if inbetween the two parts of the calculations, the excitation energies and residual masses and charges are modified to take into account losses during the expansion. These modifications are compared to expansion models [4,5].
The following observations with light projectiles support a thermal multifragmentation scenario of hot and expanded nuclear matter: (i) The energy spectra indicate an emission from an expanded system, yet, with a ``slow'' expansion as no collective flow component is observed. (ii) The IMF emission occurs within a short time scale. (iii) The angular distribution of IMF's is isotropic in the center-of-mass frame. (iv) As just mentioned an expansion stage has to be introduced in model calculations. 1. S.~Avdeyev et al., Nucl.~Instrum.~Meth. A332 (1993) 149. 2. S.~Avdeyev et al., European Physics Journal A3 (1998) 75. 3. V.~Lips et al., Phys. Lett. B338 (1994) 141; S.Y. Shmakov et al., Yad. Fiz. 58 (1995) 1735; (Phys. of Atomic Nucl. 58 (1995) 1635.\\
4. G.~Papp and W.~N\"orenberg, Heavy Ion Physics 1 (1995) 241. 5. W.A.~Friedman, Phys. Rev. C42 (1990) 667.

Thermal Multifragmentation Induced with Light Relativistic Projectiles
Oeschler H., TU Darmstadt for the FASA Collaboration
Abstract: Multiple emission of intermediate mass fragments (IMF) has been studied in collisions of proton (up to 8 GeV) and $\alpha$ and $^{12}$C (both up to 3.65 AGeV) on Au using the 4$\pi$ setup FASA [1] installed at the Synchrophasotron, Dubna. This data set gives a complete survey on multifragmentation studies using light projectiles at energies from the onset of this process up to highest IMF multiplicities [2]. The mean IMF multiplicity for events with at least one IMF depends mainly on the total energy and little on the mass of the projectile. An emission time scale of less than 100 fm/c is extracted from small angular correlations [3]. The charge distributions and kinetic energy spectra of IMF's differ little when comparing reactions with light projectiles but strongly when comparing those with heavy projectiles. Our results are compared with model calculations using an intranuclear cascade followed by a statistical multifragmentation model [2]. Satisfactory agreement can only be obtained, if inbetween the two parts of the calculations, the excitation energies and residual masses and charges are modified to take into account losses during the expansion. These modifications are compared to expansion models [4,5]. The following observations with light projectiles support a thermal multifragmentation scenario of hot and expanded nuclear matter: (i) The energy spectra indicate an emission from an expanded system, yet, with a ``slow'' expansion as no collective flow component is observed. (ii) The IMF emission occurs within a short time scale. (iii) The angular distribution of IMF's is isotropic in the center-of-mass frame. (iv) As just mentioned an expansion stage has to be introduced in model calculations. 1. S.~Avdeyev et al., Nucl.~Instrum.~Meth. A332 (1993) 149. 2. S.~Avdeyev et al., European Physics Journal A3 (1998) 75. 3. V.~Lips et al., Phys. Lett. B338 (1994) 141; S.Y. Shmakov et al., Yad. Fiz. 58 (1995) 1735; (Phys. of Atomic Nucl. 58 (1995) 1635.\\ 4. G.~Papp and W.~N\"orenberg, Heavy Ion Physics 1 (1995) 241. 5. W.A.~Friedman, Phys. Rev. C42 (1990) 667.

AMD study of multifragmentation
Horiuchi, H., Dept. of Phys., Kyoto Univ.; Ono, A., Dept. of Phys., Tohoku Univ.
Abstract: Au + Au collisions at 150 and 250 MeV/u are analysed with AMD-V model which takes into account the quantum branching due to wave packet splitting in addition to the two-nucleon collision process. The effect of coalescence is discussed. The reproduction of the data by the theory is good.

AMD study of multifragmentation
Horiuchi, H., Dept. of Phys., Kyoto Univ.; Ono, A., Dept. of Phys., Tohoku Univ.
Abstract: Au + Au collisions at 150 and 250 MeV/u are analysed with AMD-V model which takes into account the quantum branching due to wave packet splitting in addition to the two-nucleon collision process. The effect of coalescence is discussed. The reproduction of the data by the theory is good.

Renormalizing into the mixed phase
Polonyi J. Alexandre J. Branchina V. (Laboratory of Theoretical Physics, Louis Pasteur University)
Abstract: It is pointed out that models with condensates have nontrivial renormalization group flow on the tree level. The infinitesimal form of the tree level renormalization group equation is obtained and solved numerically for the $\phi^4$ model in the symmetry broken phase. We find an attractive infrared fixed point which eliminates the metastable region and reproduces the Maxwell construction. This result opens the way for a more systematical treatment of the spinodal instability.

Renormalizing into the mixed phase
Polonyi J. Alexandre J. Branchina V. (Laboratory of Theoretical Physics, Louis Pasteur University)
Abstract: It is pointed out that models with condensates have nontrivial renormalization group flow on the tree level. The infinitesimal form of the tree level renormalization group equation is obtained and solved numerically for the $\phi^4$ model in the symmetry broken phase. We find an attractive infrared fixed point which eliminates the metastable region and reproduces the Maxwell construction. This result opens the way for a more systematical treatment of the spinodal instability.

Multifragmentation of heavy systems around the Fermi energy: compression, expansion and volume instabilities.
Rivet, M.F., Bacri, C.O., Borderie, B., Frankland, J.D., Parlog, M. Tabacaru, G. and the INDRA collaboration
Abstract: The multifragmentation of a "fused system" was evidenced for very heavy systems (A-250-400) between 30 and 50 MeV/u. Thanks to the performances of the INDRA 4$\pi$ multidetector, most of the resulting charged products were identified.. A detailed study of the fragment kinetic energy showed that the system is expanding when multifragmenting. A systematics was established near this radial expansion threshold through the use of an event generator. Complete calculations in which multifragmentation arises from the spinodal decomposition of finite systems were performed and give excellent agreement with the experimental data.

Multifragmentation of heavy systems around the Fermi energy: compression, expansion and volume instabilities.
Rivet, M.F., Bacri, C.O., Borderie, B., Frankland, J.D., Parlog, M. Tabacaru, G. and the INDRA collaboration
Abstract: The multifragmentation of a "fused system" was evidenced for very heavy systems (A-250-400) between 30 and 50 MeV/u. Thanks to the performances of the INDRA 4$\pi$ multidetector, most of the resulting charged products were identified.. A detailed study of the fragment kinetic energy showed that the system is expanding when multifragmenting. A systematics was established near this radial expansion threshold through the use of an event generator. Complete calculations in which multifragmentation arises from the spinodal decomposition of finite systems were performed and give excellent agreement with the experimental data.

Nuclear caloric curve: Microcanonical investigation
Raduta Ad. R. (NIPNE, Bucharest), Raduta Al. H. (NIPNE, Bucharest)
Abstract: A microcanonical model sharply conserving mass, charge, energy and momentum is used to investigate the primary nuclear caloric curve. Microcanonical temperature calculations are performed for three representative sample nuclei. For all cases a plateau of around 5 MeV temperature is manifested for the excitation energy range 2.5 to 8.5 MeV, fact resembling the experimental evidence and sign of liquid-gas phase transition. Calculated He-Li isotopic temperature curves manifest a similar behavior. The results are strongly distinctive from the MMMC microcanonical model which obtains plateaus or backbandings only of around 1 MeV/nucleon width. Comparisons between calculated caloric curves and experimental He-Li temperature curves are discussed in detail. Contributions brought by secondary decay and collective flow to the primary decay caloric curve are commented.

Nuclear caloric curve: Microcanonical investigation
Raduta Ad. R. (NIPNE, Bucharest), Raduta Al. H. (NIPNE, Bucharest)
Abstract: A microcanonical model sharply conserving mass, charge, energy and momentum is used to investigate the primary nuclear caloric curve. Microcanonical temperature calculations are performed for three representative sample nuclei. For all cases a plateau of around 5 MeV temperature is manifested for the excitation energy range 2.5 to 8.5 MeV, fact resembling the experimental evidence and sign of liquid-gas phase transition. Calculated He-Li isotopic temperature curves manifest a similar behavior. The results are strongly distinctive from the MMMC microcanonical model which obtains plateaus or backbandings only of around 1 MeV/nucleon width. Comparisons between calculated caloric curves and experimental He-Li temperature curves are discussed in detail. Contributions brought by secondary decay and collective flow to the primary decay caloric curve are commented.

Nuclear caloric curve: Interplay between various degrees of freedom in shape determination
Raduta Al. H. (NIPNE, Bucharest), Raduta Ad. R. (NIPNE, Bucharest)
Abstract: Primary decay nuclear caloric curves are calculated via a sharp microcanonical model. Wide plateaus of the caloric curves at around 5 MeV temperature similar with the experimental results and sign of liquid-gas phase transition are obtained. Correlations between different parts of the caloric curves with the energy amounts deposited in the availables degrees of freedom are identified and discussed. Calculated relative probabilities of different fragmentation modes are demonstrating that the three principal (first increasing, plateau and second increasing) parts of the caloric curve are effectively corresponding to three distinct phases of nuclear matter (liquid, liquid-gas mixture and gas). A detailed discussion is made concerning the extent to which various degrees of freedom are influencing the shape of the caloric curve.

Nuclear caloric curve: Interplay between various degrees of freedom in shape determination
Raduta Al. H. (NIPNE, Bucharest), Raduta Ad. R. (NIPNE, Bucharest)
Abstract: Primary decay nuclear caloric curves are calculated via a sharp microcanonical model. Wide plateaus of the caloric curves at around 5 MeV temperature similar with the experimental results and sign of liquid-gas phase transition are obtained. Correlations between different parts of the caloric curves with the energy amounts deposited in the availables degrees of freedom are identified and discussed. Calculated relative probabilities of different fragmentation modes are demonstrating that the three principal (first increasing, plateau and second increasing) parts of the caloric curve are effectively corresponding to three distinct phases of nuclear matter (liquid, liquid-gas mixture and gas). A detailed discussion is made concerning the extent to which various degrees of freedom are influencing the shape of the caloric curve.

Clusterization at SIS energies: non-equilibrium effects and flow back-influence
Reisdorf,W (FOPI Collaboration)
Abstract: Observations obtained with the FOPI detector system in heavy-ion reactions at SIS/GSI indicate that 1) complete mixing of isospin is not achieved in central collisions 2) that clusterization probabilities in expanding participant matter ( in contrast to spectator matter) is system-size dependent. Large systems developping bulk flow seem to favour cooling and hence clusterization.

Clusterization at SIS energies: non-equilibrium effects and flow back-influence
Reisdorf,W (FOPI Collaboration)
Abstract: Observations obtained with the FOPI detector system in heavy-ion reactions at SIS/GSI indicate that 1) complete mixing of isospin is not achieved in central collisions 2) that clusterization probabilities in expanding participant matter ( in contrast to spectator matter) is system-size dependent. Large systems developping bulk flow seem to favour cooling and hence clusterization.

On the variation of the Coulomb Repulsion in Multifragmentation
V. Rodionov, H. Oeschler, A.S. Botvina, D.H.E. Gross, S.P. Avdeyev, V.A. Karnaukhov, L.A. Petrov, O.V. Bochkarev, L.V. Chulkov, E.A. Kuzmin, A. Budzanowski, W. Karcz, M. Janicki, E. Norbeck
Abstract: In multifragment emission the respective Coulomb repulsion allows to trace back the geometry and the time evolution at break up. In collisions of 8.1 GeV protons with gold, it is found that for a given isotope the maxima of the energy spectra decrease with increasing number of emitted fragments. This could indicate a variation in density at break up. Calculations with statistical multifragmentation models with fixed density exhibit, however, a similar trend.

On the variation of the Coulomb Repulsion in Multifragmentation
V. Rodionov, H. Oeschler, A.S. Botvina, D.H.E. Gross, S.P. Avdeyev, V.A. Karnaukhov, L.A. Petrov, O.V. Bochkarev, L.V. Chulkov, E.A. Kuzmin, A. Budzanowski, W. Karcz, M. Janicki, E. Norbeck
Abstract: In multifragment emission the respective Coulomb repulsion allows to trace back the geometry and the time evolution at break up. In collisions of 8.1 GeV protons with gold, it is found that for a given isotope the maxima of the energy spectra decrease with increasing number of emitted fragments. This could indicate a variation in density at break up. Calculations with statistical multifragmentation models with fixed density exhibit, however, a similar trend.

Instabilities of finite hot expanded nuclear matter
Rozmej P (IF, Uniwersytet MCS, Lublin, Poland), Noerenberg W (GSI Darmstadt), Papp G (CNR Dep. of
Abstract: The stability of hot, expanded droplets of nuclear matter against small bulk and surface oscillations is examined and possible consequences for multifragmentation are discussed. An arbitrary, irrotational dispalcement field is defined from a potential which is given by an expansion in terms of spherical harmonics and Bessel functions. The expansion coefficients are the collective coordinates. For small amplitudes one finds eigenvalue equations which determine either the frequency of stable oscillations or the exponential growth of an instable mode.
Calculations have been performed for different densities, temperatures and nucleon numbers. We find that the region of instabilities for nuclear droplets is substantially smaller than that for infinite nuclear matter. This effect is mainly due to the Weizsacker term in the energy density. For small densities and temperatures below 3-4 MeV many different modes become unstable. We also discuss effects from pure surface vibrations that appear to be important for higher densities and temperatures. Furthermore we compare results obtained for both a soft and a stiff EOS.

Instabilities of finite hot expanded nuclear matter
Rozmej P (IF, Uniwersytet MCS, Lublin, Poland), Noerenberg W (GSI Darmstadt), Papp G (CNR Dep. of
Abstract: The stability of hot, expanded droplets of nuclear matter against small bulk and surface oscillations is examined and possible consequences for multifragmentation are discussed. An arbitrary, irrotational dispalcement field is defined from a potential which is given by an expansion in terms of spherical harmonics and Bessel functions. The expansion coefficients are the collective coordinates. For small amplitudes one finds eigenvalue equations which determine either the frequency of stable oscillations or the exponential growth of an instable mode. Calculations have been performed for different densities, temperatures and nucleon numbers. We find that the region of instabilities for nuclear droplets is substantially smaller than that for infinite nuclear matter. This effect is mainly due to the Weizsacker term in the energy density. For small densities and temperatures below 3-4 MeV many different modes become unstable. We also discuss effects from pure surface vibrations that appear to be important for higher densities and temperatures. Furthermore we compare results obtained for both a soft and a stiff EOS.

The nature of the phase transition in nuclear multifragmentation
R. P. Scharenberg for EOS Collaboration
Abstract: Exclusive 1A GeV Au on C data is compared to the variable volume SMM model. Critical exponents and critical scaling are seen in both data and SMM . The nature of the phase transition is explored using the microcanonical temperature from SMM.

The nature of the phase transition in nuclear multifragmentation
R. P. Scharenberg for EOS Collaboration
Abstract: Exclusive 1A GeV Au on C data is compared to the variable volume SMM model. Critical exponents and critical scaling are seen in both data and SMM . The nature of the phase transition is explored using the microcanonical temperature from SMM.

Caloric curve of atomic clusters - solid-liquid phase transitions.
Schmidt, M. ;Kusche, R.; von Issendorff, B.; Haberland, H.
Abstract: Caloric curves of free, mass selected sodium clusters are measured by using the fragmentation pattern of thermalized and laser excited clusters as a ``nano--calorimeter". The solid/liquid phase transition is studied for clusters containing between 50 and 200 atoms. The influence of the finite size to the thermodynamics of the clusters will been discussed.

Caloric curve of atomic clusters - solid-liquid phase transitions.
Schmidt, M. ;Kusche, R.; von Issendorff, B.; Haberland, H.
Abstract: Caloric curves of free, mass selected sodium clusters are measured by using the fragmentation pattern of thermalized and laser excited clusters as a ``nano--calorimeter". The solid/liquid phase transition is studied for clusters containing between 50 and 200 atoms. The influence of the finite size to the thermodynamics of the clusters will been discussed.

Breakup Density in Spectator Fragmentation
C. Schwarz for the ALADIN collaboration
Abstract: Proton-proton correlations and correlations of protons, deuterons, and tritons with alpha particles from spectator decay following Au+Au collisions at 1000 AMeV have been measured with two highly efficient detector hodoscopes. The constructed correlation functions , interpreted within the approximation of a simultaneous volume decay, indicate a moderate expansion and low breakup densities similar to assumptions made in statistical multifragmentation models.
[1] A. Schuettauf et al., Nucl. Phys. A 607, 457 (1996) [2] Hongfei Xi et al., Z. Phys. A 359, 397 (1997)

Breakup Density in Spectator Fragmentation
C. Schwarz for the ALADIN collaboration
Abstract: Proton-proton correlations and correlations of protons, deuterons, and tritons with alpha particles from spectator decay following Au+Au collisions at 1000 AMeV have been measured with two highly efficient detector hodoscopes. The constructed correlation functions , interpreted within the approximation of a simultaneous volume decay, indicate a moderate expansion and low breakup densities similar to assumptions made in statistical multifragmentation models. [1] A. Schuettauf et al., Nucl. Phys. A 607, 457 (1996) [2] Hongfei Xi et al., Z. Phys. A 359, 397 (1997)

Isospin and cluster formation in intermediate energy HI reactions
Sobotka, L.G. (Washington University)
Abstract: Data will be presented which shows, that for mid-central and peripheral collisions, that the intermediate mass fragments with intermediate velocity are neutron rich relative to those with velocities near that of the projectile. Equilibrium and dynamical calculations will be presented to address the issue of whether this apparent enrichment of neutrons at midrapidity is the result of an inflow of neutrons into the newly forming surface region, between the reseperating fragments, or the result of a rather strong tendency for low density nuclear systems to alpha-cluster which would amplify the initial asymmetry of the remaining material.

Isospin and cluster formation in intermediate energy HI reactions
Sobotka, L.G. (Washington University)
Abstract: Data will be presented which shows, that for mid-central and peripheral collisions, that the intermediate mass fragments with intermediate velocity are neutron rich relative to those with velocities near that of the projectile. Equilibrium and dynamical calculations will be presented to address the issue of whether this apparent enrichment of neutrons at midrapidity is the result of an inflow of neutrons into the newly forming surface region, between the reseperating fragments, or the result of a rather strong tendency for low density nuclear systems to alpha-cluster which would amplify the initial asymmetry of the remaining material.

Conditional Moment Analysis of 1A GeV Au+C Data and the Statistical Multifragmentation Model (SMM).
Brijesh Srivastava for EOS Collaboration
Abstract: Conditional moments of the fragment size distributions and its fluctuations in Au+C data have been calculated and compared with the results of statistical multifragmentation model. The effect of fragment cooling on the conditional moments and their fluctuations are explored. The results agree with other studies which suggest that SMM can exhibit a continuous phase transition.

Conditional Moment Analysis of 1A GeV Au+C Data and the Statistical Multifragmentation Model (SMM).
Brijesh Srivastava for EOS Collaboration
Abstract: Conditional moments of the fragment size distributions and its fluctuations in Au+C data have been calculated and compared with the results of statistical multifragmentation model. The effect of fragment cooling on the conditional moments and their fluctuations are explored. The results agree with other studies which suggest that SMM can exhibit a continuous phase transition.

Reaction mechanisms and multifragmentation
B. Tamain
Abstract: Reaction mechanisms observed in intermediate energy heavy ion reactions are mainly binary. From this point of view, they look like deep inelastic reactions observed at low bombarding energy and very strong dissipations are observed. However, mid-rapidity emission occurs which is a first manifestation of the important role played by the geometry of the collision in the relativistic energy regime. This emission can have various origins which will be described. Some of them correspond to preequilibrium emission but some fragments are emitted after partial equilibrium.

Reaction mechanisms and multifragmentation
B. Tamain
Abstract: Reaction mechanisms observed in intermediate energy heavy ion reactions are mainly binary. From this point of view, they look like deep inelastic reactions observed at low bombarding energy and very strong dissipations are observed. However, mid-rapidity emission occurs which is a first manifestation of the important role played by the geometry of the collision in the relativistic energy regime. This emission can have various origins which will be described. Some of them correspond to preequilibrium emission but some fragments are emitted after partial equilibrium.

A new type of shape instability of hot nuclei
T\~oke J. and Schr\"oder W.U., University of Rochester
Abstract: It is shown that an enhancement of the accessible phase space volume due to the diffuseness of nuclear surface leads to shape instabilities of hot nuclei and to a fragmentation that is prompt on the timescale of the microcanonical equilibration.

A new type of shape instability of hot nuclei
T\~oke J. and Schr\"oder W.U., University of Rochester
Abstract: It is shown that an enhancement of the accessible phase space volume due to the diffuseness of nuclear surface leads to shape instabilities of hot nuclei and to a fragmentation that is prompt on the timescale of the microcanonical equilibration.

Fragment kinetic energies in spectator decays
Trautmann, W. (GSI), ALADIN collaboration
Abstract: Kinetic energies of fragments and light particles from the fragmentation of gold nuclei at relativistic energies have been measured in four different experiments. The memory of the entrance channel is apparent in the kinetic energies of nucleons while evaporation components can be identified in the spectra of nucleons and alpha particles. Beyond that, the mean kinetic energies are typically 40 to 50 MeV, independent of the particle species and the bombarding energy, but not in equilibrium with the chemical or thermal degrees of freedom.

Fragment kinetic energies in spectator decays
Trautmann, W. (GSI), ALADIN collaboration
Abstract: Kinetic energies of fragments and light particles from the fragmentation of gold nuclei at relativistic energies have been measured in four different experiments. The memory of the entrance channel is apparent in the kinetic energies of nucleons while evaporation components can be identified in the spectra of nucleons and alpha particles. Beyond that, the mean kinetic energies are typically 40 to 50 MeV, independent of the particle species and the bombarding energy, but not in equilibrium with the chemical or thermal degrees of freedom.

Antiproton- and hadron-induced multifragmentation
Viola, V.E., Indiana University, for the ISiS Collaboration
Abstract: Multifragmentation studies induced by GeV light-ion beams permit investigation of the influence of intrinsic thermal properties of hiot nuclear matter, with minimal interference from the compression/ decompression cycle and rotational instabilities. We will summarize recent data obtained with 3He, proton and pion beams up to 15 GeV/c and present the initial results from a recent experiment with 8 GeV/c antiproton and pion beams. The results are compared with INC, EES and SMM models and the caloric curve for 3He data wil be discussed.

Antiproton- and hadron-induced multifragmentation
Viola, V.E., Indiana University, for the ISiS Collaboration
Abstract: Multifragmentation studies induced by GeV light-ion beams permit investigation of the influence of intrinsic thermal properties of hiot nuclear matter, with minimal interference from the compression/ decompression cycle and rotational instabilities. We will summarize recent data obtained with 3He, proton and pion beams up to 15 GeV/c and present the initial results from a recent experiment with 8 GeV/c antiproton and pion beams. The results are compared with INC, EES and SMM models and the caloric curve for 3He data wil be discussed.

Fluctuations and dynamical instabilities in heavy ion reactions
H. Wolter, LMU M"unchen
Abstract: A new method to implement fluctuations in transport descriptions of heavy ion reactions is proposed. We determine the variance of the density under the assumption of local statistical equilibrium. Fluctuations are introduced into the distribution function at various time steps, and the evolution of the fluctuations is followed by the mean field dynamics. The final configurations is analyzed with repect to fragments formation. The method is applied to study the role of fluctuations in both stable and unstable situations. While in stable situation its leads to an increase of the width of distributions around the mean value, the role of fluctuations becomes crucial in unstable situations, where bifurcations occur and different exit channels can be chosen. We illustrate these points by investigating the breakup of di-nuclear systems exhibiting neck instabilities.