Neutron density distribution and neutron skin thickness of $^{208}$Pb

We present and discuss numerical predictions for the neutron density distribution of $^{208}$Pb using various non-relativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.