Abstract:
The isospin splitting of the nucleon mean field is derived from the Brueckner theory extended to asymmetric nuclear matter. The Argonne V18 has been adopted as bare interaction in combination with a microscopic three body force. The isospin splitting of the effective mass is determined from the Brueckner-Hartree-Fock self-energy: It is linear acording to the Lane ansatz and such that $m^*_n > m^*_p$ for neutron-rich matter. The symmetry potential is also determined and a comparison is made with the predictions of the Dirac-Brueckner approach and the phenomenological interactions. The theoretical predictions are also compared with the empirical parametrizations of neutron and proton optical-model potentials based on the experimental nucleon-nucleus scattering and the phenomenological ones adopted in transport-model simulations of heavy-ion collisions. The direct contribution of the rearrangement term due to three-body forces to the single particle potential and symmetry potential is discussed.

Abstract:
We investigate nucleon mass splitting at finite isospin chemical potential in the frame of the two-flavour Nambu-Jona-Lasinio model. It is analytically proven that in the phase with explicit isospin symmetry breaking, the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.

Abstract:
We investigate nucleon mass splitting at finite isospin chemical potential in the frame of two flavor Nambu--Jona-Lasinio model. It is analytically proved that, in the phase with explicit isospin symmetry breaking the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.

Abstract:
The calculation of transport properties of Fermi liquids, based on the formalism developed by Abrikosov and Khalatnikov, requires the knowledge of the probability of collisions between quasiparticles in the vicinity of the Fermi surface. We have carried out a numerical study of the shear viscosity of pure neutron matter, whose value plays a pivotal role in determining the stability of rotating neutron stars, in which these processes are described using a state-of-the-art nucleon-nucleon potential model. Within our approach medium modifications of the scattering cross section are consistently taken into account, through an effective interaction obtained from the matrix elements of the bare interaction between correlated states. Inclusion of medium effects lead to a large increase of the viscosity at densities larger than $\sim 0.1$ fm^{-3}.

Abstract:
We review the present status of the nucleon effective mass splitting $puzzle$ in asymmetric matter, with controversial predictions within both non-relativistic $and$ relativistic approaches to the effective in medium interactions. Based on microscopic transport simulations we suggest some rather sensitive observables in collisions of asymmetric (unstable) ions at intermediate ($RIA$) energies: i) Energy systematics of Lane Potentials; ii) Isospin content of fast emitted nucleons; iii) Differential Collective Flows. Similar measurements for light isobars (like $^3H-^3He$) could be also important.

Abstract:
We use QCD sum rules for the three point function of a pseudoscalar and two nucleonic currents in order to estimate the charge dependence of the pion nucleon coupling constant coming from isospin violation in the strong interaction. The effect can be attributed primarily to the difference of the quark condensates and . Assuming that the pi0 is a pure isostate we obtain for the splitting between the coupling of proton and neutron to the neutral pion an interval of [0.008 ; 0.023], the uncertainties coming mainly from the input parameters. In order to obtain the coupling to a physical pi0 we have to take pi - eta mixing into account leading to an interval of [0.012 ; 0.037]. The charged pion nucleon coupling is found to be the average of the two neutral ones. Electromagnetic effects are not included.

Abstract:
Based on mean field calculations with Skyrme interactions, we extract a constraint on the isovector effective mass in nuclear matter at saturation density $\rho_0$, i.e., $m_{v}^{\ast}(\rho_0)=(0.77\pm0.03) m$ by combining the experimental data of the centroid energy of the isovector giant dipole resonance (IVGDR) and the electric dipole polarizability in $^{208}$Pb. Meanwhile, the isoscalar effective mass at $\rho_0$ is determined to be $m_{s}^{\ast}(\rho_0)=(0.91\pm0.05) m$ by analyzing the measured excitation energy of the isoscalar giant quadrupole resonance (ISGQR) in $^{208}$Pb. From the constrained $m_{s}^{\ast}(\rho_0)$ and $m_{v}^{\ast}(\rho_0)$, we obtain the isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry $\delta$ at $\rho_0$ as $(m_n^{\ast}(\rho_0,\delta)-m_p^{\ast}(\rho_0,\delta))/m = \Delta m^*_1(\rho_0) \delta + O(\delta^3)$ with the linear isospin splitting coefficient $\Delta m^*_1(\rho_0) = 0.33\pm0.16$. Furthermore, the constraints on $m_{v}^{\ast}(\rho)$, $m_{s}^{\ast}(\rho)$ and $\Delta m^*_1(\rho)$ at other densities are obtained from the similar analyses and we find that the $\Delta m^*_1(\rho)$ increases with the density.

Abstract:
In the real-time thermal field theory, the standard expression of shear viscosity for the nucleonic constituents is derived from the two point function of nucleonic viscous stress tensors at finite temperature and density. The finite thermal width or Landau damping is traditionally included in the nucleon propagators. This thermal width is calculated from the in-medium self-energy of nucleon for different possible pion-baryon loops. The dynamical part of nucleon-pion-baryon interactions are taken care by the effective Lagrangian densities of standard hadronic model. The shear viscosity to entropy density ratio of nucleonic component decreases with the temperature and increases with the nucleon chemical potential. However, adding the contribution of pionic component, total viscosity to entropy density ratio also reduces with the nucleon chemical potential when the mixing effect between pion and nucleon components in the mixed gas is considered. Within the hadronic domain, viscosity to entropy density ratio of the nuclear matter is gradually reducing as temperature and nucleon chemical potential are growing up and therefore the nuclear matter is approaching toward the (nearly) perfect fluid nature.

Abstract:
Within a relaxation time approach using free nucleon-nucleon cross sections modified by the in-medium nucleon masses that are determined from an isospin- and momentum-dependent effective nucleon-nucleon interaction, we investigate the specific shear viscosity ($\eta/s$) of neutron-rich nucleonic matter near its liquid-gas phase transition. It is found that as the nucleonic matter is heated at fixed pressure or compressed at fixed temperature, its specific shear viscosity shows a valley shape in the temperature or density dependence, with the minimum located at the boundary of the phase transition. Moreover, the value of $\eta/s$ drops suddenly at the first-order liquid-gas phase transition temperature, reaching as low as $4\sim5$ times the KSS bound of $\hbar/4\pi$. However, it varies smoothly for the second-order liquid-gas phase transition. Effects of the isospin degree of freedom and the nuclear symmetry energy on the value of $\eta/s$ are also discussed.

Abstract:
In this talk I report my recent study on the shear viscosity of neutron-rich nuclear matter from a relaxation time approach. An isospin- and momentum-dependent interaction is used in the study. Effects of density, temperature, and isospin asymmetry of nuclear matter on its shear viscosity have been discussed. Similar to the symmetry energy, the symmetry shear viscosity is defined and its density and temperature dependence are studied.