Multifragmentation Reactions Research Articles

Isospin properties of the pasta phase with an extended statistical model from microscopic energy functionals

In this work, we have developed an extended statistical model to study nuclear multifragmentation reactions at intermediate energies, and we link the associated observables to the properties of supernova matter. The canonical thermodynamical model, used for this study, is modified by including inputs from the relativistic mean-field energy functionals. Even though the length scale of the supernova matter is very large compared to that of the multifragmentation reaction, we find an isospin observable, the average $\ensuremath{\langle}Z/N\ensuremath{\rangle}$ of the fragments, which is almost independent of the size of system, and can be directly compared to the estimation of fractionation in infinite nuclear matter. The isospin ratio $\ensuremath{\langle}Z/N\ensuremath{\rangle}$ of the heaviest cluster produced in nuclear fragmentation and of the corresponding pasta structure occurring in supernova matter are significantly lower than the spinodal estimation in uncharged nuclear matter, due to the presence of lighter isospin symmetric clusters that dominate the mass fraction in full equilibrium at finite temperature. The screening effect of electrons is also studied.

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.

Isospin dependent hybrid model for studying isoscaling in heavy ion collisions around the Fermi energy domain

Investigation of observables from nuclear multifragmentation reactions depending on isospin led to the development of a hybrid model. The mass and charge distribution as well as isotopic distribution was studied using this model for 112Sn+112Sn reaction as well as 124Sn+124Sn reactions at different energies. The agreement of the results obtained from the model with those from experimental data confirms the accuracy of the model. Isoscaling coefficients were extracted from these observables which can throw light on the symmetry energy coefficient. Another important facet of this model is that temperature of the studied reaction can be directly extracted using this model.

Statistical ensembles and fragmentation of finite nuclei

Statistical models based on different ensembles are very commonly used to describe the nuclear multifragmentation reaction in heavy ion collisions at intermediate energies. Canonical model results are more appropriate for finite nuclei calculations while those obtained from the grand canonical ones are more easily calculable. A transformation relation has been worked out for converting results of finite nuclei from grand canonical to canonical and vice versa. The formula shows that, irrespective of the particle number fluctuation in the grand canonical ensemble, exact canonical results can be recovered for observables varying linearly or quadratically with the number of particles. This result is of great significance since the baryon and charge conservation constraints can make the exact canonical calculations extremely difficult in general. This concept developed in this work can be extended in future for transformation to ensembles where analytical solutions do not exist. The applicability of certain equations (isoscaling, etc.) in the regime of finite nuclei can also be tested using this transformation relation.

Nuclear thermodynamics from chiral low-momentum interactions

We investigate the thermodynamic equation of state of isospin-symmetric nuclear matter with microscopic nuclear forces derived within the framework of chiral effective field theory. Two- and three-body nuclear interactions constructed at low resolution scales form the basis for a perturbative calculation of the finite-temperature equation of state. The nuclear force models and many-body methods are benchmarked against bulk properties of isospin-symmetric nuclear matter at zero temperature, which are found to be well reproduced when chiral nuclear interactions constructed at the lowest resolution scales are employed. The calculations are then extended to finite temperatures, where we focus on the liquid-gas phase transition and the associated critical point. The Maxwell construction is applied to construct the physical equation of state, and the value of the critical temperature is determined to be T_c =17.2-19.1 MeV, in good agreement with the value extracted from multifragmentation reactions of heavy ions.

Nuclear multifragmentation: Basic concepts

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 bound, 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.

Analysis of multi-fragmentation reactions induced by relativistic heavy ions using the statistical multi-fragmentation model

The fragmentation cross-sections of relativistic energy nucleus–nucleus collisions were analyzed using the statistical multi-fragmentation model (SMM) incorporated with the Monte-Carlo radiation transport simulation code particle and heavy ion transport code system (PHITS). Comparison with the literature data showed that PHITS-SMM reproduces fragmentation cross-sections of heavy nuclei at relativistic energies better than the original PHITS by up to two orders of magnitude. It was also found that SMM does not degrade the neutron production cross-sections in heavy ion collisions or the fragmentation cross-sections of light nuclei, for which SMM has not been benchmarked. Therefore, SMM is a robust model that can supplement conventional nucleus–nucleus reaction models, enabling more accurate prediction of fragmentation cross-sections.

Nuclear Multifragmentation Time Scale and Fluctuations of the Largest Fragment Size

Distributions of the largest fragment charge, Zmax, in multifragmentation reactions around the Fermi energy can be decomposed into a sum of a Gaussian and a Gumbel distribution, whereas at much higher or lower energies one or the other distribution is asymptotically dominant. We demonstrate the same generic behavior for the largest cluster size in critical aggregation models for small systems, in or out of equilibrium, around the critical point. By analogy with the time-dependent irreversible aggregation model, we infer that Zmax distributions are characteristic of the multifragmentation time scale, which is largely determined by the onset of radial expansion in this energy range.

Temperature Measurements in Low Excitation Energy Reactions to Probe a Possible Phase Transition

Several methods have been used to determine the temperatures of systems formed in multifragmentation reactions. From these temperatures, caloric curves can be constructed and possible nuclear phase transitions can be explored. This work presents a previously observed, low temperature phase transition predicted by a theoretical simulation, and an experimental proposal to observe this transition. The proposed experiment will explore what types of reactions produce fragments near the phase transition temperature, and expand the range of fragments that can be detected in this low temperature region.

Cluster correlations in multifragmentation

The possibility of strong cluster correlations in multifragmentation reactions is explored based on the antisymmetrized molecular dynamics calculations. The number of emitted protons, which is smaller than predicted by usual transport models, can be explained by introducing the two-nucleon collision process to the final states in which one or both of the scattered nucleons may form clusters (such as deuterons, tritons and α particles) with other nucleons in the system. The cluster correlation has strong impacts on the whole collision dynamics. The multifragmentation data at 50 MeV/nucleon and above are well reproduced with this strong cluster correlation if pairs of clusters with small relative velocities are assumed to form light nuclei such as Li and Be isotopes. An analysis is shown on symmetry energy effects in emission of nucleons and clusters.

A comparative study of statistical models for nuclear equation of state of stellar matter

We compare three different statistical models for the equation of state (EOS) of stellar matter at subnuclear densities and temperatures (0.5–10 MeV) expected to occur during the collapse of massive stars and supernova explosions. The models introduce the distributions of various nuclear species in nuclear statistical equilibrium, but use somewhat different nuclear physics inputs. It is demonstrated that the basic thermodynamical quantities of stellar matter under these conditions are similar, except in the region of high densities and low temperatures. We demonstrate that mass and isotopic distributions have considerable differences related to the different assumptions of the models on properties of nuclei at these stellar conditions. Overall, the three models give similar trends, but the details reflect the uncertainties related to the modeling of medium effects, such as the temperature and density dependence of surface and bulk energies of heavy nuclei, and the nuclear shell structure effects. We discuss importance of new physics inputs for astrophysical calculations from experimental data obtained in intermediate energy heavy-ion collisions, in particular, the similarities of the conditions reached during supernova explosions and multifragmentation reactions.

Experimental determination of the quasi-projectile mass with measured neutrons

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.

Isotopic yields and symmetry energy in nuclear multifragmentation reactions

Isotopic yields of light intermediate mass fragments (Z ⩽ 8) were studied with data from the MSU experiments for central collisions of 124Sn + 124Sn and 112Sn + 112Sn at E/A = 50 MeV. Within the statistical multifragmentation model, microcanonical Markov-chain calculations were performed with the aim to reproduce experimental elemental and isotopic distributions. The effects of varying liquid-drop parameters of hot fragments formed inside the freeze-out volume on charge and isotopic distributions are demonstrated. It is seen that the isotopic distributions of these fragments are very sensitive to the variation of the symmetry energy of fragments. Comparing our results with the experimental data, it is seen that a significant reduction of the symmetry term coefficient leads to better reproduction of the isotopic distributions. Comparison with other statistical calculations has been made. This is in agreement with previous conclusions obtained from the interpretation of both central and peripheral heavy ion collisions.

Fragmentation paths in dynamical models

We undertake a quantitative comparison of multi-fragmentation reactions, as modeled by two different approaches: the Antisymmetrized Molecular Dynamics (AMD) and the momentum-dependent stochastic mean-field (SMF) model. Fragment observables and pre-equilibrium (nucleon and light cluster) emission are analyzed, in connection to the underlying compression-expansion dynamics in each model. Considering reactions between neutron-rich systems, observables related to the isotopic properties of emitted particles and fragments are also discussed, as a function of the parametrization employed for the isovector part of the nuclear interaction. We find that the reaction path, particularly the mechanism of fragmentation, is different in the two models and reflects on some properties of the reaction products, including their isospin content. This should be taken into account in the study of the density dependence of the symmetry energy from such collisions.

Isobaric yield ratios and the symmetry energy in heavy-ion reactions near the Fermi energy

The relative isobaric yields of fragments produced in a series of heavy-ion-induced multifragmentation reactions have been analyzed in the framework of a modified Fisher model, primarily to determine the ratio of the symmetry energy coefficient to the temperature, ${a}_{\mathrm{sym}}/T$, as a function of fragment mass $A$. The extracted values increase from 5 to $~$16 as $A$ increases from 9 to 37. These values have been compared to the results of calculations using the antisymmetrized molecular dynamics (AMD) model together with the statistical decay code gemini. The calculated ratios are in good agreement with those extracted from the experiment. In contrast, the values extracted from the ratios of the primary isobars from the AMD model calculation are $~$4 to 5 and show little variation with $A$. This observation indicates that the value of the symmetry energy coefficient derived from final fragment observables may be significantly different than the actual value at the time of fragment formation. The experimentally observed pairing effect is also studied within the same simulations. The Coulomb coefficient is also discussed.

Relevance of equilibrium in multifragmentation

Relavence of equilibrium in a multifragmentation reaction is studied by simulating both reaction and equilibrium systems with the antisymmetrized molecular dynamics. Fragment observables in reaction is well explained by an equilibrium assumption, though there are other observables which do not agree between reaction and equilibrium.

Symmetry energy and the isoscaling in reactions on enriched tin isotopes

The coefficients of symmetry energy term for fragments with Z=4,11,12 measured in multifragmentation reactions initiated by proton and deuteron with energy of 3.65A GeV on enriched tin isotopes 112,118,120,124Sn are determined. The dependence of isoscaling parameter on the excitation energy, the temperature of fragmenting systems and the density ratio for heavy mass products are analised.

Towards the equation of state for dense stellar matter

The thermal nuclear multifragmentation reaction can be used to investigate the nuclear liquid-gas phase coexistence region and its relation to the astrophysical processes such as the collapse of massive stars, and the supernova type-II explosions. We have performed some calculations to estimate stellar equation of state (EOS) on the basis of statistical multifragmentation model.

RELEVANCE OF EQUILIBRIUM IN MULTIFRAGMENTATION

The relevance of equilibrium in a multifragmentation reaction of very central 40 Ca +40 Ca collisions at 35 MeV/nucleon is investigated by using simulations of Antisymmetrized Molecular Dynamics (AMD). Two types of ensembles are compared. One is the reaction ensemble of the states at each reaction time t in collision events simulated by AMD, and the other is the equilibrium ensemble prepared by solving the AMD equation of motion for a many-nucleon system confined in a container for a long time. The comparison of the ensembles is performed for the fragment charge distribution and the excitation energies. Our calculations show that there exists an equilibrium ensemble which well reproduces the reaction ensemble at each reaction time t for the investigated period 80 ≤ t ≤ 300 fm /c.

Surface and symmetry energies in isoscaling for multifragmentation reactions

The possibilities of modifications for symmetry and surface energy coefficients of nuclear matter at freeze-out density are investigated theoretically by means of isoscaling (isotopic scaling) on the basis of a statistical multifragmentation model. It is seen that while the isoscaling parameters as predicted by Markov chain calculations for the single sources 124Sn and 112Sn are very sensitive to the symmetry term, the surface energy variation slightly affects the isoscaling parameters in the multifragmentation region. The influence of these changes on the mean neutron to proton ratios of light fragments for 2 ⩽ Z ⩽ 10 is also shown. Comparing our results with MSU experimental data, it is confirmed that a significant reduction of the symmetry-term coefficient is found necessary to reproduce the isoscaling parameters of Z ⩽ 8 fragments.