The systematic data set on isotopic effects in spectator fragmentation collected recently at the GSI laboratory permits the investigation of the N/Z dependence of the nuclear caloric curve which is of interest in several respects. In particular, new light is shed on the proposed interpretation of chemical breakup temperatures as a manifestation of the limiting temperatures predicted by the Hartree-Fock model. The obtained results are discussed within the general context of temperature measurements in multifragmentation reactions.
Critical temperature Tc for the nuclear liquid-gas phase transition is stimated both from the multifragmentation and fission data. In the first case,the critical temperature is obtained by analysis of the IMF yields in p(8.1 GeV)+Au collisions within the statistical model of multifragmentation (SMM). In the second case, the experimental fission probability for excited 188Os is compared with the calculated one with Tc as a free parameter. It is concluded for both cases that the critical temperature is higher than 16 MeV.
A statistical multifragmentation model (SMM) is applied to the experimentally observed multifragmentation events in an intermediate heavy ion reaction.Using the temperature and symmetry energy extracted from the isobaric yield ratio (IYR) method based on the Modified Fisher Model (MFM), SMM is applied to the reaction $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon. The experimental isotope distribution and mass distribution of the primary reconstructed fragments are compared without afterburner and they are well reproduced. The extracted temperature $T$ and symmetry energy coefficient $a_{sym}$ from …
An overview of the recent progress in the studies of nuclear multifragmentation is presented. Special emphasis is put on the exploration of isotopic trends in nuclear multifragmentation and the possibilities to extract physical information related to the nuclear equation of state. Relevant experimental methods of isotope identification are described. The isotopic composition of fragments is used to extract the values of thermodynamical observables of the system undergoing multifragmentation such as temperature and chemical potentials. Various methods for extraction of thermodynamical variables…
The fragment production in multifragmentation of finite nuclei is affected by the critical temperature of nuclear matter. We show that this temperature can be determined on the basis of the statistical multifragmentation model (SMM) by analyzing the evolution of fragment distributions with the excitation energy. This method can reveal a decrease of the critical temperature that, e.g., is expected for neutron-rich matter. The influence of isospin on fragment distributions is also discussed.
For nuclei in five different mass regions the critical temperatures, at which the surface tension vanishes, are derived from information on the liquid branch of the coexistence curve. These critical temperatures increase with increasing mass and, for higher masses are well above recently reported critical temperatures obtained from Fisher Droplet model and percolation model analyses. However, for the lowest mass region nuclei, with 30<A<60, this analysis indicates that nucleonic matter has been produced essentially at the critical point, characterized by Tc and rho_c.
A systematic analysis of the moments of the fragment size distribution has been carried out for the multifragmentation (MF)of 1A GeV Au, La, and Kr on carbon. The breakup of Au and La is consistent with a continuous thermal phase transition. The data indicate that the excitation energy per nucleon and isotopic temperature at the critical point decrease with increasing system size. This trend is attributed primarily to the increasing Coulomb energy with finite size effects playing a smaller role.
A systematic analysis of the multifragmentation (MF) in fully reconstructed events from 1A GeV Au, La and Kr collisions with C has been performed. This data is used to provide a definitive test of the variable volume version of the statistical multifragmentation model (SMM). A single set of SMM parameters directly determined by the data and the semi-empiricalmass formula are used after the adjustable inverse level density parameter, $ε_{o}$ is determined by the fragment distributions. The results from SMM for second stage multiplicity, size of the biggest fragment and the intermediate mass fra…
The mean transverse kinetic energies of the fragments formed in the interaction of 1 A GeV Au+C have been determined. An energy balance argument indicates the presence of a collective energy which increases in magnitude with increasing multiplicity and accounts for nearly half of the measured mean transverse kinetic energy. The radial flow velocity associated with the collective energy yields estimates for the time required to expand to the freeze-out volume. Isentropic trajectories in the temperature-density plane are shown for the expansion and indicate that the system goes through the criti…
Isotopic effects in spectator fragmentations following heavy-ion collisions at relativistic energies are investigated using data from recent exclusive experiments with SIS beams at GSI. Reactions of 12C on 112,124Sn at incident energies 300 and 600 MeV per nucleon were studied with the INDRA multidetector while the fragmentation of stable 124Sn and radioactive 107Sn and 124La projectiles was studied with the ALADIN spectrometer. The global characteristics of the reactions are very similar. This includes the rise and fall of fragment production and deduced observables as, e.g., the breakup temp…
Experimental data for central collisions of $^{129}$Xe on $^{119}$Sn at beam energies of (a) 32 MeV/nucleon, (b) 39 MeV/nucleon, (c) 45 MeV/nucleon and (d) 50 MeV/nucleon are compared with results calculated using a hybrid model. We use a transport model (BUU) to obtain the excitation energy per nucleon in the center of mass of the multifragmenting system. The canonical thermodynamic model is then used to determine the temperature which would lead to this excitation energy. With this temperature we use the canonical thermodynamic model to calculate various experimental data such as multiplicit…
The cumulant ratios up to fourth order of the $Z$ distributions of the largest fragment in spectator fragmentation following $^{107,124}$Sn+Sn and $^{124}$La+Sn collisions at 600 MeV/nucleon have been investigated. They are found to exhibit the signatures of a second-order phase transition established with cubic bond percolation and previously observed in the ALADIN experimental data for fragmentation of $^{197}$Au projectiles at similar energies. The deduced pseudocritical points are found to be only weakly dependent on the $A/Z$ ratio of the fragmenting spectator source. The same holds for t…
The Statistical Multifragmentation Model is modified to incorporate the Helmholtz free energies calculated in the finite temperature Thomas-Fermi approximation using Skyrme effective interactions. In this formulation, the density of the fragments at the freeze-out configuration corresponds to the equilibrium value obtained in the Thomas-Fermi approximation at the given temperature. The behavior of the nuclear caloric curve at constant volume is investigated in the micro-canonical ensemble and a plateau is observed for excitation energies between 8 and 10 MeV per nucleon. A kink in the caloric …
In the framework of a 2D Vlasov model, we study the time evolution of the "coarse-grained" Generalized Entropy (GE) in a nuclear system which undergoes a multifragmentation (MF) phase transition. We investigate the GE both for the gas and the fragments (surface and bulk part respectively). We find that the formation of the surface causes the growth of the GE during the process of fragmentation. This quantity then characterizes the MF and confirms the crucial role of deterministic chaos in filling the new available phase-space: at variance with the exact time evolution, no entropy change is fou…
Investigation of the effect of the dynamical stage of heavy-ion collisions indicates that the increasing width of the initial isospin distributions is reflected by a significant modification of the isoscaling slope for the final isotopic distributions after de-excitation. For narrow initial distributions, the isoscaling slope assumes the limiting value of the two individual initial nuclei while for wide initial isotopic distributions the slope for hot fragments approaches the initial value. The isoscaling slopes for final cold fragments increase due to secondary emissions. The experimentally o…
A phase transition signature associated with cumulants of the largest fragment size distribution has been identified in statistical multifragmentation models and examined in analysis of the ALADIN S254 data on fragmentation of neutron-poor and neutron-rich projectiles. Characteristics of the transition point indicated by this signature are weakly dependent on the A/Z ratio of the fragmenting spectator source. In particular, chemical freeze-out temperatures are estimated within the range 5.9 to 6.5 MeV. The experimental results are well reproduced by the SMM model.
Breakup temperatures were deduced from double ratios of isotope yields for target spectators produced in the reaction Au + Au at 1000 MeV per nucleon. Pairs of $^{3,4}$He and $^{6,7}$Li isotopes and pairs of $^{3,4}$He and H isotopes (p, d and d, t) yield consistent temperatures after feeding corrections, based on the quantum statistical model, are applied. The temperatures rise with decreasing impact parameter from 4 MeV for peripheral to about 10 MeV for the most central collisions. The good agreement with the breakup temperatures measured previously for projectile spectators at an incident …
The fragment yields from the multifragmentation of gold, lanthanum and krypton nuclei obtained by the EOS Collaboration are examined in terms of Fisher's droplet formalism modifed to account for Coulomb energy. The critical exponents sigma and tau and the surface energy coefficient c0 are obtained. Estimates are made of the pressure-temperature and temperature-density coexistence curves of finite neutral nuclear matter as well as the location of the critical point.
We report on new measurements of breakup temperatures for target spectators from 197Au + 197Au reactions at 1000 MeV per nucleon. The temperatures rise with decreasing impact parameter from 4 MeV for peripheral to about 10 MeV for the most central collisions, in good agreement with previous results for projectile spectators at 600 MeV per nucleon. The measured temperatures agree quantitatively with the breakup temperatures predicted by the statistical multifragmentation model. For these calculations a relation between the initial excitation energy and mass was derived which gives good simultan…
We have demonstrated that the isospin of nuclei influences the fragment production during the nuclear liquid-gas phase transition. Calculations for Au197, Sn124, La124 and Kr78 at various excitation energies were carried out on the basis of the statistical multifragmentation model (SMM). We analyzed the behavior of the critical exponent tau with the excitation energy and its dependence on the critical temperature. Relative yields of fragments were classified with respect to the mass number of the fragments in the transition region. In this way, we have demonstrated that nuclear multifragmentat…
We have demonstrated that the isospin of nuclei influences the fragment production during the nuclear liquid-gas phase transition. Calculations for Au197, Sn124, La124 and Kr78 at various excitation energies were carried out on the basis of the statistical multifragmentation model (SMM). We analyzed the behavior of the critical exponent tau with the excitation energy and its dependence on the critical temperature. Relative yields of fragments were classified with respect to the mass number of the fragments in the transition region. In this way, we have demonstrated that nuclear multifragmentat…
The high-resolution spectrometer FRS at GSI Darmstadt provides the full isotopic and kinematical identification of fragmentation residues in relativistic heavy-ion collisions. Recent measurements of the isotopic distribution of heavy projectile fragments led to a very surprising new physical finding: the residue production does not lose the memory of the N/Z of the projectile ending up in a universal de-excitation corridor; an ordering of the residues in relation to the neutron excess of the projectile has been observed. These unexpected features can be interpreted as a new manifestation of mu…
The properties of the nuclear isoscaling at finite temperature are investigated and the extent to which its parameter $α$ holds information on the symmetry energy is examined. We show that, although finite temperature effects invalidate the analytical formulas that relate the isoscaling parameter $α$ to those of the mass formula, the symmetry energy remains the main ingredient that dictates the behavior of $α$ at finite temperatures, even for very different sources. This conclusion is not obvious as it is not true in the vanishing temperature limit, where analytical formulas are available. Our…
From experimental observations of limiting temperatures in heavy ion collisions we derive Tc, the critical temperature of infinite nuclear matter. The critical temperature is 16.6 +- 0.86 MeV. Theoretical model correlations between Tc, the compressibility modulus, K the effective mass, $m^*$ and the saturation density, rho_s, are exploited to derive the quantity (K/m^*)**1/2*rho_s^{-1/3}$. This quantity together with calculations employing Skyrme and Gogny interactions indicates a nuclear matter incompressibility in moderately excited nuclei that is in excellent agreement with the value determ…
For the first time primary hot isotope distributions are experimentally reconstructed in intermediate heavy ion collisions and used with antisymmetrized molecular dynamics (AMD) calculations to determine density, temperature and symmetry energy coefficient in a self-consistent manner. A kinematical focusing method is employed to reconstruct the primary hot fragment yield distributions for multifragmentation events observed in the reaction system $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon. The reconstructed yield distributions are in good agreement with the primary isotope distributions of AMD si…
ALADIN multifragmentation data show features characteristic of a critical behavior, which are very well reproduced by a bond percolation model. This suggests, in the context of the lattice gas model, that fragments are formed at nearly normal nuclear densities and temperatures corresponding to the Kertesz line. Calculations performed with a lattice gas model have shown that similarly good reproduction of the data can also be achieved at lower densities, particularly in the liquid-gas coexistence region.
The study of liquid gas phase transition in fragmentation of nuclei in heavy ion collisions has been extended to the strangeness sector using the statistical model for multifragmentation. Helmholtz's free energy, specific heat and few other thermodynamic observables have been analyzed in order to examine the occurence of phase transition in the strange matter. The bimodal behaviour of the largest cluster formed in fragmentation also strongly indicates coexistence of both the phases. The presence of hyperons strengthens the signals and also shifts the transition temperature to lower values.
The internal temperatures of fragments produced by an excited nuclear source are investigated using the microcanonical version of the Statistical Multifragmentation Model, with discrete energy. We focus on the fragments' properties at the breakup stage, before they have time to deexcite by particle emission. Since the adopted model provides the excitation energy distribution of these primordial fragments, it allows one to calculate the temperatures of different isotope families and infer on the sensitivity to their isospin composition. It is found that, due to the functional form of the nuclea…
