Vol.24,

The symmetry energy at the time of the production of intermediate mass fragments (IMFs) is studied using experimentally observed IMF multiplicities combined with quantum statistical model calculations (QSM of Hahn and Stöcker). The ratios of difference in chemical potentials between neutrons and protons relative to the temperature, (μn−μp)/T, and the double ratio temperature, T, were extracted experimentally in the reactions of ^64,70Zn, ⁶⁴Ni+^58,64Ni, ^112,124Sn, ¹⁹⁷Au, ²³²Th at 40A MeV. The extracted (μn−μp)/T scales linearly with δ_NN, where δ_NN is the asymmetry parameter, (N–Z)/A, of the emitting source and (μn−μp)/T=(11.1±1.4)δNN−0.21 was derived. The experimentally extracted (μn−μp)/T and the double ratio temperatures are compared with those from the QSM calculations. The temperatures, T, and densities, ρ, extracted from the (μn−μp)/T values agreed with those from the double ratio thermometer which used the yield ratios of d, t, h and α particles. However the two analyses of the differential chemical potential analysis and the initial temperature analysis end up almost identical relation between T and ρ. T=5.25±0.75 MeV is evaluated from the (μn−μp)/T analysis, but no density determination was possible. From the extracted T value, the symmetry energy coefficient E_sym=14.6±3.5 MeV is determined for the emitting source of T=5.25±0.75 MeV.

806

An improved isospin dependent Boltzmann Langevin model, in which the inelastic channels and momentum dependent interactions are incorporated, is used to investigate the high-density behavior of nuclear symmetry energy. By taking several forms of nuclear symmetry energy, we calculate the time evolutions of neutron over proton ratio, π multiplicity and π−/π+ ratio, and the kinetic energy and transverse momentum spectra of π−/π+ ratio in the heavy ion collisions at 400A MeV. It is found that the neutron over proton ratio and π−/π+ ratio are very sensitive to the nuclear symmetry energy, and the π^– is more sensitive to the nuclear symmetry energy than the π⁺. A supersoft symmetry energy results in a larger π−/π+ ratio.

522

A new version of improved quantum molecular dynamics model that includes standard Skyrme interactions has been developed. Based on the new code, four commonly used parameter sets, SLy4, SkI2, SkM^* and Gs are adopted in the improved quantum molecular dynamics model and the isospin sensitive observables, namely isospin transport ratios, single and double ratios of the yields of neutrons and protons are investigated. The isospin transport ratios are strongly sensitive to the slope of symmetry energy, and are not very sensitive to the nucleon effective mass splitting. On the other hand, the high energy neutrons and protons yields ratios from reactions at different incident energies provide a good observable to the momentum dependence of nucleon effective mass splitting. By comparing our calculations with the data, we find that the constrained L value (the slope of density dependence of symmetry energy) is about ~46 MeV when the Skyrme type interaction is considered in transport models, and the isospin diffusion data prefer to mn*>mp*, but it is not a strong constraint with deep χ² minimum.

537

Two different isospin splittings of nucleon effective mass in nuclear medium as the form of mn*>mp* and mn*<mp* have been implemented in an isospin and momentum dependent transport model. Their impacts on the isospin emission in heavy-ion collisions is investigated thoroughly. It is found that the yield ratios of energetic neutrons to protons squeezed out during the compression stage of two colliding nuclides are sensitive to the isospin splitting. The elliptic flows of free nucleons are also to be promising observables for extracting the nucleon effective mass splitting. Further experimental measurements are being expected, in particular at the CSR-CEE platform in Lanzhou. Several observables are proposed for constraining the density dependence of symmetry energy, such as the transverse flow difference of neutrons and protons, double ratios of n/p and π⁻/π⁺, excitation functions of π⁻/π⁺ and K⁰/K⁺.

746

The equation of state of symmetric nuclear matter is studied with an equivalent mass model. The equivalent mass of a nucleon has been expanded to order 4 in density. We first determine the first-order expansion coefficient in the quantum hadron dynamics, then calculate the coefficients of the second to fourth order for the given binding energy and incompressibility at the normal nuclear saturation density. It is found that there appears a density isomeric state if the incompressibility is smaller than a critical value. The model dependence of the conclusion has also been checked by varying the first-order coefficient.

668

We calculated the nucleon self-energies in iso-spin asymmetric nuclear matter and obtained the nuclear symmetry energy by taking difference of these of neutron and proton. We find that the scalar (vector) self-energy part gives a negative (positive) contribution to the nuclear symmetry energy, consistent with the result from relativistic mean-field theories. Also, we found exact four-quark operator product expansion for nucleon sum rule. Among them, twist-4 matrix elements which can be extracted from deep inelastic scattering experiment constitute an essential part in the origin of the nuclear symmetry energy from QCD. Our result also extends early success of QCD sum rule in the symmetric nuclear matter to the asymmetric nuclear matter.

607

767

The eigen-frequencies of the axial w-modes of neutron star described by a super-soft equation of state (EOS) are investigated, by considering the non-Newtonian gravity. The results show that at the same stellar mass, the frequencies of w_I and w_I2 for our model are lower than that of the typical EOSs (such as APR); and the frequencies increase with the stellar masses, which is contrary to that of the typical EOSs. These characters may provide a probe to testify the super soft symmetry energy and the non-Newtonian gravity in the future. Moreover, our model also has the universal behavior of the mass-scaled eigen-frequencies as a function of the compactness.

537

By extending the minimum spanning tree (MST) clusterization algorithm for the binding energy cut, the isospin asymmetry dependence of directed flow for isospin sensitive isobar pairs (neutrons-protons, ³H-³He) is studied from low towards high incident energies. The modified clusterization method (MSTB) has the advantage to identify the fragments at quite early time. It enhances (reduces) the production of free nucleons (fragments) over MST method. The directed flow of isobaric pair ³H-³He is more sensitive towards isospin asymmetry caused by MSTB than isobaric pair n-p. This sensitivity becomes quite strong towards the high incident energy and neutron-rich reaction system. In conclusion, the inclusion of binding energy in clusterization method for the flow studies has been uniquely important for understanding the isospin physics, especially for high density behavior of symmetry energy.

664

In this work we study the symmetry-energy coefficient of neutron-rich nuclei, and the temperature dependence of nuclear symmetry energy at low temperatures. An isobaric method is used to extract the symmetry-energy coefficients of neutron-rich nucleus (a_sym) at zero temperature (T) and a_sym/T at nonzero temperature in the measured 1A GeV ^124,136Xe+Pb reactions. T of fragment is obtained from the ratio of its a_sym to a_sym/T. The results show that, for fragment with the same neutron-excess (I=N‒Z), the heavier the fragment is, the higher T it has, and T tends to saturate around 1 MeV for the large mass fragments. It is also shown that the more neutron-rich the isobar is, the higher temperature it has. The T² dependence of symmetry energy of finite nucleus at low temperatures is verified by the extracted results.

602

An experimental method was used to evaluate the primary isotope yields of semi-central collisions in the reaction system ⁶⁴Zn+¹¹²Sn at 40A MeV. The characteristic nature of the hot nuclear matter at the time of the isotope formation was studied. The multiplicities of light particles (LPs) associated with intermediate mass fragments (IMFs) were determined experimentally by using a kinematical focusing technique. The primary isotope distributions, reconstructed by a Monte Carlo method, were compared with those of the AMD-Gemini simulations. a_c/T=0.11 and a_sym/T=3.34 were extracted from the reconstructed primary fragments yield. These are consistent with those of the primary fragments of the AMD simulation.

535

A novel method to determine the density and temperature of a system constituted by fermions and/or bosons is proposed based on quantum fluctuations. For fermions system, the results in the limit where the reached temperature T is small and where there is no constraint for the reached temperature T compared to the Fermi energy εf at a given density ρ are given, respectively. Quadrupole and multiplicity fluctuation relations are derived in terms of T/εf. We compared the two set results in the limit when T is much smaller compared to Fermi energy εf and they are consistent, as expected. The classical limit is also obtained for high temperatures and low densities. For bosons system, quadrupole and multiplicity fluctuations using Landau's theory of fluctuations near the critical point for a Bose-Einstein condensate (BEC) at a given density ρ are derived. As an example, we apply our approach to heavy ion collisions using the Constrained Molecular Dynamics model (CoMD) which includes the fermionic statistics. The multiplicity fluctuation quenching for fermions is found in the model and confirmed by experimental data. To reproduce the available experimental data better, we propose a modification of the collision term in the approach to include the possibility of α−αcollisions. The relevant Bose-Einstein factor in the collision term is properly taken into account. This approach increases the yields of bosons relative to fermions closer to data. Boson fluctuations become larger than one as expected.

691

The temperature of fragmenting source in central heavy-ion collisions at Fermi energy is investigated by the isospin-dependent quantum molecular dynamics model in combination with the statistical decay model GEMINI. Five different nuclear thermometers are used to extract nuclear temperature. We find that the He and Li isotope temperature reaches a plateau at about 70–100 MeV/nucleon of beam energy. The slope temperature and the quadrupole fluctuation temperature give high values. The quantum slope temperature and the quantum quadrupole fluctuation temperature are more close to the He and Li isotope temperatures.

612

468

The work is devoted to the implementation of the hydrodynamic laws to the head-on heavy ion collisions within the energy range 50–100 MeV/A. The hydrodynamic mechanisms of the bubble and ring structures formation are investigated. It is shown that there is a possible hydrodynamic explanation of the different structures being formed in the case of soft (K=200 MeV) and stiff (K=400 MeV) equations of state. Within the suggested approach the final geometry of the system is defined in the initial stage of the collision and is very dependent on the sound velocity in the nuclear matter. The obtained results are in a good correspondence with the Boltzmann-like transport theory calculations and the experimental data for the selected energy range.

612

The experimental data concerning the ⁵⁸Ni+⁴⁸Ca reaction at E_lab(Ni)=25A MeV, collected by using the CHIMERA 4π device, have been analyzed in order to investigate the competition among different reaction mechanisms for central collisions in the Fermi energy domain. As a main criterion for centrality selection we have chosen the flow angle (ϑ_flow) method, making an event-by-event analysis that considers the shape of events, as it is determined by the eigenvectors of the experimental kinetic-energy tensor. For the selected central events (ϑ_flow>60°) some global variables, good to characterize the pattern of central collisions have been constructed. The main features of the reaction products were explored by using different constraints on some of the relevant observables, like mass and velocity distributions and their correlations. Much emphasis was devoted, for central collisions, to the competition between fusion-evaporation processes with subsequent identification of a heavy residue and a possible multifragmentation mechanism of a well defined (if any) transient nuclear system. Dynamical evolution of the system and pre-equilibrium emission were taken into account by simulating the reactions in the framework of transport theories. Different approaches have been envisaged (dynamical stochastic BNV calculations + sequential SIMON code, QMD, CoMD, etc.). Preliminary comparison of the experimental data with BNV calculations shows reasonable agreement with the assumption of sequential multifragmentation emission in the mass region of IMFs close to the heavy residues. Possible deviations from sequential processes were found for those IMFs in the region of masses intermediate between the mass of heavy residues and the mass of light IMFs. Further simulations are in progress. The experimental analysis will be enriched also by information obtained inspecting the IMF–IMF correlation function, in order to elucidated the nature of space-time decay property of the emitting source associated with events having the largest IMF multiplicity.

489

Two-proton radioactivity from ¹⁸Ne is discussed in terms of sequential decay. The branch ratios for one-proton emission from excited states are calculated, which including spectroscopic factors, obtained from a Shell-model calculation with realistic interactions. The branch ratios show that the two-proton emission from the 1^- state of ¹⁸Ne at 7.94 MeV is most likely to go through the sequential decay. The same mechanism is discussed for other excited states at higher energy by different interactions.

550

Recently, we analyze the α-decay data of even-Z nuclei and propose the new Geiger-Nuttall law where the effects of the quantum numbers of α-core relative motion are naturally embedded in the law [Physical Review C 85, 044608 (2012)].In this paper, we firstly test whether the new law without any change of parameters can be applied to the α-decays of odd-Z nuclei which are more complicated than those of even-even nuclei. Then the nuclear shell effect around N=126 is analyzed for very proton-rich nuclei with Z=85–92 based on the data of α-decay energies and half-lives. A long-lived island beyond the stable line is proposed where the half-lives of nuclei on this island are abnormally long. The mechanism of the appearance of the island and its significance to other mass ranges are discussed.

665

We discuss a hardship in synthesis of heaviest super heavy elements in massive nuclei reactions due to the hindrance to complete fusion of reacting nuclei caused on the onset of quasifission process which strongly competes with complete fusion and due to the strong increase of fission yields along the de-excitation cascade of the compound nucleus in comparison with the evaporation residue formation. The hindrance to formation of compound nucleus and evaporation residue is determined by the characteristic of the entrance channel.

594

The nuclear dynamical deformation, the fusion probability and the evaporation residue (ER) cross sections for the synthesis of superheavy nuclei are studied with the di-nuclear system model and the related dynamical potential energy surface. The intrinsic energy and the maximum dynamical deformations for ⁴⁸Ca+²⁴⁸Cm are calculated. The effect of dynamical deformation on the potential energy surface and fusion is investigated. It is found that the dynamical deformation influences the potential energy surface and fusion probability significantly. The dependence of the fusion probability on the angular momentum is investigated. The ER cross sections for some superheavy nuclei in ⁴⁸Ca induced reactions are calculated and it is found that the theoretical results are in good agreement with the experimental results.

675

We study in the framework of the Langevin model the influence of initial excitation energy (E^*) of Hg compound nuclei (CNs) on the sensitivity of the excitation energy at scission (Esc*) to the nuclear friction strength (β). It is shown that the sensitivity is enhanced substantially with increasing E^*. Moreover, we find that the significant sensitivity of Esc* to β at high E^* is little affected by a marked difference in the neutron-to-proton ratio of a CN and in its size and fissility. Our findings suggest that, on the experimental side, a measurement of Esc* in energetic proton-induced spallation reactions can provide not only a sensitive but also a robust probe of nuclear dissipation in fission of highly excited nuclei. Further development of a suitable approach to spallation reaction is discussed.

657

We investigate the space-time evolution of the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by Heavy Ion Jet Interaction Generator (HIJING). In order to detect the event-by-event inhomogeneity of the sources, we examine the distribution of the error-inverse-weighted fluctuations, f, between the two-pion Bose-Einstein correlation functions of single and mixed events. We find that the distribution of f becomes wide for the fluctuating initial conditions. The large values of the distribution width and the root-mean-square f_rms are the signatures of the hydrodynamic particle-emitting sources with the fluctuating initial conditions.

475

The hadron-quark phase transition is studied with the newly constructed Hadron–Poyakov-Nambu– Jona-Lasinio (PNJL) model. Particularly, in the description of quark matter, we include the isoscalar-vector interaction. With the constraints of neutron star observations, our calculation shows the isoscalar-vector interaction between quarks is indispensable if massive hybrids star exist in the universe. Its strength determines the onset density of quark matter, and the mass-radius relations of hybrid stars. Also, as a connection with heavy-ion-collision experiments, we discuss the strength of isoscalar-vector interaction and its effect on the signals of hadron-quark phase transition in heavy-ion collisions, such as NICA at JINR-Dubna and FAIR at GSI-Darmstadt.

807

This pilot study was to assess the high temperature and zero baryon density region of quantum chromodynamics (QCD) phase diagram with thermal photon emission, where the nature of QCD phase transition is ambiguous. Based on a (3+1)-D ideal hydrodynamical model to describe macroscopically the collision system, thermal photons emitted from Pb+Pb collisions at 2.76 TeV are investigated. The result reveals that photons from heavy ion collisions at high energy and centrality are possible to distinguish the structure of the hot dense matter, in QGP phase or hadronic phase, thus may provide an approach to explore the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover).

598

We report our recent work on mean-field potential effects on the elliptic flows of matters and antimatters in heavy ion collisions leading to the production of a baryon-rich matter. Within the framework of a multiphase transport (AMPT) model that includes both initial partonic and final hadronic interactions, we have found that including mean-field potentials in the hadronic phase leads to a splitting of the elliptic flows of particles and their antiparticles, providing thus a plausible explanation of the different elliptic flows between p and anti-p, K⁺ and K^–, and π⁺ and π^– observed by the STAR Collaboration in the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC). Using a partonic transport model based on the Nambu-Jona-Lasinio (NJL) model, we have also studied the effect of scalar and vector mean fields on the elliptic flows of quarks and antiquarks in these collisions. Converting quarks and antiquarks at hadronization to hadrons via the quark coalescence model, we have found that the elliptic flow differences between particles and antiparticles also depend on the strength of the quark vector coupling in baryon-rich quark-gluon plasma, providing thus the possibility of extracting information on the latter’s properties from the BES program at RHIC.

535