Spin-isospin correlated configurations in complex nuclei and neutron skin effect in W$^\pm$ production in high-energy proton-lead collisions

We extend our Monte Carlo generator of global configurations in nuclei to include different spatial distributions of protons and neutrons in heavy nuclei taking into account the difference of spatial correlations between two protons, two neutrons and proton-neutron pairs. These configurations are used for building an event generator for proton-heavy nucleus collisions at the LHC for final states with a hard interaction in the channels where cross section for p-p and p-n scattering differ. Soft interactions are taken into account in the color fluctuation extension of the Glauber algorithm taking into account the inherently different transverse geometry of soft and hard p-N collisions. We use the new event generator to test an interesting observation of Physics Letters B745 (2015) 73-78, that the ratio of W$^+$/W$^-$ production rates in p-Pb collisions should significantly deviate from the inclusive value for peripheral collisions due to the presence of a neutron skin. We qualitatively confirm expectation of Physics Letters B745 (2015) 73-78, though for a realistic centrality trigger, we find the effect to be a factor of two smaller than the original estimate.