The relative current density n(i) of "conduction" neutrons in a neutron star crust beyond the neutron drip threshold can be expected to be related to the corresponding particle momentum covector pi by a linear relation of the form n(i) = K-i j p j in terms of a physically well-defined mobility tensor K-i j. This result is describable as an "entrainment" whose effect-wherever the crust lattice is isotropic-will simply be to change the ordinary neutron mass m to a "macroscopic" effective mass m(*) such that in terms of the relevant number density n of unconfined neutrons we shall have K-i j = (n/m(*))y(i j). In a preceding work based on a independent particle treatment beyond the Wigner-Seitz approximation, using Bloch type boundary conditions to obtain the distribution of energy epsilon(k) and associated group velocity v(k)(i) = a epsilon(k)/ahk(i) as a function of wave vector k(i), it was shown that the mobility tensor would be proportional to a phase space volume integral K-i j proportional to integral d(3) k v (i)(k)v(k)(j) delta {E-k - mu}, where mu is the Fermi energy. Using the approach due to Bogoliubov, it is shown here that the effect of BCS pairing with a superfluid energy gap Delta(F) and corresponding quasiparticle energy function euro(k) = root(E-k - mu)(2) + Delta(F)(2) will just be to replace the Dirac distributional integrand by the smoother distribution in the formula K-i j alpha integral d(3) k v(k)(i) v(k)(j) Delta(F)(2) /euro(k)(3). It is also shown how the pairing condensation gives rise to superfluidity in the technical sense of providing (meta) stability against resistive perturbations for a current that is not too strong (its momentum pi must be small enough to give 2 vertical bar p(i)v(k)(i) < euro(k)(2)/backslash E-k - mu vertical bar for all modes). It is concluded that the prediction of a very large effective mass enhancement in the middle layers of the star crust will not be significantly effected by the pairing mechanism. (c) 2005 Elsevier B.V. All rights reserved.
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