Statistical Multifragmentation Model Research Articles

Nucleation of baryons in relativistic hadron-nucleus collisions

We suggest a new theoretical method to describe the baryon clusterization of nuclei in hadron-nucleus reactions. As an example we have explored the nuclei production in π−+C and π−+W collisions at plab=1.7 GeV by using the hybrid approach consisting of the Ultra Relativistic Quantum Dynamics Model (UrQMD) and the Statistical Multifragmentation Model (SMM). The UrQMD describes the production of new baryons, and the propagation toward the subnuclear densities with the fluctuations leading to the formation of excited baryonic clusters. The SMM describes the production of final nuclei and hypernuclei after interaction of baryons inside these clusters. We demonstrate the transverse momenta, rapidity, mass distributions and excitation energies of both primary clusters and final nuclei (including hypernuclei). The results of the UrQMD and UrQMD+SMM model calculations for different clusterization parameters are compared with the available HADES experimental data on baryon production, providing a very promising window for future research on nuclei and hypernuclei formation in these reactions.

Probing nuclear equation of state with the cdm3y version of B3y-fetal effective interaction

This paper is a study of the nuclear Equation of State (EOS) of cold nuclear matter with the B3Y-Fetal effective interaction in its CDM3Y density-dependent version within the framework of Hartree-Fock approximation. The well-known saturation properties of both symmetric and asymmetric nuclear matter are well-reproduced in this work. Using the CDM3Y-K approach, this study has evolved a new set of user interactions, some of which are CDB3Y1-, CDB3Y2-, CDB3Y3-, CDB3Y4-, CDB3Y5-, CDB3Y6-Fetal interactions with corresponding incompressibilities K0 = 188, 204, 217,228, 241 and 252 MeV respectively, in excellent agreement with those of the M3Y-Paris and M3Y-Reid effective interactions. For asymmetric nuclear matter, the new set of interactions has produced the symmetry energy Esym = 32.00 MeV with an associated slope parameter L = 55 MeV at a saturation density ρ = 0.17fm−3 and asymmetry parameter δ = 1.00 (pure neutron matter) in good agreement with the standard values obtained from coupled channel analysis of charge exchange reactions, statistical multifragmentation model and terrestrial Nuclear Physics experimental analyses. Furthermore, the new set of interactions has been found to have bright prospects in a nuclear reaction as the real folded potential computed with the CDB3Y6-Fetal interaction within the framework of double folding potential has been found to be good and similar to that of CDB3Y6-Paris whose optical potential has a repulsive direct component.

Isospin compositions of correlated sources in the Fermi energy domain

Isotopic yield distributions of nuclei produced in peripheral collisions of $^{80}$Kr+$^{40,48}$Ca at 35 MeV/nucleon are studied. Experimental results obtained by the FAZIA Collaboration at the LNS facility in Catania are compared with calculations performed with the statistical multifragmentation model (SMM). The fragments with atomic number $Z=19-24$ observed at forward angles are successfully described with the ensemble method previously established for reactions at higher energy. Using the SMM results, the isotopic compositions of the projectile residues are reconstructed. The results indicate a significant isospin exchange between the projectile and target nuclei, not far from isospin equilibrium, during the initial phase of the reaction. The two groups of light fragments with $Z=1-4$, experimentally distinguished by their velocities relative to coincident heavy projectile fragments, are found to originate from different sources. The isotopic composition of the slower group is consistent with emission from a low-density neck, enriched in neutrons, and satisfactorily reproduced with SMM calculations for a corresponding neck source of small mass.

Statistical Multifragmentation Model within the Extended Morphological Thermodynamics Approach

On the basis of the morphological thermodynamics, we develop an exactly solvable version of the statistical multifragmentation model for the nuclear liquid-gas phase transition. It is shown that the hard-core repulsion between spherical nuclei generates only the bulk (volume), surface, and curvature parts of the free energy of the nucleus, while the Gaussian curvature one does not appear in the derivation. The phase diagram of the nuclear liquid-gas phase transition is studied for a truncated version of the developed model.

Isoscaling in central Sn+Sn collisions at 270 MeV/u

Experimental information on fragment emissions is important in understanding the dynamics of nuclear collisions and in the development of transport model simulating heavy-ion collisions. The composition of complex fragments emitted in the heavy-ion collisions can be explained by statistical models, which assume that thermal equilibrium is achieved at collision energies below 100 MeV/u. Our new experimental data together with theoretical analyses for light particles from Sn+Sn collisions at 270 MeV/u, suggest that the hypothesis of thermal equilibrium breaks down for particles emitted with high transfer momentum. To inspect the system's properties in such limit, the scaling features of the yield ratios of particles from two systems, a neutron-rich system of ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and a nearly symmetric system of ${}^{108}\mathrm{Sn}+{}^{112}\mathrm{Sn}$, are examined in the framework of the statistical multifragmentation model and the antisymmetrized molecular dynamics model. The isoscaling from low energy particles agree with both models. However the observed breakdown of isoscaling for particles with high transverse momentum cannot be explained by the antisymmetrized molecular dynamics model.

Constraints from isoscaling on the source size in energetic heavy ion collisions

In the framework of the statistical multifragmentation model, the nuclear isoscaling analysis is extended to constrain the ratio between the sizes of the decaying sources formed in a collision between two heavy ions. It is found that the ratio between the probabilities of observing $n$ fragments in each event, for each of the sources, follows a scaling law, similar to the traditional nuclear isoscaling. However, the corresponding slope is sensitive to the source sizes. This property is explained analytically using the grand-canonical ensemble. The extent to which our findings are affected by finite size effects and by the deexcitation of the hot primary fragments is investigated. The scaling turns out to be robust and weakly affected by effects implied by these two aspects. We also find that the Poisson distribution is a fairly good approximation to the above mentioned probabilities, associated with both the primordial fragments, produced at the breakup stage, and the final ones, found at the end of the fragment deexcitation process.

Dissipation of energy and higher-order fluctuations of the largest fragment charge in projectile fragmentation

Abstract The higher-order fluctuations of the largest fragment charge were found to exhibit the signatures of a second-order phase transition in experimental data and simulations of the statistical multifragmentation model recently (Pietrzak et al 2020 Phys. Lett. B 809 135763). This work is devoted to study the dissipation of energy and higher-order fluctuations of the largest fragment charge in projectile fragmentation. The isospin-dependent quantum molecular dynamics (IQMD) model is used to study the non-equilibrium thermalization and fragmentation. The statistical code GEMINI is applied to simulate the second decay of the pre-fragments. To reveal how the incident energy dissipates into the excitation energy of the projectile-like system, the time evolution of the density, collective velocity, and random kinetic energy are displayed. It is found that the competition between the heat conduction and heat flux affects the excitation energy of the projectile-like system, which is the key variable in the fragmenting process. Displaying the mean multiplicity of the intermediate mass fragments and the higher-order fluctuations of the largest fragment charge, it is found that the decay mechanism of the projectile-like system transfers from the multi-fragmentation at mid-peripheral collision into the nucleon-evaporation at peripheral collision. The pseudo-critical point of this transition can be indicated by the zero of third order fluctuation together with the minimum of fourth order fluctuation. The calculations of the pseudo-critical point by the IQMD + GEMINI model agree with that extracted from the experimental data. Finally, the influences of the pseudo-critical point by the second decay, the mass number of the colliding system, and the incident energy are studied.

Fisyon ve Buharlaşma ile Üretilen Hiperçekirdeklerin Analizi

In heavy-ion reactions, nuclei and hypernuclei yields can be emitted from target/projectile redisuals in peripheral collisions. The evaporation and fission yields are investigated at 0.25-2.5 MeV/nucleon excitation energy intervals for source nuclei 235U, 235_Lambda_U, 235_2Lambda_U, 235_3Lambda_U, 235_4Lambda_U, 168Ho, 168_Lambda_Ho, 168_2Lambda_Ho, 168_3Lambda_Ho ve 168_4Lambda_Ho. We have reproduced mass distributions via computer codes by using hyper-SMM model which is based on the statistical multifragmentation model for hypernuclei. Our results can be used for the analyses of the future experiments at FAIR(GSI) and NICA(Dubna).

Investigation of the Products of Heavy Hypernuclei

Evaporation of hypernuclei is investigated similar to evaporation of normal nuclei taking place in deep-inelastic nuclear collisions. Final cold hypernuclei can be obtained in such processes and offer a new direction for investigation. This may concern the production of exotic states which can exist due to the presence of a hyperon. It will be difficult to obtain such exotic states in other reactions since there are practical limitations on the use of radioactive targets in experiments. We have investigated the evaporation mechanism of some heavy hypernuclei for emission of light hypernuclei which take place from the target and projectile residues. Theoretical calculations are carried out by using computer codes developed for the statistical multifragmentation model generalized to hypernuclei.

Has the neutral double hypernucleus been observed?

The BNL-AGS E906 experiment was the first fully electronic experiment to produce and study double hypernuclei with large statistics. Unfortunately, the interpretation of the measured π−−π− momentum correlation is still blurry because the hypothesized production of pairs remains questionable. We show, that neither a scenario where the hypernuclei are produced after the capture of a stopped Ξ− by a 9Be nucleus nor interactions of energetic Ξ− with 9 Be nuclei in the target material can produce a sufficient amount of such pairs. We have therefore explored the conjecture that decays of themay be responsible for the observed structure. Indeed, the inclusion of with a two-body π− branching ratio of 50% in the statistical multifragmentation model allows to describe the E906 data remarkably well.

Bose–Einstein Condensation as a Deposition Phase Transition of Quantum Hard Spheres and New Relations between Bosonic and Fermionic Pressures

We investigate the phase transition of Bose–Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose–Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent тF = 5/2 , which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the system of classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi–Dirac particles in terms of pressures of Bose–Einstein particles of two sorts.

Isobar correlations bearing information on the properties of hot disassembling nuclear sources

Two-particle correlations based on the multiplicity of selected isobars are found to be sensitive to the parameterization of the fragments' binding energies and the breakup volume assumed in the model calculations. The properties of these correlations have been examined in the framework of the Statistical Multifragmentation Model as a function of the breakup temperature. The model calculations suggest that the maxima of these correlation functions occur at well separated temperatures as the breakup volumes used in the model vary from 3 to 6 times that at normal density. These volumes are within the range assumed in most statistical calculations and supported by experiments. Besides their position, the height and width of the maxima are also found to be sensitive to the parameterization of the fragments' binding energy. The magnitude of all these effects also depends on the isobars considered in the correlations. We found that, due to an interplay between the symmetry energy and the volume dependent terms of the Helmholtz free energy, in the case of nearly symmetric sources, correlations involving light mirror nuclei seem to enhance these effects. We suggest that the proposed correlation functions could be used to extract information on the fragments' energies and on the breakup volume of nuclear sources.

The percolation phase transition and statistical multifragmentation in finite systems

The cumulant ratios up to fourth order of the Z distributions of the largest fragment in spectator fragmentation following 107,124Sn+Sn and 124La+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 197Au 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 the corresponding chemical freeze-out temperatures of close to 6 MeV.The experimental cumulant distributions are quantitatively reproduced with the Statistical Multifragmentation Model and parameters used to describe the experimental fragment multiplicities, isotope distributions and their correlations with impact-parameter related observables in these reactions. The characteristic coincidence of the zero transition of the skewness with the minimum of the kurtosis excess appears to be a generic property of statistical models and is found to coincide with the maximum of the heat capacity in the canonical thermodynamic fragmentation model.

Evaluation of hypernuclei in relativistic ion collisions

In this paper, we present the results of the transport, coalescence and statistical model calculations to describe the production of hypernuclei and study their properties in relativistic nucleus-nucleus collisions. Such hypernuclei and low-temperature hypermatter can be produced as a result of hyperon capture by nuclear residues and free nucleons. The dynamical reaction stage leading to the strangeness production is described within the transport cascade and UrQMD models. Large excited hypernuclear species can be formed from target and projectile residues in peripheral collisions. To describe its following evolution at high excitation energies we have generalized the statistical multifragmentation model (SMM) on hypernuclei, as well as the evaporation, fission and Fermi-break-up models at low energies. We calculated the yields, the mass with isotopic distributions of produced nuclei and hypernuclei, and found important regularities and correlations. We have also established how the binding energies of hypernuclei can be evaluated via the comparison of isotope yields. Our approach can be used also for multistrange nuclei. We have extended the coalescence model for the formation of excited hyperclusters from individual baryons in the central collisions. De-excitation of hot coalescence clusters presents a novel mechanism for the hypernuclei production and shows new possibilities for their investigation.

On the survey of nuclei and hypernuclei in multifragmentation

Multifragmentation reactions are dominating processes for the decomposition of highly excited nuclei leading to the fragment production in heavy-ion collisions. In high energy reactions strange particles are abundantly produced. We present a novel development of the Statistical multifragmentation model (SMM), namely, its generalization for the hyper-matter which is formed after the hyperon capture. This way, it is possible to describe its disintegration into normal and hyper-nuclei. Some properties of hyper-nuclei and their binding energies can be determined from the comparison of the isotope yields. The main focus of this method is to investigate strange and multi-strange hypernuclei since their properties are not easy to measure in traditional hyper-nuclei experiments.

Probing the neutron-proton asymmetry dependence of the nuclear source temperature with light charged particles

The dependence of the nuclear temperature on the source neutron-proton ($N/Z$) asymmetry has been experimentally investigated with the light charged particles (LCPs) generated from 13 reaction systems with different $N/Z$ asymmetries, $^{64}\mathrm{Zn}$ on $^{112}\mathrm{Sn}$, and $^{70}\mathrm{Zn}$, $^{64}\mathrm{Ni}$ on $^{112,124}\mathrm{Sn}$, $^{58,64}\mathrm{Ni}$, $^{197}\mathrm{Au}$, and $^{232}\mathrm{Th}$ at 40 MeV/u. A rather weak $N/Z$ asymmetry dependence of the source temperature has been qualitatively inferred from the extracted $N/Z$ asymmetry dependence of the apparent temperature and that of the relative temperature change by the sequential decay effects with the help of the theoretical simulations. Comparing the present result with those from our previous work and other available experimental results, a weak $N/Z$ asymmetry dependence of nuclear temperature is commonly observed in different independent experiments and with different thermometers, except for the result reported by McIntosh et al. [Phys. Lett. B 719, 337 (2013)]. The origin of the difference between the conclusion of the former group and that of McIntosh et al. is addressed, using statistical multifragmentation model (SMM) simulations.

Monte-Carlo Generator of Heavy Ion Collisions DCM-SMM

The new monte-carlo generator of heavy ion collisions, DCM-SMM, based on Dubna Cascade Model (DCM-QGSM) and Statistical Multifragmentation Model (SMM) is described. The model aimed to generate particle--nucleus and nucleus--nucleus collisions at a wide range of energy was created to provide the computer simulation support to new experimental facilities BMN and MPD at the accelerator complex NICA. It can simulate the production of both light particles and nuclear fragments and hyperfragments on the event by event basis.

Isoscaling of mass A ≃ 40 reconstructed quasiprojectiles from collisions in the Fermi energy regime

Isoscaling studies of fragments with Z=1-8 from reconstructed quasiprojectiles of mass A ≃40 from the 40Ca + 112,124Sn and 40Ar + 112,124Sn reactions at beam energy of 45 MeV/nucleon were performed. After initial efforts to obtain isoscaling using pairs of systems differing in their neutron-to-proton ratio N/Z, “intra-system” isoscaling for each of these four systems was obtained using fragment sources restricted in two narrow N/Z zones, one neutron rich and one neutron poor. The observed isoscaling behaviour was excellent and the isoscaling parameter α was found to decrease as the excitation energy increases. Corrections due to undetected neutrons were also taken into account in the source N/Z determination by using the theoretical models DIT (Deep Inelastic Transfer) and SMM (Statistical Multifragmentation Model) along with a software replica of the experimental setup. The reduced isoscaling parameter α/∆ was found to decrease as the excitation energy of the quasiprojectile source increases, in good agreement with recent work on reconstructed mass A ≃ 80 quasiprojectiles. This decrease of α/∆ may point to a decrease of the symmetry energy coefficient with increasing excitation energy.

Post breakup dynamical evolution of fragments produced in nuclear multifragmentation

The deexcitation of the primary hot fragments, produced in the breakup of an excited nuclear source, during their propagation under the influence of their mutual Coulomb repulsion is studied in the framework of a recently developed hybrid model. The latter is based on the Statistical Multifragmentation Model (SMM), describing the prompt breakup of the source, whereas the particle emission from the hot fragments, that decay while traveling away from each other, is treated by the Weisskopf-Ewing evaporation model. Since this treatment provides an event by event description of the process, in which the classical trajectories of the fragments are followed using molecular dynamics techniques, it allows one to study observables such as two-particle correlations and infer the extent to which the corresponding observables may provide information on the multifragment production mechanisms. Our results suggest that the framework on which these treatments are based may be considerably constrained by such analyses. They imply that information obtained from these model calculations may provide feedback to the theory of nuclear interferometry. In particular, our results do not support the hypothesis that the total momentum of the selected pair of particles used in the two-particle correlations remains constant during the post-breakup dynamics. Furthermore, the correlations may be appreciably affected by this fact. We also found that neutron deficient fragments should hold information more closely related to the breakup region than neutron rich ones, as they are produced in much earlier stages of the post breakup dynamics than the latter.

Solidarity of signal of measures for the liquid-gas phase transition in the statistical multifragmentation model

A systematic study of system size, $N/Z$ asymmetry, and fragmenting volume effects as well as the Coulomb effect on experimental measures for the nuclear liquid-gas phase transition and the mechanism of phase transition are carried out in the framework of the statistical multifragmentation model (SMM). The measures examined here are the caloric curve, the specific heat capacity (${C}_{v}$), the multiplicity derivative ($dM/dT$), the moment parameters (${M}_{2}$ and ${\ensuremath{\gamma}}_{2}$), the fluctuation of maximum fragment charge number (NVZ), the Fisher exponent ($\ensuremath{\tau}$), and the Zipf's law parameter ($\ensuremath{\xi}$). A signal for the first-order phase transition for all the measures is observed. A stronger signal is observed in the system with smaller sizes or with more neutron rich or in smaller fragmenting volumes for the caloric curve, ${C}_{v}$, and $dM/dT$. The phase-transition temperatures are independent of the system size, $N/Z$ asymmetry, fragmenting volume, and Coulomb force, which indicates these measures give a solid signal for the liquid-gas phase transition in SMM. On the other hand, the phase transition temperature and its behavior of the others slightly depend on the size, the $N/Z$ asymmetry and the volume of the system. A negative heat capacity is observed for systems with ${A}_{s}\ensuremath{\ge}$ 100 without the Coulomb force but disappears with the Coulomb. An instructive picture is given in the charge distributions for the observed first-order phase transition.