Search

Properties of the nuclear equation of state (EoS) can be probed by measuring the dynamical properties of nucleus-nucleus collisions. In this study, we present the directed flow ($v_1$), elliptic flow ($v_2$) and stopping (VarXZ) measured in fixed target Sn + Sn collisions at 270 AMeV with the S$\pi$RIT Time Projection Chamber. We perform Bayesian analyses in which EoS parameters are varied simultaneously within the Improved Quantum Molecular Dynamics-Skyrme (ImQMD-Sky) transport code to obtain a multivariate correlated constraint. The varied parameters include symmetry energy, $S_0$, and slope of the symmetry energy, $L$, at saturation density, isoscalar effective mass, $m_{s}^*/m_{N}$, isovector effective mass, $m_{v}^{*}/m_{N}$ and the in-medium cross-section enhancement factor $\eta$. We find that the flow and VarXZ observables are sensitive to the splitting of proton and neutron effective masses and the in-medium cross-section. Comparisons of ImQMD-Sky predictions to the S$\pi$RIT data suggest a narrow range of preferred values for $m_{s}^*/m_{N}$, $m_{v}^{*}/m_{N}$ and $\eta$.

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.

Systematic examination of fusion for $^{39,41,45,47}$K + $^{28}$Si and $^{36,44}$Ar + $^{28}$Si provides insight into the impact of neutron and proton exchange on fusion for nuclei at and near the N=20 and N=28 shells. Comparison of the reduced excitation functions reveals a marked difference between the behavior of open-shell and closed-shell systems. While coupled channels calculations provide a good description for the closed-shell nuclei they significantly under-predict the fusion cross-section for open-shell nuclei. The observed trends are examined in the context of a potential energy surface, including shell effects, and multi-nucleon exchange with consideration of Pauli-blocking., Comment: 7 pages, 4 figures

We present our recent study of cross sections and angular distributions of projectile fragments from heavy-ion reactions at beam energy of 15 MeV/nucleon. We studied the production cross sections and the angular distributions of neutron-rich nuclides from collisions of a 86 Kr (15 MeV/nucleon) beam with heavy targets ( 64 Ni, 124 Sn and 238 U). Experimental data from our previous work at Texas A & M were compared with model calculations. Our calculations were based on a two-step approach: the dynamical stage of the collision was described with, first, the phenomenological Deep-Inelastic Transfer model (DIT) and, alternatively, with the microscopic Constrained Molecular Dynamics model (CoMD). The de-excitation of the hot heavy projectile fragments was performed with the Statistical Multifragmentation Model (SMM). An overall good discription of the available data was obtained with the models employed. Furthermore, we performed calculations with a radioactive beam of 92 Kr (15 MeV/nucleon) interacting with a target of 238 U. We observed that the multinucleon transfer mechanism leads to extremely neutron-rich nuclides toward and beyond the astrophysical r-process path., Comment: 15 pages, 8 figures

Many neutron star (NS) properties, such as the proton fraction within a NS, reflect the symmetry energy contributions to the Equation of State that dominate when neutron and proton densities differ strongly. To constrain these contributions at supra-saturation densities, we measure the spectra of charged pions produced by colliding rare isotope tin (Sn) beams with isotopically enriched Sn targets. Using ratios of the charged pion spectra measured at high transverse momenta, we deduce the slope of the symmetry energy to be $42 < L < 117$ MeV. This value is slightly lower but consistent with the $L$ values deduced from a recent measurement of the neutron skin thickness of $^{208}$Pb.

In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central $^{132}$Sn+$^{124}$Sn, $^{112}$Sn+$^{124}$Sn, and $^{108}$Sn+$^{112}$Sn collisions at $E/A=270~\mathrm{MeV}$ with the S$\pi$RIT Time Projection Chamber. While the uncertainties of individual pion multiplicities are measured to 4\%, those of the charged pion multiplicity ratios are measured to 2\%. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron to proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy., Comment: 8 pages, 4 figures, 1 table (accepted for publication in PLB)

The SAMURAI Pion Reconstruction and Ion-Tracker Time Projection Chamber (S$\pi$RIT TPC) was designed to enable measurements of heavy ion collisions with the SAMURAI spectrometer at the RIKEN Radioactive Isotope Beam Factory and provide constraints on the Equation of State of neutron-rich nuclear matter. The S$\pi$RIT TPC has a 50.5 cm drift length and an 86.4 cm $\times$ 134.4 cm pad plane with 12,096 pads that are equipped with the Generic Electronics for TPCs readout electronics. The S$\pi$RIT TPC allows excellent reconstruction of particles and provides isotopic resolution for pions and other light charged particles across a wide range of energy losses and momenta. Details of the S$\pi$RIT TPC are presented, along with discussion of the TPC performance based on cosmic ray and experimental data., Comment: 12 pages, 20 figures

In this paper, we present a software framework, S$\pi$RITROOT, which is capable of track reconstruction and analysis of heavy-ion collision events recorded with the S$\pi$RIT time projection chamber. The track-fitting toolkit GENFIT and the vertex reconstruction toolkit RAVE are applied to a box-type detector system. A pattern recognition algorithm which performs helix track finding and handles overlapping pulses is described. The performance of the software is investigated using experimental data obtained at the Radioactive Isotope Beam Facility (RIBF) at RIKEN. This work focuses on data from $^{132}$Sn + $^{124}$Sn collision events with beam energy of 270 AMeV. Particle identification is established using $\left$ and magnetic rigidity, with pions, hydrogen isotopes, and helium isotopes., Comment: 10 pages, 17 figures

When two heavy ions near the Fermi energy collide, a warm and low-density region can form in which fragments appear. This region is mainly dominated by proton (p) and alpha particles. In such an environment, the alphas interact with each other, and especially through strong resonances, form complex systems such as 8Be and 12C. Our experiments show that in the reactions 70(64)Zn(64Ni)+70(64)Zn(64Ni) at E/A=35 MeV/nucleon levels of 8Be appear around relative energies Eij=0.092 MeV, 3.03 MeV as well as above 10 MeV and 100 MeV. For the 3 alpha systems, multi resonance processes give rise to excited levels of 12C. In particular, the Hoyle state at 7.654 MeV excitation energy shows a decay component through the ground state of 8Be and also shows components where two different alpha couples are at relative energies consistent with the ground state of 8Be at the same time. A component where the three alpha relative energies are consistent with the ground state of 8Be (i.e., E12=E13=E23=0.092 MeV) is also observed at the 7.458 MeV excitation energy, which was suggested as an Efimov state., Comment: 8 pages, 5 figures

We studied the production of neutron-rich nuclides in multinucleon transfer collisions of stable and radioactive beams in the mass range A=40-60. We first presented our experimental cross section data of projectile fragments from the reaction of 40Ar(15 MeV/nucleon) with 64Ni, 58Ni and 27Al. We then compared them with calculations based on either the deep-inelastic transfer (DIT) model or the constrained molecular dynamics (CoMD) model, followed by the statistical multifragmentation model (SMM). An overall good agreement of the calculations with the experimental data is obtained. We continued with calculations of the reaction of 40Ar (15 MeV/nucleon) with 238U target and then with reactions of 48Ca (15 MeV/nucleon) with 64Ni and 238U targets. In these reactions, neutron-rich rare isotopes with large cross sections are produced. These nuclides, in turn, can be assumed to form radioactive beams and interact with a subsequent target (preferably 238U), leading to the production of extremely neutron-rich and even new isotopes (e.g. 60Ca) in this mass range. We conclude that multinucleon transfer reactions with stable or radioactive beams at the energy of around 15 MeV/nucleon offer an effective route to access extremely neutron-rich rare isotopes for nuclear structure or reaction studies., Comment: 28 pages, 11 figures

We derive the free energy for fermions and bosons from fragmentation data. Inspired by the symmetry and pairing energy of the Weizsacker mass formula we obtain the free energy of fermions (nucleons) and bosons (alphas and deuterons) using Landau's free energy approach. We confirm previously obtained results for fermions and show that the free energy for alpha particles is negative and very close to the free energy for ideal Bose gases. Deuterons behave more similarly to fermions (positive free energy) rather than bosons. This is due to their low binding energy, which makes them very 'fragile', i.e., easily formed and destroyed. We show that the {\alpha}-particle fraction is dominant at all temperatures and densities explored in this work. This is consistent with their negative free energy, which favors clusterization of nuclear matter into {\alpha}-particles at subsaturation densities and finite temperatures. The role of finite open systems and Coulomb repulsion is addressed.

A new method of accessing information on the symmetry free energy from yields of fragments produced in Fermi-energy heavy-ion collisions is proposed. Furthermore, by means of quantum fluctuation analysis techniques, correlations between extracted symmetry free-energy coefficients with temperature and density were studied. The obtained results are consistent with those of commonly used isoscaling techniques., Comment: 6 pages, 3 figures Heavy-ion nuclear reactions at Fermi energies, Nuclear equation of State, Fragmentation

A Time-Projection Chamber (TPC) called the SAMURAI Pion-Reconstruction and Ion-Tracker (S$\pi$RIT) has recently been constructed at Michigan State University as part of an international effort to constrain the symmetry-energy term in the nuclear Equation of State (EoS). The S$\pi$RIT TPC will be used in conjunction with the SAMURAI spectrometer at the Radioactive Isotope Beam Factory (RIBF) at RIKEN to measure yield ratios for pions and other light isospin multiplets produced in central collisions of neutron-rich heavy ions, such as $^{132}$Sn + $^{124}$Sn. The S$\pi$RIT TPC can function both as a TPC detector and as an active target. It has a vertical drift length of 50 cm, parallel to the magnetic field. Gas multiplication is achieved through the use of a multi-wire anode. Image charges are produced in the 12096 pads, and are read out with the recently developed Generic Electronics for TPCs., Comment: 7 pages, 3 figures, 2 tables. Submitted to NIM A Proceedings

Heavy-ion collisions provide a versatile terrestrial probe of the nuclear equation of state through the formation of nuclear matter at a wide variety of temperatures, densities, and pressures. Direct and indirect approaches for constraining the density dependence of the symmetry energy using heavy-ion collisions have been developed. The direct approach relies on scaling methods which attempt to connect isotopic fragment distributions to the symmetry energy. Using the indirect approach constraints on the equation of state are extracted from comparison of experimental results and theoretical transport calculations which utilize effective nucleon-nucleon interactions. Besides exploring the density dependence of the equation of state, heavy-ion collisions are simultaneously probing different temperature gradients of nuclear matter allowing for the temperature dependence of the symmetry energy to be examined. The current progress and open questions related to constraining the density and temperature dependence of the symmetry energy with heavy-ion collisions are discussed in the review., Comment: Review to appear in the upcoming EPJA special volume on nuclear symmetry energy

Equilibration of N/Z in binary breakup of an excited and transiently deformed projectile-like fragment (PLF*), produced in peripheral collisions of 64Zn + 27Al, 64Zn, 209Bi at E/A = 45 MeV, is examined. The composition of emitted light fragments (3<=Z<=6) changes with the decay angle of the PLF*. The most neutron-rich fragments observed are associated with a small rotation angle. A clear target dependence is observed with the largest initial N/Z correlated with the heavy, neutron-rich target. Using the rotation angle as a clock, we deduce that N/Z equilibration persists for times as long as 3-4 zs (1zs = 1 x 10^-21 s = 300 fm/c). The rate of N/Z equilibration is found to depend on the initial neutron gradient within the PLF*., Comment: 6 pages, 4 figures

A systematic study on the effect of secondary decay on the symmetry energy coefficient extracted by isoscaling and the recently proposed isobaric yield ratio methods within the Statistical Multifragmentation Model is performed. The correlations between the input symmetry energy coefficients and the calculated ones from both primary and secondary fragment yields are analysed. Results for secondary fragments show that the best estimation of the input symmetry energy coefficient within SMM is obtained by the isoscaling method, using the yields of light fragments. A comparison to experimental results is also presented., Comment: 4 figures, 6 pages, Submitted to Phys. Rev. C

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., Comment: 10 pages, 8 figures. To be submitted to Nucl. Instr. and Meth. A

The thermodynamics of excited nuclear systems allows one to explore the second-order phase transition in a two-component quantum mixture. Temperatures and densities are derived from quantum fluctuations of fermions. The pressures are determined from the grand partition function of Fisher's model. Critical scaling of observables is found for systems which differ in neutron to proton concentrations thus constraining the equation of state of asymmetric nuclear matter. The derived critical exponent {\beta}= 0.35 \pm 0.01, belongs to the liquid-gas universality class. The critical compressibility factor Pc /{\rho}c Tc increases with increasing neutron number., Comment: 11 pages, 4 figures

The symmetry energy contribution to the nuclear Equation of State (EoS) impacts various phenomena in nuclear astrophysics, nuclear structure, and nuclear reactions. Its determination is a key objective of contemporary nuclear physics with consequences for the understanding of dense matter within neutron stars. We examine the results of laboratory experiments that have provided initial constraints on the nuclear symmetry energy and its density dependence at and somewhat below normal nuclear matter density. Some of these constraints have been derived from properties of nuclei. Others have been derived from the nuclear response to electroweak and hadronic probes. We also examine the most frequently used theoretical models that predict the symmetry energy and its slope. By comparing existing constraints on the symmetry pressure to theories, we demonstrate how the contribution of the three-body force, an essential ingredient in neutron matter models, can be determined., Comment: 28 pages, 4 figures

Methods of extraction of the symmetry energy (or enthalpy) coefficient to temperature ratio from isobaric and isotopic yields of fragments produced in Fermi-energy heavy-ion collisions are discussed. We show that the methods are consistent when the hot fragmenting source is well characterized and its excitation energy and isotopic composition are properly taken into account. The results are independent of the mass number of the detected fragments, which suggests that their fate is decided very early in the reaction., Comment: 12 pages, 9 figures, submitted to Phys. Rev. C and accepted for publication

The first experimental results of a new quantum method for calculating nuclear temperature and density of fragmenting heavy ions is presented. This method is based on fluctuations in the event quadrupole momentum and fragment multiplicity distributions of light Fermions. The cal- culated temperatures are lower than those obtained with a similar classical method. Quenching of the normalized multiplicity distributions of light fermions due to Pauli blocking is also observed. These results indicate a need for a quantum treatment when dealing with statistical properties of fragmenting heavy-ions., Comment: 4 pages, 4 figures

The critical phenomena of the liquid-gas phase transition has been investigated in the reactions 78,86Kr+58,64Ni at beam energy of 35 MeV/nucleon using the Landau free energy approach with isospin asymmetry as an order parameter. Fits to the free energy of fragments showed three minima suggesting the system to be in the regime of a first order phase transition. The relation m =-{\partial}F/{\partial}H, which defines the order parameter and its conjugate field H, has been experimentally verified from the linear dependence of the mirror nuclei yield ratio data, on the isospin asymmetry of the source. The slope parameter, which is a measure of the distance from a critical temperature, showed a systematic decrease with increasing excitation energy of the source. Within the framework of the Landau free energy approach, isoscaling provided similar results as obtained from the analysis of mirror nuclei yield ratio data. We show that the external field is primarily related to the minimum of the free energy, which implies a modification of the source concentration \Delta used in isospin studies.

A new thermometer based on fragment momentum fluctuations is presented. This thermometer exhibited residual contamination from the collective motion of the fragments along the beam axis. For this reason, the transverse direction has been explored. Additionally, a mass dependence was observed for this thermometer. This mass dependence may be the result of the Fermi momentum of nucleons or the different properties of the fragments (binding energy, spin etc..) which might be more sensitive to different densities and temperatures of the exploding fragments. We expect some of these aspects to be smaller for protons (and/or neutrons); consequently, the proton transverse momentum fluctuations were used to investigate the temperature dependence of the source.

The nuclear symmetry energy is a fundamental quantity important for studying the structure of systems as diverse as the atomic nucleus and the neutron star. Considerable efforts are being made to experimentally extract the symmetry energy and its dependence on nuclear density and temperature. In this article, we review experimental studies carried out up-to-date and their current status., Comment: 10 pages, 3 figures, talk presented at the International Symposium in Nuclear Physics, Mumbai, India, Dec. 2009. Added few more references. Minor correction in Reference

Interest in the influence of the neutron-to-proton (N/Z) ratio on multifragmenting nuclei has demanded an improvement in the capabilities of multi-detector arrays as well as the companion analysis methods. The particle identification method used in the NIMROD-ISiS 4 $\pi$ array is described. Performance of the detectors and the analysis method are presented for the reaction of 86Kr+64Ni at 35MeV/u., Comment: Conference procedings

Assuming a schematic form of the nucleon effective mass as a function of nuclear excitation energy and mass, we provide a simple explanation for understanding the experimentally observed mass dependence of the nuclear caloric curve. It is observed that the excitation energy at which the caloric curve enters into a plateau region, could be sensitive to the nuclear mass evolution of the effective nucleon mass., Comment: 5 pages, 5 figures, Accepted for publication in Phys. Rev. C. Minor changes made

The decrease in the symmetry energy of hot nuclei populated in $^{58}$Ni + $^{58}$Ni, $^{58}$Fe + $^{58}$Ni and $^{58}$Fe + $^{58}$Fe reactions at beam energies of 30, 40, and 47 MeV/nucleon, as a function of excitation energy is studied. It is observed that this decrease is mainly a consequence of increasing expansion or decreasing density rather than the increasing temperature. The results are in good agreement with the recently reported microscopic calculation based on the Thomas-Fermi approach. An empirical relation to study the symmetry energy of finite nuclei in various mass region is proposed., Comment: 10 pages, 2 figures

The signal of isospin-asymmetric phase transition in the evolution of the chemical potential was observed for hot quasi-projectiles produced in the reactions 40,48Ca + 27Al confirming an analogous observation in the lighter system 28Si + 112,124Sn. With increasing mass, the properties of hot quasi-projectiles become increasingly influenced by the secondary emission. Thermodynamical observables exhibit no sensitivity to the different number of missing neutrons in the two reactions 40,48Ca + 27Al, thus providing a signal of dynamical emission of neutrons, which can be related to formation of a very neutron-rich low-density region (neck) between the projectile and target., Comment: LaTeX, article expanded, 2 figures added, 17 pages, 7 figures

The density dependence of the symmetry energy in the equation of state of isospin asymmetric nuclear matter is of significant importance for studying the structure of systems as diverse as the neutron-rich nuclei and the neutron stars. A number of reactions using the dynamical and the statistical models of multifragmentation, and the experimental isoscaling observable, is studied to extract information on the density dependence of the symmetry energy. It is observed that the dynamical and the statistical model calculations give consistent results assuming the sequential decay effect in dynamical model to be small. A comparison with several other independent studies is also made to obtain important constraint on the form of the density dependence of the symmetry energy. The comparison rules out an extremely " stiff " and " soft " form of the density dependence of the symmetry energy with important implications for astrophysical and nuclear physics studies., Comment: 16 pages, 14 figures

The density dependence of the symmetry energy in the equation of state of asymmetric nuclear matter (N/Z $>$ 1) is important for understanding the structure of systems as diverse as the atomic nuclei and neutron stars. Due to a proper lack of understanding of the basic nucleon-nucleon interaction for matters that are highly asymmetric and at non-normal nuclear density, this very important quantity has remained largely unconstrained. Recent studies using beams from the Cyclotron Institute of Texas A$&$M University, constraining the density dependence of the symmetry energy, is presented. A dependence of the form E$_{sym}(\rho)$ = C($\rho/\rho_{o})^{\gamma}$, where C = 31.6 MeV and $\gamma$ = 0.69, is obtained from the dynamical and statistical model analysis. Their implications to both astrophysical and nuclear physics studies are discussed., Comment: Invited talk, Proceedings of CAARI 2006, Forth Worth, Texas, Aug 20 -25, 2006

The symmetry energy, temperature, density and isoscaling parameter, in $^{58}$Ni + $^{58}$Ni, $^{58}$Fe + $^{58}$Ni and $^{58}$Fe + $^{58}$Fe reactions at beam energies of 30, 40 and 47 MeV/nucleon, are studied as a function of excitation energy of the multifragmenting source. It is shown that the decrease in the isoscaling parameter is related to the near flattening of the temperature in the caloric curve, and the decrease in the density and the symmetry energy with increasing excitation energy. The decrease in the symmetry energy is mainly a consequence of decreasing density with increasing excitation rather than the increasing temperature. The symmetry energy as a function of density obtained from the correlation is in close agreement with the form, E$_{sym}(\rho)$ $=$ 31.6 ($\rho/\rho_{\circ})^{0.69}$., Comment: 5 pages, 5 figures

Simultaneous measurement of both neutrons and charged particles emitted in the reaction $^{64}$Zn + $^{64}$Zn at 45 MeV/nucleon allows comparison of the neutron to proton ratio at midrapidity with that at projectile rapidity. The evolution of N/Z in both rapidity regimes with increasing centrality is examined. For the completely re-constructed midrapidity material one finds that the neutron-to-proton ratio is above that of the overall $^{64}$Zn + $^{64}$Zn system. In contrast, the re-constructed ratio for the quasiprojectile is below that of the overall system. This difference provides the most complete evidence to date of neutron enrichment of midrapidity nuclear matter at the expense of the quasiprojectile.

We show that the large sequential decay corrections obtained by Ono {\it et al} [nucl-ex/0507018], is in contradiction with both the other dynamical and statistical model calculations carried out for the same systems and energy. On the other hand, the conclusion of Shetty {\it {et al.}} $[$Phys. Rev. C 70, 011601R (2004)$]$, that the experimental data favors Gogny$-$AS interaction (obtained assuming a significantly smaller sequential decay effects), is consistent with several other independent studies., Comment: 2 pages, 1 figure

The sizes, temperatures and free neutron to proton ratios of the initial interaction zones produced in the collisions of 40 MeV/nucleon $^{40}$Ar + $^{112}$Sn and 55 MeV/nucleon$^{27}$Al + $^{124}$Sn are derived using total detected neutron plus charged particle multiplicity as a measure of the impact parameter range and number of participant nucleons. The size of the initial interaction zone, determined from a coalescence model analysis, increases significantly with decreasing impact parameter. The temperatures and free neutron to proton ratios in the interaction zones are relatively similar for different impact parameter ranges and evolve in a similar fashion., Comment: 7 pages, 8 figures

In [1,2]the observed decrease in spectral peak energies of IMFs emitted from hot nuclei was interpreted in terms of a breakup density that decreased with increasing energy. Subsequently, Raduta et al. [3] performed MMM simulations that showed decreasing spectral peaks could be obtained at constant density. In this letter we examine this apparent inconsistency., Comment: 9 pages, 2 figures, 1 table

The evolution of the symmetry energy coefficient of the binding energy of hot fragments with increasing excitation is explored in multifragmentation processes following heavy-ion collisions below the Fermi energy. In this work, high-resolution mass spectrometric data on isotopic distributions of projectile-like fragments from collisions of 25 MeV/nucleon 86Kr and 64Ni beams on heavy neutron-rich targets are systematically compared to calculations involving the Statistical Multifragmentation Model. The study reveals a gradual decrease of the symmetry energy coefficient from 25 MeV at the compound nucleus regime (E*/A < 2 MeV) towards 15 MeV in the bulk multifragmentation regime (E*/A > 4 MeV). The ensuing isotopic distributions of the hot fragments are found to be very wide and extend towards the neutron drip-line. These findings may have important implications to the composition and evolution of hot astrophysical environments, such as core-collapse supernova., Comment: 5 pages, 4 figures, submitted to Phys. Rev. C

The symmetry energy is an important quantity in the equation of state of isospin asymmetric nuclear matter. This currently unknown quantity is key to understanding the structure of systems as diverse as the neutron-rich nuclei and neutron stars. At TAMU, we have carried out studies, aimed at understanding the symmetry energy, in a variety of reactions such as, the multifragmentation of $^{40}$Ar, $^{40}$Ca + $^{58}$Fe, $^{58}$Ni and $^{58}$Ni, $^{58}$Fe + $^{58}$Ni, $^{58}$Fe reactions at 25 - 53 AMeV, and deep-inelastic reactions of $^{86}$Kr + $^{124,112}$Sn, $^{64,58}$Ni (25 AMeV), $^{64}$Ni + $^{64,58}$Ni, $^{112,124}$Sn, $^{232}$Th, $^{208}$Pb (25 AMeV) and $^{136}$Xe + $^{64,58}$Ni, $^{112,124}$Sn, $^{232}$Th, $^{197}$Au (20 AMeV). Here we present an overview of some of the results obtained from these studies. The results are analyzed within the framework of statistical and dynamical models, and have important implications for future experiments using beams of neutron-rich nuclei., Comment: 10 pages, 4 figures, talk presented at VI Latin American Symposium on Nuclear Physics and Applications

The symmetry energy and the isoscaling properties of the fragments produced in the multifragmentation of $^{40}$Ar, $^{40}$Ca + $^{58}$Fe, $^{58}$Ni reactions at 25 - 53 MeV/nucleon were investigated within the framework of statistical multifragmentation model. The isoscaling parameters $\alpha$, from the primary (hot) and secondary (cold) fragment yield distributions, were studied as a function of excitation energy, isospin (neutron-to-proton asymmetry) and fragment symmetry energy. It is observed that the isoscaling parameter $\alpha$ decreases with increasing excitation energy and decreasing symmetry energy. The parameter $\alpha$ is also observed to increase with increasing difference in the isospin of the fragmenting system. The sequential decay of the primary fragments into secondary fragments, when studied as a function of excitation energy and isospin of the fragmenting system, show very little influence on the isoscaling parameter. The symmetry energy however, has a strong influence on the isospin properties of the hot fragments. The experimentally observed scaling parameters can be explained by symmetry energy that is significantly lower than that for the ground state nuclei near saturation density. The results indicate that the properties of hot nuclei at excitation energies, densities and isospin away from the normal ground state nuclei could be significantly different., Comment: 14 pages, 15 figures

The isoscaling properties of isotopically resolved projectile residues from peripheral collisions of 86Kr (25 MeV/nucleon), 64Ni (25 MeV/nucleon) and 136Xe (20 MeV/nucleon) beams on various target pairs are employed to probe the symmetry energy coefficient of the nuclear binding energy. The present study focuses on heavy projectile fragments produced in peripheral and semiperipheral collisions near the onset of multifragment emission E*/A = 2-3 MeV). For these fragments, the measured average velocities are used to extract excitation energies. The excitation energies, in turn, are used to estimate the temperatures of the fragmenting quasiprojectiles in the framework the Fermi gas model. The isoscaling analysis of the fragment yields provided the isoscaling parameters "alpha" which, in combination with temperatures and isospin asymmetries provided the symmetry energy coefficient of the nuclear binding energy of the hot fragmenting quasiprojectiles. The extracted values of the symmetry energy coefficient at this excitation energy range (2-3 MeV/nucleon) are lower than the typical liquid-drop model value ~25 MeV corresponding to ground-state nuclei and show a monotonic decrease with increasing excitation energy. This result is of importance in the formation of hot nuclei in heavy-ion reactions and in hot stellar environments such as supernova., Comment: 11 pages, 9 figures, submitted to Phys. Rev. C

The density dependence of the symmetry energy in the equation of state of isospin asymmetric nuclear matter is studied using the isoscaling of the fragment yields and the antisymmetrized molecular dynamic calculation. It is observed that the experimental data at low densities are consistent with the form of symmetry energy,E$_{sym}$ $\approx$ 31.6 ($\rho/\rho_{\circ})^{0.69}$, in close agreement with those predicted by the results of variational many-body calculation. A comparison of the present result with those reported recently using the NSCL-MSU data suggests that the heavy ion studies favor a dependence of the form, E$_{sym}$ $\approx$ 31.6 ($\rho/\rho_{\circ})^{\gamma}$, where $\gamma$ = 0.6 - 1.05. This constraints the form of the density dependence of the symmetry energy at higher densities, ruling out an extremely " stiff " and " soft " dependences., Comment: 4 pages, 3 figures, minor revison to the text, added few more references

Calorimetric and coalescence techniques have been employed to probe equilibration for hot nuclei produced in heavy ion collisions of 35 to 55 MeV/u projectiles with medium mass targets. Entrance channel mass asymmetries and energies were selected in order that very hot composite nuclei of similar mass and excitation would remain after early stage pre-equilibrium particle emission. Inter-comparison of the properties and de-excitation patterns for these different systems provides evidence for the production of hot nuclei with decay patterns relatively independent of the specific entrance channel., Comment: 7 pages, 2 figures

The critical behavior for the light nuclei with A$\sim 36$ has been investigated experimentally by the NIMROD multi-detectors. The wide variety of observables indicate the critical point has been reached in the disassembly of hot nuclei at an excitation energy of 5.6$\pm$0.5 MeV/u., Comment: 4 pages, 2 figures; Proceeding of 18th Nuclear Physics Division Conference of the Euro. Phys. Society (NPDC18) "Phase transitions in strongly interacting matter", Prague, 23.8.-29.8. 2004. To be published in Nuclear Physics A

An extensive experimental survey of the features of the disassembly of a small quasi-projectile system with $A \sim$ 36, produced in the reactions of 47 MeV/nucleon $^{40}$Ar + $^{27}$Al, $^{48}$Ti and $^{58}$Ni, has been carried out. Nuclei in the excitation energy range of 1-9 MeV/u have been investigated employing a new method to reconstruct the quasi-projectile source. At an excitation energy $\sim$ 5.6 MeV/nucleon many observables indicate the presence of maximal fluctuations in the de-excitation processes. The fragment topological structure shows that the rank sorted fragments obey Zipf's law at the point of largest fluctuations providing another indication of a liquid gas phase transition. The caloric curve for this system shows a monotonic increase of temperature with excitation energy and no apparent plateau. The temperature at the point of maximal fluctuations is $8.3 \pm 0.5$ MeV. Taking this temperature as the critical temperature and employing the caloric curve information we have extracted the critical exponents $\beta$, $\gamma$ and $\sigma$ from the data. Their values are also consistent with the values of the universality class of the liquid gas phase transition. Taken together, this body of evidence strongly suggests a phase change in an equilibrated mesoscopic system at, or extremely close to, the critical point., Comment: Physical Review C, in press; some discussions about the validity of excitation energy in peripheral collisions have been added; 24 pages and 32 figures; longer abstract in the preprint

The isotopic properties of the primary and secondary fragment yield distribution in the multifragmentation of $^{58}$Fe + $^{58}$Ni and $^{58}$Fe + $^{58}$Fe reactions are studied with respect to the $^{58}$Ni + $^{58}$Ni reaction at 30, 40 and 47 MeV/nucleon. The reduced neutron and proton densities from the observed fragment yield distribution show primary fragment yield distribution to undergo strongly secondary de-excitations. The effect is small at the lowest excitation energy and smallest neutron-to-proton ratio and becomes large at higher excitation energies and higher neutron-to-proton ratio. The symmetry energy of the primary fragments deduced from the reduced neutron density is significantly lower than that for the normal nuclei at saturation density, indicating that the fragments are highly excited and formed at a reduced density. Furthermore, the symmetry energy is also observed to decrease slowly with increasing excitation energy. The observed effect is explained using the statistical multifragmentation model., Comment: 7 pages, 5 figures

The kinetic energy variation of emitted light clusters has been employed as a clock to explore the time evolution of the temperature for thermalizing composite systems produced in the reactions of 26A, 35A and 47A MeV $^{64}$Zn with $^{58}$Ni, $^{92}$Mo and $^{197}$Au. For each system investigated, the double isotope ratio temperature curve exhibits a high maximum apparent temperature, in the range of 10-25 MeV, at high ejectile velocity. These maximum values increase with increasing projectile energy and decrease with increasing target mass. The time at which the maximum in the temperature curve is reached ranges from 80 to 130 fm/c after contact. For each different target, the subsequent cooling curves for all three projectile energies are quite similar. Temperatures comparable to those of limiting temperature systematics are reached 30 to 40 fm/c after the times corresponding to the maxima, at a time when AMD-V transport model calculations predict entry into the final evaporative or fragmentation stage of de-excitation of the hot composite systems. Evidence for the establishment of thermal and chemical equilibrium is discussed., Comment: 9 pages, 5 figures

The isoscaling parameter $\alpha$, from the fragments produced in the multifragmentation of $^{58}$Ni + $^{58}$Ni, $^{58}$Fe + $^{58}$Ni and $^{58}$Fe + $^{58}$Fe reactions at 30, 40 and 47 MeV/nucleon, was compared with that predicted by the antisymmetrized molecular dynamic (AMD) calculation based on two different nucleon-nucleon effective forces, namely the Gogny and Gogny-AS interaction. The results show that the data agrees better with the choice of Gogny-AS effective interaction, resulting in a symmetry energy of $\sim$ 18-20 MeV. The observed value indicate that the fragments are formed at a reduced density of $\sim$ 0.08 fm$^{-3}$., Comment: 5 pages, 5 figures, Accepted for publication in Phys. Rev. C (Rapid Communication)

A novel method was developed for the extraction of short emission times of light particles from the projectile-like fragments in peripheral deep-inelastic collisions in the Fermi energy domain. We have taken an advantage of the fact that in the external Coulomb field particles are evaporated asymmetrically. It was possible to determine the emission times in the interval 50-500 fm/c using the backward emission anisotropy of alpha-particles relative to the largest residue, in the reaction 28Si + 112Sn at 50 MeV/nucleon. The extracted times are consistent with predictions based on the evaporation decay widths calculated with the statistical evaporation model generalized for the case of the Coulomb interaction with the target., Comment: 13 pages, 5 figures, submitted to Phys. Lett. B

Effects of in-medium cross-sections and of optical potential on pre-equilibrium emission and on formation of a thermal source are investigated by comparing the results of transport simulations with experimental results from the p+{197}Au reaction at 6.2-14.6 GeV/c. The employed transport model includes light composite-particle production and allows for inclusion of in-medium particle-particle cross-section reduction and of momentum dependence in the particle optical-potentials. Compared to the past, the model incorporates improved parameterizations of elementary high-energy processes. The simulations indicate that the majority of energy deposition occurs during the first ~25 fm/c of a reaction. This is followed by a pre-equilibrium emission and readjustment of system density and momentum distribution toward an equilibrated system. Good agreement with data, on the d/p and t/p yield ratios and on the residue mass and charge numbers, is obtained at the time of ~ 65 fm/c from the start of a reaction, provided reduced in-medium cross-sections and momentum-dependent optical potentials are employed in the simulations. By then, the pre-equilibrium nucleon and cluster emission, as well as mean-field readjustments, drive the system to a state of depleted average density, rho/rho_{0} ~ 1/4-1/3 for central collisions, and low-to-moderate excitation, i.e. the region of nuclear liquid-gas phase transition., Comment: 35 pages, 14 figures

The isospin properties of primary and secondary fragments produced in multifragmentation of Fe + Ni and Fe + Fe systems with respect to Ni + Ni system are analyzed within the statistical multifragmentation model framework. The reduced neutron and proton densities show an asymmetry in the primary fragments, that is lessened after secondary decay. with increasing isospin (N/Z) this effect increases, while the sensitivity of fragment isospin towards excitation energy and N/Z of the primary fragments remains unchanged., Comment: 12 pages, 4 figures

The reaction systems, 64Zn + 58Ni, 64Zn + 92Mo, 64Zn + 197Au, at 26A, 35A and 47A MeV, have been studied both in experiments with a 4$\pi$ detector array, NIMROD, and with Antisymmetrized Molecular Dynamics model calculations employing effective interactions corresponding to soft and stiff equations of state (EOS). Direct experimental observables, such as multiplicity distributions, charge distributions, energy spectra and velocity spectra, have been compared in detail with those of the calculations and a reasonable agreement is obtained. The velocity distributions of $\alpha$ particles and fragments with Z >= 3 show distinct differences in calculations with the soft EOS and the stiff EOS. The velocity distributions of $\alpha$ particle and Intermediate Mass Fragments (IMF's) are best described by the stiff EOS. Neither of the above direct observables nor the strength of the elliptic flow are sensitive to changes in the in-medium nucleon-nucleon (NN) cross sections. A detailed analysis of the central collision events calculated with the stiff EOS revealed that multifragmentation with cold fragment emission is a common feature predicted for all reactions studied here. A possible multifragmentation scenario is presented; after the preequilibrium emission ceases in the composite system, cold light fragments are formed in a hotter gas of nucleons and stay cold until the composite system underdoes multifragmentation. For reaction with 197Au at 47A MeV a significant radial expansion takes place. For reactions with 58Ni and 92Mo at 47A MeV semi-transparency becomes prominent. The differing reaction dynamics drastically change the kinematic characteristics of emitted fragments. This scenario gives consistent explanations for many existing experimental results in the Fermi energy domain., Comment: 34 pages, 43 figures