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The study of heavy-ion collisions in the Fermi energy domain (20 MeV/nucleon < E/A < 100 MeV/nucleon) is a fundamental research topic in modern nuclear physics. In the case of semi-peripheral collisions, the Fermi energy regime is characterized by the formation of a transient, neck-like structure that connects a projectile-like fragment (PLF) with a target-like fragment (TLF). The neck structure represents a precursor of the fireball which is a typical overlap of participating nucleons at relativistic energies (E/A> 200 MeV/nucleon). It undergoes an expansion phase in a short time scale of the order of 100 fm/c with the formation of a low-density region of nuclear matter, therefore favoring the clusterization of intermediate mass fragments (IMFs) of atomic number Z (typically) less than 20. Particular emphasis is given to some relevant results obtained by the CHIMERA collaboration in the last decade, regarding the time scale of the production mechanisms of the intermediate mass fragments in neck fragmentation and their neutron enrichment.

In this review article, we first briefly introduce the transport theory and quantum molecular dynamics model applied in the study of the heavy ion collisions from low to intermediate energies. The developments of improved quantum molecular dynamics model (ImQMD) and ultra-relativistic quantum molecular dynamics model (UrQMD), are reviewed. The reaction mechanism and phenomena related to the fusion, multinucleon transfer, fragmentation, collective flow and particle production are reviewed and discussed within the framework of the two models. The constraints on the isospin asymmetric nuclear equation of state and in-medium nucleon-nucleon cross sections by comparing the heavy ion collision data with transport models calculations in last decades are also discussed, and the uncertainties of these constraints are analyzed as well. Finally, we discuss the future direction of the development of the transport models for improving the understanding of the reaction mechanism, the descriptions of various observables, the constraint on the nuclear equation of state, as well as for the constraint on in-medium nucleon-nucleon cross sections. [ABSTRACT FROM AUTHOR]

Abstract This review article takes stock of the progress made in understanding the phase transition in hot nuclei and highlights the coherence of observed signatures. [ABSTRACT FROM AUTHOR]

We have recently observed, both experimentally and computationally, the phenomenon of postcollision multifragmentation in sub-keV surface collisions of a C 60 projectile. Namely, delayed multiparticle breakup of a strongly impact deformed and vibrationally excited large cluster collider into several large fragments, after leaving the surface. Molecular dynamics simulations with extensive statistics revealed a nearly simultaneous event, within a sub-psec time window. Here we study, computationally, additional essential aspects of this new delayed collisional fragmentation which were not addressed before. Specifically, we study here the delayed (binary) fission channel for different impact energies both by calculating mass distributions over all fission events and by calculating and analyzing lifetime distributions of the scattered projectile. We observe an asymmetric fission resulting in a most probable fission channel and we find an activated exponential (statistical) decay. Finally, we also calculate and discuss the fragment mass distribution in (triple) multifragmentation over different time windows, in terms of most abundant fragments. [ABSTRACT FROM AUTHOR]

We probe the density-dependent behavior of symmetry energy using the yield of various fragments in central collisions of various isotopic and isobaric colliding pairs. We calculate the yields of free nucleons, light charged particles and intermediate mass fragments in neutron-rich colliding systems as well as the ratio of relative yields of above fragments and free nucleons. Our findings reveal that the ratio of relative yield of light charged particles poses better candidate to probe the density dependence of nuclear symmetry energy. [ABSTRACT FROM AUTHOR]

Existence of strangelets in cosmic rays has been predicted even at mountain altitudes ~3-4km with extremely low abundance. We exposed an appropriate passive detector to cosmic rays at Darjeeling, India, at an atmospheric pressure of 765 hPa, as a pilot study to determine its suitability for the detection of strangelets in a large area detector array through long-term exposure. During the analysis we found a highly unusual event consisting of a cluster of six identical nuclear tracks. We argue that even the most mundane explanation of this event requires unusual physics, the first possible observation of multifragmentation involving cosmic rays. [ABSTRACT FROM AUTHOR]

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of the largest cluster at different Z, differential charge distribution and cross-section of neutron-rich nuclei of different projectile fragmentation reactions at different energies are described. Application of nuclear multifragmentation reaction in basic research as well as in other domains is outlined. [ABSTRACT FROM AUTHOR]

Abstract: With the aid of our recent experiment, the fragmentation of 56Fe at 471 A MeV interacting with C and Al targets has been systematically studied by the improved quantum molecular dynamics model together with the statistical GEMINI model. The fragment distributions in heavy-ion collisions at intermediate energies can be well reproduced by using this combination of the two models. It is found that the odd–even effect of the partial cross sections observed in experiments appears in the de-excitation process of the excited primary fragments as a result of pairing effect and is mainly formed in the grazing collisions. The peaked angular distributions of primary ions and their fragments are dominantly due to the heavier fragments produced in the grazing collisions and reveal the nonequilibrium property of collisions and the memory effects of outgoing fragments on the entrance channel. [Copyright &y& Elsevier]

Abstract: The investigation of the isospin dependence of multifragmentation reactions relies on precise reconstruction of the fragmenting source. The criteria used to assign free emitted neutrons, detected with the TAMU Neutron Ball, to the quasi-projectile source are investigated in the framework of two different simulation codes. Overall and source-specific detection efficiencies for multifragmentation events are found to be model independent. The equivalence of the two different methods used to assign experimentally detected charged particles and neutrons to the emitting source is shown. The method used experimentally to determine quasi-projectile emitted free neutron multiplicity is found to be reasonably accurate and sufficiently precise as to allow for the study of well-defined quasi-projectile sources. Experimental QP neutron multiplicity distributions for three similar reactions with different isospin content are also presented. An increase in neutron emission is found for more n-rich systems. [Copyright &y& Elsevier]

To understand the role of isospin effects on fragmentation due to the collisions of charge asymmetric nuclei, we have performed a complete systematical study using isospin-dependent quantum molecular dynamics model. Here simulations have been carried out for $^{124}{\rm X}_{n}+^{124}{\rm X}_{n}$, where n varies from 47 to 59 and for $^{40}{\rm Y}_{m}+^{40}{\rm Y}_{m}$, where m varies from 14 to 23. Our study shows that isospin-dependent cross-section shows its influence on fragmentation in the collision of neutron-rich nuclei. [ABSTRACT FROM AUTHOR]

The effect of neutron enrichment of the neck formed during reseparation of two colliding nuclei was studied with the aim to infer an information on the density dependence of the asymmetry energy term in the equation of state. By using a version of the QMD model of Łukasik it is shown that the neutrons-to-protons ratio of the intermediate mass fragments (IMF) emitted from the neck, 〈N/Z〉, is not a sufficiently sensitive observable to discriminate between different assumptions regarding the symmetry term of the equation of state. As an alternative, isotopic ratios of selected pairs of isotopes turned out to be useful observables more sensitive to the assumed form of the symmetry term of the equation of state. A comparison with experimental data on isotopic ratios for beryllium and boron IMFs from the 124Sn + 64Ni reaction at 35 MeV/nucleon tentatively suggests that the ASY-SOFT option of the symmetry energy term in EOS is preferred. [ABSTRACT FROM AUTHOR]

The role of momentum correlations in the production of light and medium mass fragments is studied by imposing momentum cut in the clusterization of the phase space. Our detailed investigation shows that momentum cut has a major role to play in the emission of fragments. A comparison with the experimental data is also presented. The calculations showed better agreement with the experimental data when momentum cut is imposed. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the fragmentation of colliding nuclei around the energy of vanishing flow (EVF) and evaluated its mass dependence throughout the periodic table using isospin-dependent quantum molecular dynamic model. The free nucleons, light mass fragments (LMFs) are emitted from the participant source that scales with the size of the emitting source while medium mass fragments (MMFs) and intermediate mass fragments (IMFs) come from the spectator part showing well known universality in the multiplicity. No particular fragment structure found at the energy of vanishing flow. [Copyright &y& Elsevier]

The characteristics of fragment emission in peripheral Au+Au collisions 35 MeV/A are studied using the two clusterization approaches within framework of quantum molecular dynamics model. Our model calculations using minimum spanning tree (MST) algorithm and advanced clusterization method namely simulated annealing clusterization algorithm (SACA) showed that fragment structure can be realized at an earlier time when spectators contribute significantly toward the fragment production even at such a low incident energy. Comparison of model predictions with experimental data reveals that SACA method can nicely reproduce the fragment charge yields and mean charge of the heaviest fragment. This reflects suitability of SACA method over conventional clusterization techniques to investigate spectator matter fragmentation in low energy domain. [ABSTRACT FROM AUTHOR]

Abstract: We have investigated the multifragmentation event of sub-keV impacting a gold surface using kinetic energy measurements of both positively and negatively charged outgoing fragments and molecular dynamics simulations. We have found that the energy losses are practically independent of fragment charge and that all emitted ions, irrespective of mass and charge, have the same peak velocity. These observations establish the validity of the precursor mediated multifragmentation model, previously demonstrated only for outgoing negative ions, also for the formation of positive fragment ions. The actual disintegration of the superhot precursor and resulting formation of the fragment ion occurs “post-collision” after leaving the surface. Molecular dynamics simulations carried out using the relevant experimental parameters provide further insight into the microscopic dynamics of the process and nature of the superhot precursor. [Copyright &y& Elsevier]

Abstract: We demonstrate the role of the mass asymmetry in the energy of vanishing flow by studying asymmetric reactions throughout the periodic table and over entire colliding geometry. Our results, which are almost independent of the system size and as well as of the colliding geometries indicate a sizable effect of the asymmetry of the reaction on the energy of vanishing flow. [Copyright &y& Elsevier]

Abstract: The projectile fragmentation reactions using 58Ni and 64Ni beams at 140 MeV/n on targets 9Be and 181Ta are studied using the canonical thermodynamical model coupled with an evaporation code. The isoscaling property of the fragments produced is studied using both the primary and the secondary fragments and it is observed that the secondary fragments also respect isoscaling though the isoscaling parameters α and β changes. The temperature needed to reproduce experimental data with the secondary fragments is less than that needed with the primary ones. The canonical model coupled with the evaporation code successfully explains the experimental data for isoscaling for the projectile fragmentation reactions. [ABSTRACT FROM AUTHOR]

Abstract: The entropy production in medium energy heavy-ion collisions is analyzed in terms of ratio of deuteronlike to protonlike clusters () using quantum molecular dynamics (QMD) model. The yield ratios of deuteronlike-to-protonlike clusters calculated as a function of participant proton multiplicity closely agree with experimental trends. Our model predictions indicate that full thermodynamical equilibrium may not be there even for the central geometry. The apparent entropy extracted from the yield ratios of deuteronlike-to-protonlike clusters, however, reflects the universality characteristics i.e. it is governed by the volume of reaction independent of the target-projectile combination. Our calculations for apparent entropy produced in central collisions of Ca+Ca and Nb+Nb at different bombarding energies are in good agreement with 4π Plastic Ball data. [ABSTRACT FROM AUTHOR]

Abstract: We formulate a statistical approach for description of nuclear composition and equation of state of stellar matter at subnuclear densities and temperature up to 20 MeV, which are expected during the collapse and explosion of massive stars. The model includes nuclear, electromagnetic and weak reactions between all constituents of matter, under condition of statistical equilibrium. We construct a realistic ensemble of nuclear species, and demonstrate the differences from the models employing a single-nucleus approximation for heavy nuclei. Thermodynamical characteristics, isentropic trajectories, EOS, and nuclear composition of supernova matter are calculated for different values of the lepton fraction. Special attention is paid to a possible in-medium reduction of the nuclear symmetry energy, as suggested by nuclear multifragmentation experiments. We demonstrate that this effect may lead to significant modifications of the nuclear composition and electron capture rates, which are important for stellar dynamics and nucleosynthesis. [Copyright &y& Elsevier]

The relative velocity correlation function of pairs of intermediate mass fragments has been studied for d+Au collisions at 4.4 GeV. Experimental correlation functions are compared to that obtained by multibody Coulomb trajectory calculations under the assumption of various decay times of the fragmenting system. The combined approach with the empirically modified intranuclear cascade code followed by the statistical multifragmentation model was used to generate the starting conditions for these calculations. The fragment emission time is found to be less than 40 fm/c. [ABSTRACT FROM AUTHOR]

We aim to understand the role of NN cross-sections, equation of state as well as different model ingredients such as width of Gaussian, clusterization range and different clusterization algorithms in multifragmentation using quantum molecular dynamics model. We notice that all model ingredients have sizable effect on the fragment pattern. [ABSTRACT FROM AUTHOR]

Abstract: The time-scale for emission of three fragments (Z ≥8) in the 12.7GeV 4He+ 197Au reaction has been studied using a sandwich configuration of the Makrofol polycarbonate track detector. In events with different multiplicity of heavy fragments (Z >20), the differences of the correlation functions for relative angle and relative velocity between pairs of fragments have been studied in order to determine the fragment emission-time scale. A sequential decay mechanism for the excited residual nuclei was found to be consistent with experimental data. It was determined that the fragment emission-time decreased with decreasing multiplicity of heavy fragments: from 1000fm/c for events with two heavy fragments, through 300fm/c for events with one heavy fragment, to 40fm/c for events with no emission of heavy fragments. [Copyright &y& Elsevier]

Abstract: Isotopic effects in projectile fragmentation at relativistic energies have been studied with the ALADIN forward spectrometer at SIS. Stable and radioactive Sn and La beams with an incident energy of 600 MeV per nucleon have been used in order to explore a wide range of isotopic compositions. Chemical freeze-out temperatures are found to be nearly invariant with respect to the ratio of the produced spectator sources, consistent with predictions for expanded systems. Consequences for the proposed interpretation of chemical breakup temperatures as representing the limiting temperatures predicted by microscopic models are discussed. [Copyright &y& Elsevier]

The 4φ acceptance detectors make possible the observation of all charged particles and fragments produced in a single collision of relativistic nuclei. The event-by event analysis of different fluctuation measures of physical quantities is performed for light ion induced reactions at 4.5 A GeV/c. The multiplicity and transverse momentum fluctuations indicates a possible phase transition from liquid to gas in the most central collisions. [ABSTRACT FROM AUTHOR]

Abstract: The effect of the Coulomb interaction on the phase diagram of finite nuclei is studied within the Canonical Thermodynamic Model. If Coulomb effects are artificially switched off, this model shows a phenomenology consistent with the liquid–gas phase transition. The inclusion of Coulomb does not significantly affect the phase diagram but it drastically modifies the nature and order parameter of the transition. A clear understanding of the phenomenon can be achieved looking at the distribution of the largest fragment produced in each fragmentation event. Possible connections with experimental observations are outlined. [Copyright &y& Elsevier]

Abstract: The isoscaling parameter usually denoted by α depends upon both the symmetry energy coefficient and the isotopic contents of the dissociating systems. We compute α in theoretical models: first in a simple mean field model and then in thermodynamic models using both grand canonical and canonical ensembles. For finite systems the canonical ensemble is much more appropriate. The model values of α are compared with a much used standard formula. Next we turn to cases where in experiments, there are significant deviations from isoscaling. We show that in such cases, although the grand canonical model fails, the canonical model is capable of explaining the data. [Copyright &y& Elsevier]

Abstract: This review article is focused on the tremendous progress realized during the last fifteen years in the understanding of multifragmentation and its relationship to the liquid–gas phase diagram of nuclei and nuclear matter. The explosion of the whole nucleus, early predicted by Bohr [N. Bohr, Nature 137 (1936) 351], is a very complex and rich subject which continues to fascinate nuclear physicists as well as theoreticians who extend the thermodynamics of phase transitions to finite systems. [Copyright &y& Elsevier]

Abstract: We analyzed the 93Nb on natMg reaction at 30 MeV/nucleon in the aim of disentangling binary sequential decay and multifragmentation decay close to the energy threshold, i.e. ≃3 MeV/nucleon. Using the backtracing technique applied to the statistical models GEMINI and SMM we reconstruct simulated charge, mass and excitation energy distributions and compare them to the experimental ones. We show that data are better described by SMM than by GEMINI in agreement with the fact that multifragmentation is responsible for fragment production at excitation energies around 3 MeV/nucleon. [Copyright &y& Elsevier]