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[en] Midrapidity nucleon elliptic flow is studied within the Boltzmann-equation simulations of symmetric heavy-ion collisions. The simulations follow a lattice Hamiltonian extended to relativistic transport. It is demonstrated that in the peripheral heavy-ion collisions the high-momentum elliptic flow is strongly sensitive to the momentum dependence of mean field at supranormal densities. The high transverse-momentum particles are directly and exclusively emitted from the high-density zone in the collisions, while remaining particles primarily continue along the beam axis. The elliptic flow was measured by the KaOS Collaboration as a function of the transverse momentum at a number of impact parameters in Bi + Bi collisions at 400, 700, and 1000 MeV/nucleon. The observed elliptic anisotropies in peripheral collisions, which quickly rise with momentum, can only be explained in simulations when assuming a strong momentum dependence of nucleonic mean field. This momentum dependence must strengthen with the rise of density above normal. The mean-field parametrizations, which describe the data in simulations with various success, are confronted with mean fields from microscopic nuclear-matter calculations. Two of the microscopic potentials in the comparisons have unacceptably weak momentum-dependencies at supranormal densities. The optical potentials from the Dirac-Brueckner-Hartree-Fock calculations, on the other hand, together with the UV14 + TNI potential from variational calculations, agree rather well within the region of sensitivity with the parametrized potentials that best describe the data
[en] Studies of dedicated observables in central reactions of heavy nuclei provide significant constraints on nuclear EOS. The EOS of symmetric matter is found to be rather soft at supra normal densities, but not as soft as when assuming, a phase transition at low supra normal densities. In the nearest future, the efforts at EOS determination should aim at providing more stringent constraints on the symmetry energy and at providing ground for the experiments at the forthcoming GSI accelerator
[en] Stopping in heavy ion collisions is investigated with the aim of learning about the shear viscosity of nuclear matter. Boltzmann equation simulations are compared to available data on stopping in the energy range of 20-117 MeV/nucleon. Stopping observables used include momentum anisotropy and linear momentum transfer. The data show that modeling the transport with free nucleon-nucleon cross-sections is inaccurate and reduced cross-sections are required. Reduction of the cross-sections produces an increase in the shear viscosity of nuclear matter, compared to calculations based on free cross-sections.
[en] Energy in nuclear matter is, in practice, completely characterized at different densities and asymmetries, when the density dependencies of symmetry energy and of energy of symmetric matter are specified. The density dependence of the symmetry energy at subnormal densities produces mass dependence of nuclear symmetry coefficient and, thus, can be constrained by that latter dependence. We deduce values of the mass dependent symmetry coefficients, by using excitation energies to isobaric analog states. The coefficient systematic, for intermediate and high masses, is well described in terms of the symmetry coefficient values of aaV = (31.5-33.5) MeV for the volume coefficient and aaS = (9-12) MeV for the surface coefficient. These two further correspond to the parameter values describing density dependence of symmetry energy, of L∼95 MeV and Ksym∼25 MeV
[en] The time-dependent Green's functions formalism provides a consistent description of the time evolution of quantum many-body systems, either in the mean-field approximation or in more sophisticated correlated approaches. We describe an attempt to apply this formalism to the mean-field dynamics of symmetric reactions for one-dimensional nuclear slabs. We pay particular attention to the off-diagonal elements of the Green's functions in real space representation. Their importance is quantified by means of an elimination scheme based on a super-operator cut-off field and their relevance for the global time evolution is assessed. The Wigner function and its structure in the mean-field approximation is also discussed.
[en] Data on stopping in intermediate-energy central heavy-ion collisions are analyzed following transport theory based on the Boltzmann equation. In consequence, values of nuclear shear viscosity are inferred. The inferred values are significantly larger than obtained for free nucleon dispersion relations and free nucleon-nucleon cross sections.
[en] Nuclear equation of state plays an important role in the evolution of the Universe, in supernova explosions and, thus, in the production of heavy elements, and in stability of neutron stars. The equation constrains the two- and three-nucleon interactions and the quantum chromodynamics in nonperturbative regime. Despite the importance of the equation, though, its features had remained fairly obscure. The talk reviews new results on the equation of state from measurements of giant nuclear oscillations and from studies of particle emission in central collisions of heavy nuclei
[en] The dependence of interparticle correlations on the orientation of particle relative momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real Cartesian harmonics. Mathematical properties of the lesser known Cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regard to determining angular features of emission regions is investigated. The considered final-state effects include identity interference, strong interactions, and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of Gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs
[en] Using excitation energies to isobaric analog states (IAS) and charge invariance, we extract nuclear symmetry coefficients, representing a mass formula, on a nucleus-by-nucleus basis. Consistently with charge invariance, the coefficients vary weakly across an isobaric chain. However, they change strongly with nuclear mass and range from aa∼10 MeV at mass A∼10 to aa∼22 MeV at A∼240. Variation with mass can be understood in terms of dependence of nuclear symmetry energy on density and the rise in importance of low densities within nuclear surface in smaller systems. At A≳30, the dependence of coefficients on mass can be well described in terms of a macroscopic volume–surface competition formula with aaV≃33.2 MeV and aaS≃10.7 MeV. Our further investigation shows, though, that the fitted surface symmetry coefficient likely significantly underestimates that for the limit of half-infinite matter. Following the considerations of a Hohenberg–Kohn functional for nuclear systems, we determine how to find in practice the symmetry coefficient using neutron and proton densities, even when those densities are simultaneously affected by significant symmetry-energy and Coulomb effects. These results facilitate extracting the symmetry coefficients from Skyrme–Hartree–Fock (SHF) calculations, that we carry out using a variety of Skyrme parametrizations in the literature. For the parametrizations, we catalog novel short-wavelength instabilities. In our further analysis, we retain only those parametrizations which yield systems that are adequately stable both in the long- and short-wavelength limits. In comparing the SHF and IAS results for the symmetry coefficients, we arrive at narrow (±2.4 MeV) constraints on the symmetry-energy values S(ρ) at 0.04≲ρ≲0.13 fm−3. Towards normal density the constraints significantly widen, but the normal value of energy aaV and the slope parameter L are found to be strongly correlated. To narrow the constraints, we reach for the measurements of asymmetry skins and arrive at aaV=30.2–33.7 MeV and L=35–70 MeV, with those values being again strongly positively correlated along the diagonal of their combined region. Inclusion of the skin constraints allows to narrow the constraints on S(ρ), at 0.04≲ρ≲0.13 fm−3, down to ±1.1 MeV. Several microscopic calculations, including variational, Bruckner–Hartree–Fock and Dirac–Bruckner–Hartree–Fock, are consistent with our constraint region on S(ρ)
[en] In the past variety of codes based on different approaches have been developed to analyze the data obtained by charge exchange reactions. However, in these codes the knock-on exchange contribution is either completely ignored or is approximately considered. Thus here we present the results of (3He, t) charge exchange reaction on 90Zr and 26Mg targets at 140 AMeV energy obtained using the newly developed DCP-2 code (based on earlier version DCP-1 developed by employing distorted wave impulse (DWI) approximation