International Journal of Modern Physics E

The appearance of exotic phases in neutron stars is studied. The possible transition from hadron to quark phase is studied within the density dependent mass quark model, and the kaon condensation within the Nelson and Kaplan model. In both cases a microscopic approach is adopted for dense hadron matter. From the study of the possible coexistence between the two phases it is found that the hybrid phase may strongly hinder the onset of kaon condensation.

In this talk we present a model, Improved Quantum Molecular Dynamics (ImQMD05) model incorporated with a Statistical Decay Model (SDM), to describe intermediate energy proton induced spallation reactions. A good agreement with experimental data of double differential cross sections of emitted neutrons is obtained. We further apply this model to study the isospin effect in proton induced spallation reactions on a series Sn isotope targets. We find that the systematic behavior of the reaction cross sections for Sn isotope targets deviates from the empirical expression obtained by fitting the experimental data for proton induced spallation reactions on target nuclei along β-stability line. The extent of the deviation depends on the density dependence of the symmetry energy strongly. We also find an obvious shift of the elastic scattering angular distribution of emitted protons when the symmetry energy is taken into account for neutron-rich Sn isotope targets and the angle shifted strongly depends on the stiffness of the symmetry energy. The attractive effect of the symmetry potential of target on incident proton directly influences the motion of the incident proton leading to strong isospin effect on the reaction dynamics and thus on these reaction observables. We conclude that the measurement of reaction cross sections and the elastic scattering angular distributions in proton induced spallation reactions on Sn isotopes can provide clear constraint for the density dependence of symmetry energy.

Two principal reaction dynamics are introduced. One is the spin displacement, which is caused from the spin-dependence of the interaction, and the other is the isovector displacement, which is caused from the isospin-dependence of it. The competition of these two dynamics is a rather important factor as the target or projectile has more excess neutrons or protons. In this paper the competitive reaction mechanism is theoretically formulated, where the time-dependent mean field calculations are performed for justification.

We have studied the isospin effect and isoscaling behavior in projectile fragmentation using a modified statistical abrasion-ablation (SAA) model. The relationship between neutron skin thickness (δ_np) and neutron abrasion cross section (σ_nabr) has also been investigated. We find the normalized peak differences and reduced isoscaling parameters decrease with (Z_proj - Z)/Z_proj or the excitation energy per nucleon and have no significant dependence on the size of the reaction systems. The excitation energy dependence of the symmetry energy coefficients are tentatively extracted from α and β. Assuming Fermi-type density distributions for proton and neutron and introducing a parameter to adjust the diffuseness of the neutron density distribution for neutron-rich nucleus, δ_np and σ_nabr for neutron-rich nucleus were found to have a linear correlation. It is suggested that σ_nabr could be used as an observable to extract the neutron skin thickness for neutron-rich nucleus.

Recent experiments performed at GANIL with a crystal blocking technique have shown direct evidences of long fission times in the Super-Heavy Elements (SHE) region. Aimed to localize the SHE island of stability, can these experiments give access to the fission barrier and then to the shell-correction energy? In this paper, we calculate the fission time of heavy elements by using a new code, KEWPIE2, devoted to the study of the SHE. We also investigate the effect of potential structure beyond the saddle on the fission time.

In this paper we present a brief discussion on regular low-lying structures of many-body systems generated from random two-body interactions. In particular, we discuss the famous problem of spin zero ground state dominance, regularities of energy centroids and collectivity in the presence of random interactions.

Isoscaling properties of the primary and final products are studied via isospin dependent quantum molecular dynamics (IQMD) model and the followed sequential decay model GEMINI, respectively. Both primary and final products isoscaling parameter α keeps no significant change for light fragments, but increases with the mass for intermediate and heavy products. The dynamical effect on isoscaling is reflected on the α decreasing a little with the evolution time of the system, and opposite trend for the heavy products. The secondary decay effect on isoscaling is reflected on the increasing of the α value for the final products which experienced secondary decay process. Furthermore the density dependence of the symmetry energy has also been explored for the primary and secondary products, the symmetry energy coefficient can be expressed by the form of C_sym(ρ) ~ C₀(ρ/ρ₀)^γ, C₀ and γ extracted from the primary products are consistent with the input parameters, but C₀ and γ extracted from the final products deviate the input values. In the paper we also suggest that it might be more reasonable to describe the density dependence of the symmetry energy coefficient by the C_sym(ρ/ρ₀) ≈ C₁(ρ/ρ₀)^γ_soft + C₂(ρ/ρ₀)^γ_stiff with γ_soft ≤ 1, γ_stiff ≥ 1 and C₁, C₂ constant parameters.

The hyperon density dependence (YDD) of hyperon-nucleon interactions are studied in the relativistic mean field (RMF) model and their influences on the properties of neutron stars are studied. The extended RMF considered the interior quarks coordinates of hyperon and bring a hyperon density dependent factor, f(ρ_Y), to the meson-hyperon coupling vertexes. The hyperon density dependence of YN interaction affect the properties of neutron stars only after the corresponding hyperon appears. Then, the influences of the density dependence factors are almost ignored at low densities, which are clear at high densities. The compositions and properties of neutron stars are studied with and without the YDD of YN interactions for the different Σ^--nucleus effective potentials, (30, 0, -30)MeV. The calculated results indicated that the YDD of YN interaction soften the equation of state of neutron stars at high densities.

The halo structures in some light nuclei are investigated systemically with the nuclear asymptotic normalization coefficient (ANC) method and the relativistic mean-field (RMF) theory. Some important results about the halo structures in mirror nuclei are obtained, and some qualitative analyses are made to explore the role of Coulomb effects on the formation of proton halo nuclei.

From a serious inconsistency between theory and observations for the mass of hyperon-mixed neutron stars (NSs), it is stressed that some "extra repulsion" is missing in hypernuclear systems and three-body force repulsion is tested for the cases with phenomenological Illinoi's type, 2π-exchange via Δ-excitation type(2πΔ) and string-junction quark model(SJM). It is remarked that the "extra repulsion" should have a nature to act universally, i.e., independent of baryon species. The SJM three-body repulsion can meet the condition because of flavor-independence and {2πΔ+SJM} scheme is shown to be a promising candidate for the "extra repulsion". Occurence of Λ and Σ^- superfluidities are shown also by a realistic approach, which importantly supports the idea of nonstandard fast "hyperon cooling" scenario to explain colder class NSs. However, less attractive ΛΛ interaction suggested by the "NAGARA event" leads to the disappearance of Λ superfluidity and the breaking down of the scenario. In this connection, the revival of "Λ superfluidity" due to ΛΣ^- pairing instead of ΛΛ one is discussed in a new scheme of "bubble shell" hypothesis where the matching of two different Fermi surfaces is forced.

The strangeness production in heavy ion collisions was proposed to be probes of the nuclear equation of state, Kaon potential in nuclear medium, strange quark matter and quark-gluon plasma, etc. However, to act as reliable probes, proper understanding of the basic ingredients for the strangeness production, such as pp → pK⁺Λ, pp → ppϕ and pp → nK⁺Σ⁺ is necessary. Recent study of these reactions clearly shows that previously ignored contributions from the spin-parity 1/2^- resonances, N*(1535) and Δ*(1620), are in fact very important for these reactions, especially for near-threshold energies. It is necessary to include these contributions for getting reliable calculation for the strangeness production in heavy ion collisions.

The microscopic properties and superfluidity of the inner crust in neutron stars are investigated in the framework of the relativistic mean field(RMF) model and BCS theory. The Wigner-Seitz(W-S) cell of inner crust is composed of neutron-rich nuclei immersed in a sea of dilute, homogeneous neutron gas. The pairing properties of nucleons in the W-S cells are treated in BCS theory with Gogny interaction. In this work, we emphasize on the choice of the boundary conditions in the RMF approach and superfluidity of the inner crust. Three kinds of boundary conditions are suggested. The properties of the W-S cells with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree-Fock-Bogoliubov(HFB) models are compared.

We investigate the non-uniform structures and the equation of state (EOS) of nuclear matter in the context of the first-order phase transitions (FOPT) such as liquid-gas phase transition, kaon condensation, and hadron-quark phase transition. During FOPT the mixed phases appear, where matter exhibits non-uniform structures called "Pasta" structures due to the balance of the Coulomb repulsion and the surface tension between two phases. We treat these effects self-consistently, properly taking into account of the Poisson equation and the Gibbs conditions. Consequently, they make the EOS of the mixed phase closer to that of Maxwell construction due to the Debye screening. This is a general feature of the mixed phase consisting of many species of charged particles.

Results from particle correlation measured in heavy-ion collision experiments are shown. Information about dynamics of the reaction as well as and spectroscopy of unbound nuclear systems can be extracted, offering important opportunities for future experiments with exotic nuclear beams.

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this work we present a selection of reaction observables in dissipative collisions particularly sensitive to the isovector part of the interaction, i.e.to the symmetry term of the nuclear Equation of State (EoS). At low energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. We will first discuss the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation during the charge equilibration in fusion and deep-inelastic collisions. Important Iso - EOS are stressed. Reactions induced by unstable ¹³²Sn beams appear to be very promising tools to test the sub-saturation Isovector EoS. New Isospin sensitive observables are also presented for deep-inelastic, fragmentation collisions and Isospin equilibration measurements (Imbalance Ratios).

The high density symmetry term can be derived from isospin effects on heavy ion reactions at relativistic energies (few AGeV range), that can even allow a "direct" study of the covariant structure of the isovector interaction in the hadron medium. Rather sensitive observables are proposed from collective flows and from pion/kaon production. The possibility of the transition to a mixed hadron-quark phase, at high baryon and isospin density, is finally suggested. Some signatures could come from an expected "neutron trapping" effect. The importance of studying violent collisions with radioactive beams from low to relativistic energies is finally stressed.

The impact of a δ meson field (the scalar-isovector channel) on asymmetric nuclear matter is studied within relativistic mean-field (RMF) models with both constant and density dependent (DD) nucleon-meson couplings. The Equation of State (EOS) for asymmetric nuclear matter and the neutron star properties by the different models are compared. We find that the δ-field in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses, finally influencing the stability of the neutron stars. A broader analysis of possible δ-field effects is achieved considering also density dependent nucleon-meson coupling. A remarkable effect on the relation between mass and radius for the neutron stars is seen, showing a significant reduction of the radius along with a moderate mass reduction due to the increase of the effective δ coupling in high density regions.

We review recent progress in the determination of the subsaturation density behavior of the nuclear symmetry energy from heavy-ion collisions as well as the theoretical progress in probing the high density behavior of the symmetry energy in heavy-ion reactions induced by high energy radioactive beams. We further discuss the implications of these results for the nuclear effective interactions and the neutron skin thickness of heavy nuclei.

The N/Z dependence of projectile fragmentation at relativistic energies has been studied in a recent experiment at the GSI laboratory with the ALADiN forward spectrometer coupled to the LAND neutron detector. Besides a primary beam of ¹²⁴Sn, also secondary beams of ¹²⁴La and ¹⁰⁷Sn delivered by the FRS fragment separator have been used in order to extend the range of isotopic compositions of the produced spectator sources. With the achieved mass resolution of ΔA/A ≈ 1.5%, lighter isotopes with atomic numbers Z ≤ 10 are individually resolved. The presently ongoing analyses of the measured isotope yields focus on isoscaling and its relation to the properties of hot fragments at freeze-out and on the derivation of chemical freeze-out temperatures which are found to be independent of the isotopic composition of the studied systems. The latter result is at variance with the predictions for limiting temperatures as obtained with finite-temperature Hartree-Fock calculations.

Anisotropic flows of light nuclear clusters and hard photons are studied by nucleonic transport models in intermediate energy heavy ion collisions. The transverse momentum and rapidity dependences of the directed flow (v₁) and elliptic flow (v₂) are studied for light nuclear clusters and their scaling behaviors are found. The ratio of of nuclear clusters show a constant value of 1/2. Proton-neutron bremsstrahlung hard photon shows non-zero flows with the contrary sign of proton's flows.

The threshold energies of radial flow in central collisions are investigated within an isospin dependent quantum molecular dynamics model using three different forms of symmetry energy. It is found that the neutron-rich system had smaller threshold energy of radial flow and this quantity depends on the form of symmetry potential. It indicates that the threshold energy of radial flow can provide a new method to determine the symmetry energy of asymmetric nuclear matter.

The recently measured spin distribution of evaporation residue cross section in the reaction ¹⁶O + ¹⁸⁴W is studied in the framework of Langevin equations. Results show that the Langevin approach can describe this observable very well. Moreover, a pre-saddle nuclear viscosity coefficient of 5 × 10²¹ s^-1 is extracted by comparing theoretical calculations with experimental data. We also explore the effect of the isospin of a system on the spin distribution by evaluating the evaporation residue spin distribution of nuclei ¹⁹⁴Pb, ²⁰⁰Pb and ²⁰⁶Pb. It has been found that with increasing the isospin of the system, the sensitivity of the evaporation residue spin distribution to the nuclear viscosity is decreased significantly. This result suggests that choosing a low-isospin compound system favors an accurate determination of pre-saddle dissipation strength.

Thermodynamical properties of nuclear matter at sub-saturation densities were investigated using a simple van der Waals-like equation of state with an additional term representing the symmetry energy. First-order isospin-asymmetric liquid-gas phase transition appears restricted to isolated isospin-asymmetric systems while the symmetric systems will undergo fragmentation decay resembling the second-order phase transition. The density dependence of the symmetry energy scaling with the Fermi energy satisfactorily describes the symmetry energy at sub-saturation nuclear densities. The deconfinement-confinement phase transition from the quark-gluon plasma to the confined quark matter appears in the isolated systems continuous in energy density while discontinuous in quark density. A transitional state of the confined quark matter has a negative pressure and after hadronization an explosion scenario can take place which can offer explanation for the HBT puzzle as a signature of the phase transition.

The first order self-energy corrections of the kaon in the symmetric nuclear matter are calculated from kaon-nucleon scattering matrix elements using a chiral Lagrangian within the framework of relativistic mean field approximation. It shows that the effective mass and the potential of K⁺ meson are identical with those of K^- meson in the nuclear matter, respectively. The effective mass of the kaon in the nuclear matter decreases with the nuclear density increasing, and is not relevant to the kaon-nucleon Sigma term. The kaon-nucleus potential is positive and increases with the nuclear density. Moreover, the influence of the resonance Λ(1405) on the K^--nucleus potential due to the re-scattering term is discussed. Our results indicate the K^- meson could not be bound in the nuclei even if the contribution of Λ(1405) resonance is considered.

It is believed that quark matter can exist in neutron star interior if the baryon density is high enough. When there is a large isospin density, quark matter could be in a pion condensed phase. We compute neutrino emission from direct Urca processes in such a phase, particularly in the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states. The neutrino emissivity and specific heat are obtained, from which the cooling rate is estimated.

The liquid-gas phase transition in hot neutron-rich nuclear matter is investigated within a self-consistent thermal model using different interactions with or without isospin and/or momentum dependence. The boundary of the phase-coexistence region is shown to be sensitive to the density dependence of the nuclear symmetry energy as well as the isospin and momentum dependence of the nuclear interaction.

The fragment cross sections are calculated for reactions of Ne collisions with C, Al, Cu, Sn, Ta, and Pb targets at 600 Mev/nucleon using the the isospin-dependent Boltzmann-Langevin equation. We found that the production cross sections for fragments Z = 2 to 9 are qualitatively reproduced by the present calculations except for C target. In order to understand the effects of heavy ion interaction with biomolecules well, we calculate the fragmentation cross sections for reactions of ¹²C + ²H, ¹²C, ¹⁴N, ¹⁶O at beam energies from 50 to 100 MeV/nucleon. It is found that fragment species increase approximately with increasing target mass. The obvious increment of the fragment cross sections for heavier targets at the beam energies from 50 to 80 MeV/nucleon are shown.

Based on a modified di-nuclear system model in which the nucleon transfer is coupled with the dissipation of energy and angular momentum, the isotopic dependence and the orientation (between the target and the projectile) effects on the evaporation residue cross section for synthesizing super-heavy nuclei are investigated. The calculated results indicate that the cross sections shows an odd-even effect and does not change much with increasing neutron number of the target. The influences of deformation and relative orientation of the projectile and target are also discussed. Our results show that the waist to waist orientation is in favor of the formation of super-heavy compound nuclei.

We have investigated the ground-state properties of odd-Z superheavy isotopes with even neutron numbers in previous article (Phys. Rev. C67 064302 (2003)). In this work we extend the previous researches to the ground-state properties of odd-Z isotopic chains with odd neutron numbers. This covers the isotopic chains with Z = 109 - 115 which are current interests of experiments. The ground state properties of these odd-Z superheavy nuclei have been systematically calculated by deformed relativistic mean-field model (RMF) with two sets of force parameters TMA and NL-Z2. The theoretical results from the RMF model are compared with those from the Skyrme-Hartree-Fock model (SHF). The binding energies of two models are in good agreement with each other, but the quadrupole deformations show model dependence in some mass regions. The alpha decay energies from the two theoretical models are also compared with recent experimental data, which include three alpha decay chains of superheavy elements 115 and 113. The reasonable agreement shows the validity of the self-consistent mean-field models for superheavy mass region.

The properties of proton resonances in the p and sd shells are studied with a single-particle potential generated by self-consistent-mean field calculations. Besides, we also propose to calculate the proton-nucleus interaction by a double-folding procedure with the density of the daughter nucleus represented by the result of the same mean-field model. Without raising any adjustable parameter, these calculations provide reasonable estimates for the widths of observed proton resonances in light nuclei. The mean-field-based calculation is particularly useful for the predications of the properties of resonances in light exotic nuclei and the direct proton capture reactions of astrophysics.

We describe briefly the effects of the running coupling strength, the current quark mass, the temperature and density on the QCD phase structure and its transition in the framework of Dyson-Schwinger equation approach of QCD. With a simple model, we show that the chiral susceptibility can identify the stability of the vacuum and plays an important role in describing the QCD Phase transition.

The improved isospin dependent quantum molecular dynamics model which includes the shell correction and switch function method is employed to study the synthesis of superheavy nuclei. The shell effect on a fusion process is investigated for ³²S+²⁰⁸Pb system. For heavy reaction systems ⁴⁸Ca+¹⁵⁴Sm and ³²S+²⁰⁸Pb, the theoretical calculations of fusion cross section are in agreement with the experimental data. The nucleus-nucleus interaction potential is also calculated, and compared with the proximity potential as well.

Some considerations are reported, freely inspired from the presentations and discussions during the Beijing Normal University Meeting on the above Subject, held in July 2007. Of course this cannot be a complete summary but just a collection of personal thoughts aroused during the workshop.