Simulated Annealing Clusterization Algorithm Research Articles

Role of equation of state and clusterization algorithms on nuclear vaporization

By using the Quantum Molecular Dynamics (QMD) model, a study on the nuclear vaporization in [Formula: see text] collision is presented for different nuclear equations of state along with a systematic comparison of different clusterization methods based on simple spatial correlations, spatial-momentum correlations, mass dependent binding energy cuts and Simulated Annealing Clusterization Algorithm (SACA). The effect of different nuclear equations of state i.e., Soft, Hard and Soft with Momentum Dependent (SMD) interactions on the energy of onset of vaporization for [Formula: see text] collisions is predicted by investigating gas/liquid content and probability of vaporization versus incident energy behavior. These two observables probe the critical point of nuclear vaporization very well. Further outcome of different clusterization algorithms on the energy of onset of nuclear vaporization is also probed and a comparison of calculations with the experimental data for [Formula: see text] and [Formula: see text] collisions is carried out for different clusterization algorithms.

Probing onset of nuclear vaporisation in heavy-ion collisions

The onset of nuclear vaporisation in heavy-ion collisions is examined in the present study. For this, we perform quantum molecular dynamics (QMD) model calculations supplemented with a clusterisation algorithm for fragment identification, namely the Simulated Annealing Clusterization algorithm (SACA) approach. Our results with the very sophisticated SACA method show a good agreement with the experimental findings of vaporisation (predicted by the asymptotic behaviour of the average fragment charge) in 16O + 80Br and 16O + 107Ag collisions. Further, we predicted the energy of the onset of vaporisation for 40Ca + 40Ca, 84Kr + 84Kr, 132Xe + 132Xe and 197Au + 197Au collisions by investigating the gas/liquid content and probability of vaporisation (and its derivative) versus the incident energy behaviour. These two observables probe the critical point of nuclear vaporisation in an extremely sophisticated manner, relative to an average fragment charge. Our findings on these two novel variables to predict the energy of the onset of vaporisation is verifiable in experiments. The influence of the colliding geometry as well as the role of Coulomb interactions are also studied to understand the system size effects on nuclear vaporisation.

Fragment emission and critical behavior in light and heavy charged systems * *Supported Council of Scientific and Industrial Research (CSIR), Govt. of India (03 (1388)/16/EMR-II)

We study the emission of fragments in central collisions of light and heavily charged systems of 40Ar+45Sc and 84Kr+197Au, respectively, using the Quantum Molecular Dynamics (QMD) model as the primary model. The fragments are identified using an energy based clusterization algorithm, i.e., the Simulated Annealing Clusterization Algorithm (SACA). The charge distributions of intermediate mass fragments [3≤ ≤12] are fitted with power-law ( ) and exponential ( ) fits in order to extract the parameters τ and whose minimum values are also sometimes linked with the onset of fragmentation or the critical point for a liquid-gas phase transition. Other parameters such as the normalized second moment , , average size of the second largest cluster , phase separation parameter ( ), bimodal parameter (P), information entropy (H), and Zipf's law are also analyzed to find the exact energy of the onset of fragmentation. Our detailed analysis predicts that an energy point exists between 20-23.1 MeV/nucleon, which is very close to the experimentally observed value of 23.9 MeV/nucleon for the 40Ar+45Sc reaction. We also find that the critical energy deduced using Zipf's law is higher than those predicted from other critical exponents. Moreover, no minimum is found for τ values of the highly charged system of 84Kr+197Au, in agreement with experimental findings and various theoretical calculations. We observe that the QMD + SACA model calculations are in agreement with the experimental observations. This agreement supports our results regarding the energy point of the liquid-gas phase transition and the onset of fragmentation.

PHQMD Model for the Formation of Nuclear Clusters and Hypernuclei in Heavy Ion Collisions

Modeling of the process of the formation of nuclear clusters in the hot nuclear matter is a challenging task. We present the novel n-body dynamical transport approach - PHQMD (Parton-Hadron-Quantum-Molecular Dynamics) [1] for the description of heavy-ion collisions as well as clusters and hpernuclei formation. The PHQMD extends well established PHSD (Parton-Hadron-String Dynamics) approach - which incorporates explicit partonic degrees-of-freedom (quarks and gluons), an equation-of-state from lattice QCD, as well as dynamical hadronization and hadronic elastic and inelastic collisions in the final reaction phase, by n-body quantum molecular dynamic propagation of hadrons which allows choosing of the equation of state with different compression modulus. The formation of clusters, including hypernuclei, is realized by incorporation the Simulated Annealing Clusterization Algorithm (SACA). We present first results from PHQMD on the study of the production rates of strange hadrons, nuclear clusters and hypernuclei in e1elementary and heavy-ion collisions at NICA energies. In particular, sensitivity on the "hard" and "soft" equation of state within the PHQMD model was investigated for "bulk" observables.

Study of clusters and hypernuclei production with the NICA/MPD experiment

Heavy-ion collisions provide the unique possibility to create and investigate hot and dense matter in the laboratory. At the initial stage of the reaction a QGP is formed, while the final stage is driven by the hadronization process and the formation of clusters. The capture of the produced hyperons by clusters of nucleons leads to the hypernuclei formation which is a very rare process at strangeness threshold energies. We report on the first results on the dynamical modeling of cluster formation with the combined PHSD + SACA (Parton–Hadron–Strings dynamics + Simulated Annealing Clusterization Algorithm) model at Nuclotron and NICA energies. The clusters selection in SACA is realized by a simulated annealing procedure to obtain the most bound configuration of fragments and nucleons. Based on present predictions of the combined model we study the possibility to detect such clusters and hypernuclei in the NICA/MPD detector.

Spectator fragmentation in nucleus-nucleus collisions: Phase space approach

Dynamics of spectator matter break-up in non-central collisions of 197Au+ 197Au at 1000 MeV/A are explored within the framework of a quantum molecular dynamics (QMD) model. The phase space of nucleons bound in intermediate mass fragments are studied using two clustering subroutines. Backtracking the origin of fragments to the time of the initial contact between the colliding nuclei and applying the simulated annealing clusterization algorithm (SACA) indicates a significant yield of projectile-like and target-like fragments. The simplest clusterization approach based on the spatial correlation technique, however, predicted a much lesser production probability of fragments in the spectator zone.

Dynamical approach to spectator fragmentation in Au+Au reactions at 35 MeV/A

Abstract The characteristics of fragment emission in peripheral 197Au+197Au 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.

Study of fragmentation using clusterization algorithm with realistic binding energies

We here study fragmentation using a simulated annealing clusterization algorithm (SACA) with binding energy at a microscopic level. In an earlier version, a constant binding energy (4 MeV/nucleon) was used. We improve this binding energy criterion by calculating the binding energy of different clusters using a modified Bethe–Weizsäcker mass (BWM) formula. We also compare our calculations with experimental data of the ALADiN group. Nearly no effect of this modification is visible.

Study of fragmentation at low excitation energies within a dynamical microscopic theory

We present the theoretical study of fragmentation at low excitation energies within dynamical microscopic theory namely, simulated annealing clusterization algorithm (SACA) and quantum molecular dynamics (QMD) model. For low excitation energy reactions, we choose the balance energies for a large number of reactions throughout the periodic table. We see that SACA gives multiplicities in terms of power law. For light fragments, it is close to 1/3, whereas, for heavier fragments it is nearly mass independent suggesting their origin in terms of participant-spectator picture.

Fragment production in 16O+80Br reaction within dynamical microscopic theory

We analyze the formation of fragments in O—Br reaction at different incident energies between E/A=50 MeV and 200 MeV. This study is carried out within the quantum molecular dynamics (QMD) model coupled with recently advanced simulated annealing clusterization algorithm (SACA). For comparison, we also use the conventional minimum spanning tree (MST) method. Our detailed study shows that the SACA can detect the final stable fragment configuration as early as 60 fin/c which is marked by a dip in the heaviest fragment. On the other hand, the MST method needs several hundred fm/c to identify the final stable distribution. A comparison of the charge distribution with experimental data shows that the SACA is able to reproduce the data very nicely whereas (as reported earlier) the MST method fails to break the spectator matter into intermediate mass fragments. Furthermore, our results with SACA method indicate the onset of multi-fragmentation around 75 MeV/A which is again in good agreement with experimental findings.

Simulated Annealing Clusterization Algorithm for Studying the Multifragmentation

We here present the details of the numerical realization of the recently advanced algorithm developed to identify the fragmentation in heavy ion reactions. This new algorithm is based on the simulated annealing method and is dubbed the simulated annealing clusterization algorithm (SACA). We discuss the different parameters used in the simulated annealing method and present an economical set of the parameters which is based on the extensive analysis carried out for the central and peripheral collisions of Au-Au, Nb-Nb, and Pb-Pb. These parameters are crucial for the success of the algorithm. Our set of optimized parameters gives the same results as the most conservative choice, but is very fast. We also discuss the nucleon and fragment exchange processes which are very important for the energy minimization and finally present the analysis of the reaction dynamics using the new algorithm. This algorithm can be applied whenever one wants to identify which of a given number of constituents form bound objects.

Different nucleon-nucleon cross sections and multifragmentation

We present a systematic study of the dependence of the fragment production on the nucleon-nucleon cross section using the quantum molecular dynamics model as an event generator. We employ constant energy-dependent and in-medium cross sections. In our analysis, fragments are formed using a minimum spanning tree description. The fragment distribution with different cross sections at low energy is nearly the same. At higher energies, different nucleon-nucleon (NN) cross sections have small effects on fragment production for central collisions, whereas the fragment production is strongly influenced at semicentral and peripheral collisions. A larger NN cross section results in more intermediate mass fragments at peripheral collisions with a shift of the peak towards larger impact parameters. As a result, the rapidity distribution of fragments and the fragment flow is also affected by the choice of the cross section. This influence is reduced if fragments are constructed with a sophisticated algorithm such as the simulated annealing clusterization algorithm which searches for the most bound configuration of nucleons and fragments.