Search

In this report, we review the isospin dependence of various forms of the collective flow in heavy-ion reactions from Fermi to relativistic energies. The emphasis will be on suggested possible applications in directly exploring the underlying isovector potential and thus the Equation of State (EoS) of asymmetric nuclear matter, in particular in density regions far away from normal conditions. We also discuss forthcoming challenges and opportunities provided by high-energy radioactive beams. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The isoscaling of heavy projectile residues from peripheral heavy-ion reactions at 15-25 MeV/nucleon is employed to obtain information on the process of N/Z equilibration. Recent mass spectrometric data of projectile residues from the reactions of 86Kr (15 MeV/nucleon) with 64,58Ni and l24,ll2Sn were first analyzed. The isotopically resolved yield distributions of the fragments in the range Z = 26-39 were employed for the isoscaling analysis. The yield ratios R21(N,Z) of the fragments from each pair of systems exhibit isoscaling (i.e., an exponential dependence on the fragment neutron number N for each atomic number Z) with the isoscaling parameter a increasing with decreasing (or increasing) Z away from the projectile. This variation is related to the evolution toward N/Z equilibration with increasing energy dissipation estimated from the residue velocities. In parallel to the new heavy-residue isoscaling data of 86Kr at 15 MeV/nucleon, our previous data at 25 MeV/nucleon for the reactions 86Kr+124,112Sn and 64Ni+64,58Ni, 64Ni+l24,ll2Sn, as well as our data at 15 MeV/nucleon of the lighter system 40Ar+64,58Ni, were analyzed in a similar way. Calculations with the stochastic nucleon-exchange model DIT (deep inelastic transfer) and the microscopic many-body model CoMD (constrained molecular dynamics) provided an overall fair description of data and valuable guidance for their interpretation. Interestingly, the data of the 86Kr+Ni,Sn reactions at 15 MeV/nucleon show a retardation of the process of N/Z equilibration which, as suggested by the CoMD calculations, is indicative of the collective character of the process. This retardation is not present in the investigated systems at 25 MeV/nucleon (and the light 40Ar+Ni systems at 15 MeV/nucleon), whose behavior is found to be consistent with stochastic nucleón exchange. [ABSTRACT FROM AUTHOR]

The quantum-fluctuation method using Coulomb corrections is explored to extract temperatures and densities of hot nuclear systems produced in Fermi-energy heavy-ion collisions. The role of the neutron-proton asymmetry of the system was investigated. Temperature values were observed to not depend on the system neutron-proton asymmetry while a clear dependence is seen for density values. Coulomb corrections have been shown to lower temperature values by almost 2 MeV. On the other hand, density results exhibit a small variation. [ABSTRACT FROM AUTHOR]

Suppression of multiplicity fluctuations has been observed for three light fermions (protons, tritons and 3He) in the multifragmentation of reconstructed hot quasi-projectiles produced in collisions of 32S (45 MeV/nucleon) with 112Sn. This suppression, predicted by recent calculations, is attributed to Pauli blocking and has also been observed in experiments with trapped Fermi gases. Experimental results on nuclear temperature and density employing a quantal approach based on momentum and multiplicity fluctuations are also presented. The extracted temperatures show a noticeable reduction when compared to a similarly derived classical method. This reduction in temperature is in agreement with previous predictions indicating that classically derived methods overpredict nuclear temperature as they do not take into account the Fermi motion of the nucleons. The present results underline the role of quantum statistics in nuclear disassembly and suggest the need for proper quantum treatment when dealing with the thermodynamic properties of fragmenting heavy ions. [ABSTRACT FROM AUTHOR]

The thermodynamics of excited nuclear systems allows the exploration of a 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 the first time for fragmenting systems which differ in neutron to proton concentrations thus constraining the equation of state (EOS) of asymmetric nuclear material. The derived critical exponent, β = 0.35 ±0.01, belongs to the liquid-gas universality class. The critical compressibility factor Pc/ρcTc increases with increasing neutron concentration, which could be due to finite-size and/or Coulomb effects. [ABSTRACT FROM AUTHOR]

The experimental determination of freeze-out temperatures and densities from the yields of light elements emitted in heavy ion collisions is discussed. Results from different experimental approaches are compared with those of model calculations carried out with and without the inclusion of medium effects, which become of relevance for baryon densities above ≈5 x 10-4 fm-3. A quantum statistical (QS) model incorporating medium effects is in good agreement with the experimentally derived results at higher densities. A densitometer based on medium modified chemical equilibrium constants is proposed. [ABSTRACT FROM AUTHOR]

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 (1 zs = 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*. [ABSTRACT FROM AUTHOR]

Recently, we observed a clear dependence of the nuclear caloric curve on neutron-proton asymmetry N-Z/A through examination of fully reconstructed equilibrated quasiprojectile sources produced in heavy-ion collisions at E/A=35 MeV. In the present work, we extend our analysis using multiple light charged particle probes of the temperature. Temperatures are extracted with five distinct probes using a kinetic thermometer approach. Additionally, temperatures are extracted using two probes within a chemical thermometer approach (Albergo method). All seven measurements show a significant linear dependence of the source temperature on the source asymmetry. For the kinetic thermometer, the strength of the asymmetry dependence varies with the probe particle species in a way that is consistent with an average emission-time ordering. [ABSTRACT FROM AUTHOR]

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 (SMM) is performed. The correlations between the input symmetry energy coefficients and the calculated ones from both primary and secondary fragment yields are analyzed. 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. [ABSTRACT FROM AUTHOR]

Fragment yield data have been analyzed using the Landau free energy approach to investigate the critical phenomena of fragmenting quasi-projectiles formed in 64Zn + 64Zn, 64Ni + 64Ni, and 70Zn + 70Zn reactions at beam energy of 35 MeV/nucleon. Pairing coefficients normalized to the temperature of the fragmenting source (a64/ T) were extracted from yield data of N = Z fragments in order to correct for odd-even effects in free energy calculations. Plots of fragment free energy (F/T) versus the neutron-proton asymmetry show three minima, indicating the system to be in a first-order phase transition regime. Values of fitting parameters to the Landau free energy equation as well as a64/T, which are related to thermodynamic properties of the fragmenting systems, exhibit a dependence on the neutron-proton asymmetry in addition to their dependence on the excitation energy of the fragmenting source. [ABSTRACT FROM AUTHOR]

The production of fragments from a broad range of reconstructed quasiprojectiles obtained in the interaction of 32S (45 MeV/nucleon) with 112Sn was studied. A good description of the experimental data on the multifragmentation of these light quasi-projectiles with a model framework based on deep inelastic transfer followed by SMM(statistical multi fragmentation model)was obtained. The charge and mass distributions of the observed fragments show that the break-up of a given quasi-projectile source is highly correlated to its isospin composition. The sensitivity of the hot primary fragments to the symmetry energy was investigated in detail. It was found that for the present light systems (A~30), a good description of the experimental data on the charge distributions, the N/Z distributions and the isotopic distributions of the fragments is obtained by the SMMcalculations involving the standard (Csym = 25MeV), as well as, a reduced value of the symmetry energy (Csym = 8 MeV). However, the reduced value of the symmetry energy appears to provide a better description of the isotopic distributions in most of the cases. This is in agreement with an overall reduction of the symmetry energy of primary fragments indicated by a number of multifragmentation studies of heavier systems. [ABSTRACT FROM AUTHOR]

Correlations of midrapidity light charged particles (LCPs) and intermediate mass fragments (IMFs) with projectile-like fragments (PLFs) have been examined from the 35 MeV/u 70Zn + 70Zn, 64Zn + 64Zn, and 64Ni + 64Ni reaction systems. A new method was developed to examine the flow of the particles with respect to the PLF. The invariant PLF-scaled flow allowed for the dynamics of the midrapidity Z = 1-4 particles to be studied. Strong differences in the PLF-scaled flow were observed between the different isotopes. In particular, the most n-rich LCPs exhibited a negative PLF-scaled flow in comparison to the other LCPs. A classical molecular dynamics model and a three-body Coulomb trajectory simulation were both used to show that the PLF-scaled flow observable could be connected to the average order of emission of the LCPs. The experimental results suggest that the midrapidity region is preferentially populated with neutron-rich LCPs and Z = 3-4 IMFs at a relatively early stage in the collision. The deuteron and ³He particles are emitted later followed, lastly, by protons and alphas. The average order of emission of the midrapidity LCPs was extracted from the constrained molecular dynamics simulations and showed good agreement with the emission order suggested by the experimental PLF-scaled flow results. [ABSTRACT FROM AUTHOR]

The symmetry energy contribution to the nuclear equation of state 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 on its density dependence at and somewhat below normal nuclear matter density. Even though some of these constraints have been derived from properties of nuclei while others have been derived from the nuclear response to electroweak and hadronic probes, within experimental uncertainties-they are consistent with each other. We also examine the most frequently used theoretical models that predict the symmetry energy and its slope parameter. By comparing existing constraints on the symmetry pressure to theories, we demonstrate how contributions of three-body forces, which are essential ingredients in neutron matter models, can be determined. [ABSTRACT FROM AUTHOR]

The NIMROD-ISiS array was used to study the transverse flow of intermediate mass fragments in 35 MeV/nucleon 70Zn + 70Zn, 64Zn + 64Zn, and 64Ni + 64Ni reactions. The intermediate mass fragment flow was previously shown to be sensitive to the density dependence of the symmetry energy. To explore the model dependence of the results, the antisymmetrized molecular dynamics, constrained molecular dynamics, and stochastic mean-field models were each compared to the experimental results to extract information on the form of the symmetry energy. The results demonstrate that sensitivity of the models to the nuclear equation of state can vary significantly based on the treatment of the nuclear dynamics. Despite the differences in the sensitivity, improved agreement with the experimental data is observed for each model with a stiff density dependence of the symmetry energy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Fragment yield data, selected with different values of the isospin asymmetry of the quasiprojectile from 78, 86Kr+58, 64Ni reactions at Elab = 35 MeV/nucleon, have been analyzed within the framework of Landau free energy approach. Fits to the free energy data indicated the system to be in the regime of a first-order phase transition. The plot of free energy versus isospin asymmetry of the fragments showed a systematic change with increasing isospin asymmetry of the fragmenting source. This observation demonstrated the role of quasiprojectile isospin asymmetry as an external field which governed the minima positions in the free energy plot. The position of the central minimum was found to be in close agreement with the average isospin asymmetry of the fragments calculated excluding neutrons and protons. Significant deviations from the free energy plot were observed for N = Z fragments, particularly for the lighter ones, which could be corrected after inclusion of odd-even effects in the analysis. Analysis of yield data of N = Z nuclei gave a reasonable estimate of temperature. Analysis of free energy data gated with excitation energy of the fragmenting source showed a dependence of fit parameters of Landau free energy equation on the excitation energy as well as isospin asymmetry of the source. [ABSTRACT FROM AUTHOR]

The production cross sections of projectilelike fragments from the interaction of 15 MeV/nucleon 86Kr with 64Ni and 58Ni and with 124Sn and 112Sn were measured using a magnetic separator with emphasis on the neutron-rich isotopes. Neutron pickup isotopes (with up to six neutrons picked up from the target) were observed with large cross sections. Calculations involving the the deep-inelastic transfer model as well as the microscopic constrained molecular dynamics model (CoMD) for the primary interaction stage coupled to the statistical deexcitation code GEMINI were used to describe the gross properties of the product distributions. The present results were also compared with our previous data of the same reactions at 25 MeV/nucleon. The data at 15 MeV/nucleon show enhanced production of neutron-rich isotopes very close to the projectile, relative to the corresponding data at 25 MeV/nucleon. This enhancement in the cross sections is possibly associated with very peripheral collisions and longer interaction times of the neutron-rich 86Kr projectile with the neutron-rich targets. The large cross sections of such reactions well above the Coulomb barrier, but below the Fermi energy, involving peripheral nucleon exchange, suggest that both the N/Z of the projectile and the NIZ of the target may properly be exploited in the production of neutron-rich rare isotopes. These reactions offer a novel and attractive route to access extremely neutron-rich rare isotopes toward the the astrophysical r-process path and, possibly, the neutron drip-line. [ABSTRACT FROM AUTHOR]

The critical phenomenon 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 that the system is in the regime of a first-order phase transition. The relation m?=?-∂F/∂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. In the present work, it is shown that the external field is primarily related to the minimum of the free energy, which implies a modification of the source concentration Δ used in isospin studies. [ABSTRACT FROM AUTHOR]

The transverse flow and relative midrapidity yield of isotopically identified light charged particles (LCPs) has been examined for the 35 MeV/nucleon 70Zn + 70Zn, 64Zn + 64Zn, and 64Ni + 64Ni systems. A large enhancement of the midrapidity yield of the LCPs was observed relative to the yield near the projectile rapidity. In particular, this enhancement was increased for the more neutron-rich LCPs demonstrating a preference for the production of neutron-rich fragments in the midrapidity region. Additionally, the transverse flow of the LCPs was extracted, which provides insight into the average movement of the particles in the midrapidity region. Isotopic and isobaric effects were observed in the transverse flow of the fragments. In both cases, the transverse flow was shown to decrease with an increasing neutron content in the fragments. A clear inverse relationship between the transverse flow and the relative midrapidity yield is shown. The increased relative midrapidity emission produces a decreased transverse flow. The stochastic mean-field model was used for comparison to the experimental data. The results showed that the model was able to reproduce the general isotopic and isobaric trends for the midrapidity emission and transverse flow. The sensitivity of these observables to the density dependence of the symmetry energy was explored. The results indicate that the transverse flow and midrapidity emission of the LCPs are sensitive to the denisty dependence of the symmetry energy. [ABSTRACT FROM AUTHOR]

A signal of isospin-asymmetric phase transition in the evolution of chemical potential is observed in hot quasi-projectiles produced in the reactions 40,48Ca + 27Al confirming an analogous observation in the lighter quasi-projectiles observed in the reaction 28Si + 112,124Sn.1 With increasing mass, the properties of hot quasi-projectiles become increasingly influenced by secondary emission. Thermodynamical observables exhibit no sensitivity to a different number of missing neutrons in the two reactions 40,48Ca + 27Al and provide a signal of dynamical emission of neutrons, which can be related to a very neutron-rich low-density region (neck) between the projectile and target. [ABSTRACT FROM AUTHOR]

Isoscaling parameters α and β have been explored as a function of breakup angle in binary excited projectile-like fragment decays produced in collisions of 70Zn+70Zn and 64Zn+64Zn at 35 MeV per nucleon. In this analysis, focus was placed on isoscaling the second heaviest fragment with 4≤ZL≤8 emitted from the excited projectile-like fragment in events that contained a heavy fragment with ZH≥12. The breakup orientation θprox was defined as the angle between the heavy and light fragments' center-of-mass velocity and the fragment pairs' relative velocity. Breakups between 0°<θprox≤80° have been shown to be dominated by dynamical contributions, while break-up angles of θprox>100° are predominantly statistical. Historically, isoscaling has often been understood and applied in a statistical context, assuming that the fragments are produced after statistical equilibrium is achieved. Studying isoscaling parameters as a function of θprox reveals the sensitivity of α and β to the mechanism of fragment production. [ABSTRACT FROM AUTHOR]

We study neutron-proton equilibration in dynamically deformed nuclear systems by investigating the correlations between the three largest fragments produced in collisions of 70Zn+70Zn at 35 MeV per nucleon. The rotation angle is interpreted as a measure of the duration of contact between the regions of the excited projectile-like fragment as it decays. In this work we address questions of whether there is a simultaneous or a double rupture scenario, sizing of the fragments, and alignment of the configuration. [ABSTRACT FROM AUTHOR]

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 (α) particles. In such an environment, the α particles interact with each other and, especially through strong resonances, form complex systems such as 8Be and 12C. Our experiments show that 70(64)Zn(64Ni)+70(64)Zn(64Ni) reactions 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 and 100 MeV. We propose a different method to derive the correlation function based on the relative transverse energy distribution to minimize the experimental uncertainties. For the 3α systems, multiresonance 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 components where two different α couples are at relative energies consistent with the ground state of 8Be at the same time. [ABSTRACT FROM AUTHOR]

Previous work has quantified the degree of neutron-proton equilibration in heavy-ion nuclear collisions by observing the convergence of isospin observables (such as the isoscaling parameter a) to an expected value based on similar symmetric reaction systems. We present a new signature of equilibration: the convergence of the isospin asymmetry (as quantified by three isoscaling metrics) of two mirror asymmetric reaction systems toward each other rather than a predefined point. For the reactions of 35 MeV/u 64,70Zn+64,70Zn and 64Zn,64Ni+64Zn,64Ni the neutron-proton equilibration was found to be approximately 80%, and this result is compared directly to previous work. [ABSTRACT FROM AUTHOR]

We study neutron-proton equilibration in dynamically deformed nuclear systems by investigating the correlations between the two largest fragments produced in collisions of 70Zn + 70Zn, 64Zn + 64Zn, 64Ni + 64Ni and 64Zn + 64Ni at 35 MeV per nucleon. The extent of equilibration is investigated using the rotation angle as a clock for the equilibration. The initially dissimilar fragments converge exponentially with consistent rate constants across a wide variety of reaction partners and systems, indicating that the equilibration follows first-order kinetics. [ABSTRACT FROM AUTHOR]

We study neutron-proton equilibration in dynamically deformed atomic nuclei created in nuclear collisions. The two ends of the elongated nucleus are initially dissimilar in composition and equilibrate on a subzeptosecond time scale following first-order kinetics. We use angular momentum to relate the breakup orientation to the time scale of the breakup. The extracted rate constant is 3zs-1, which corresponds to a mean equilibration time of 0.3 zs. This technique enables new insight into the nuclear equation of state that governs many nuclear and astrophysical phenomena leading to the origin of the chemical elements. [ABSTRACT FROM AUTHOR]

We derive the free energy for fermions and bosons from fragmentation data. Inspired by the symmetry and pairing energy of the Weizsäcker 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 α particles is negative and close to the free energy for ideal Bose gases and in perfect agreement with the free energy of an interacting Bose gas under the repulsive Coulomb force. Deuterons behave more similarly to fermions (positive free energy) rather than bosons, which is probably due to their low binding energy. We show that the α-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 α particles at subsaturation densities and finite temperatures. [ABSTRACT FROM AUTHOR]