Effect of BCS pairing on entrainment in neutron superfluid current in neutron star crust Original Research Article

The relative current density ni 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 ni=Kijpj in terms of a physically well-defined mobility tensor Kij. 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 Kij=(n/m⋆)γij. 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 Ek and associated group velocity View the MathML source as a function of wave vector ki, it was shown that the mobility tensor would be proportional to a phase space volume integral View the MathML source, where μ 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 ΔF and corresponding quasiparticle energy function View the MathML source will just be to replace the Dirac distributional integrand by the smoother distribution in the formula View the MathML source. 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 View the MathML source 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.