We consider the shear viscosity of degenerate dense stellar matter under the conditions appropriate for the neutron star interiors, taking into account the exchange of transverse plasmons. The importance of transverse plasmon exchange was pointed out by Heiselberg and Pethick (1993) in their studies of transport properties of relativistic quark plasma. The exchange of transverse plasmons in collisions of relativistic charged particles (first of all, electrons) can be more efficient than the exchange of longitudinal plasmons (which describes direct Coulomb interaction). The efficiency of the transverse plasmon exchange is a consequence of the dynamical character of plasma screening associated with such an exchange. The screening momentum is proportional to some power of energy exchange and is, therefore, small in degenerate matter (in comparison to the usual Thomas-Fermi screening momentum). Interaction of particles via the exchange of transverse plasmons should be taken into account in all studies of kinetic properties of relativistic plasmas. Recently, we have included this effect in the thermal conductivity of neutron star crust and core (Shternin and Yakovlev, 2006, 2007). Here we consider the shear viscosity. The effect of transverse plasmon exchange strongly reduces the shear viscosity mediated by electron-electron collisions in a neutron star crust. However, this reduction is insufficient, and the shear viscosity remains mainly determined by electron-ion collisions (where the exchange of longitudinal plasmons dominates). In a neutron star core, the effect of transverse plasmon exchange reduces the shear viscosity of electrons and muons mediated by collisions of electrons and muons with charged particles. Its temperature dependence becomes η∝T ^-5/3, in contrast to the standard Fermi-liquid behavior η∝T ^-2. We have also reconsidered the neutron shear viscosity in neutrons star cores, that is governed by strong-interaction scattering of neutrons by neutrons and protons. We have found that the neutron and electron-muon shear viscosities are comparable. We have also taken into account the effects of proton superconductivity in the neutron star core on the shear viscosity. The proton superconductivity affects both neutron and electron-muon shear viscosities. Moreover, the temperature dependence of the electron-muon shear viscosity returns to the standard Fermi-liquid form η_eμ∝T ^-2. Our results are valid for different equations of states of dense matter and can be used in studying various processes in neutron stars.

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