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

The nucleon thermal width due to pion-baryon loops and its contribution in Shear viscosity