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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]

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]

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 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]

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]

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]

Based on an expanding matter model using Lennard-Jones potential, the instability of the system is examined. The instantaneous pressure, temperature and density fluctuation are calculated as a function of the density. The system undergoes the first order phase transition when the expanding velocity is slow. Although the system behaves dynamically for faster expansion, a kind of criticality seems to play an important role even in this case. [ABSTRACT FROM AUTHOR]

Nuclei colliding at energies in the MeV’s break into fragments in a process that resembles a liquid-to-gas phase transition of the excited nuclear matter. If this is the case, phase changes occurring near the critical point should yield a “droplet” mass distribution of the form ≈ A −T, with T (a critical exponent universal to many processes) within 2≤ T≤3. This critical phenomenon, however, can be obscured by the finiteness in space of the nuclei and in time of the reaction. With this in mind, this work studies the possibility of having critical phenomena in small “static” systems (using percolation of cubic and spherical grids), and on small “dynamic” systems (using molecular dynamics simulations of nuclear collisions in two and three dimensions). This is done investigating the mass distributions produced by these models and extracting values of critical exponents. The specific conclusion is that the obtained values of T are within the range expected for critical phenomena, i.e. around 2.3, and the grand conclusion is that phase changes and critical phenomena appear to be possible in small and fast breaking systems, such as in collisions between heavy ions. [ABSTRACT FROM AUTHOR]

We study the multifragmentation phenomenon in heavy-ion collisions by varying the spatial constraint criterion in minimum spanning tree (MST) clusterisation procedure. Within the framework of isospin-dependent quantum molecular dynamics (IQMD) model, the role of isospin-dependent spatial constraint, i.e. iso-MST version, is investigated on different fragment observables in various isobaric pair of reaction systems varying in the entrance channel isospin (N / Z) content. The fragment observables such as persistence, gain, average yield of free nucleons, light and intermediate mass fragments are slightly sensitive to the isospin-dependent spatial constraint criterion particularly in heavier reaction systems. For a given isobaric pair of reaction systems, the fragment production, however, remains indifferent to isospin content of the colliding nuclei. [ABSTRACT FROM AUTHOR]