I consider thermal conductivity and shear viscosity of electrons and muons in the nucleon NS cores where protons are in the superconducting state. The charged lepton collision frequencies are mainly determined by the transverse plasmon exchange and are mediated by the character of the plasma screening. When protons are in the paired state, they give the dominant contribution to the transverse screening. In previous works [Shternin P.S. & Yakovlev D.G., Phys. Rev. D 75, 103004 (2007); Phys. Rev. D 78, 063006 (2008)] this contribution was considered in the Pippard limit Δ ≪ ℏq v_Fp, where Δ is the proton pairing gap, v_Fp is the proton Fermi velocity, and ℏq is the typical transferred momentum in collisions. However, for large critical temperatures T_cp (large Δ) and relatively small densities in the outer NS cores (small q), the Pippard limit may become invalid. Restricting the consideration for not too high temperatures (T ≪ 0.3 T_cp), when the lepton-proton collisions can be neglected, and employing the BCS expression for transverse screening, I revisit the transport coefficients calculations. It is found that older calculations indeed severely underestimated the screening in a certain range of parameters appropriate to NS core conditions. As a consequence, values of the transport coefficients at T ≪ T_cp are smaller than previously thought.

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