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

International audienceThe relative current density n 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 p by a linear relation of the form n=Kp in terms of a physically well-defined mobility tensor K. 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=(n/m)gamma. 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 E and associated group velocity vki=∂E/∂ℏk as a function of wave vector k, it was shown that the mobility tensor would be proportional to a phase space volume integral K∝∫dkvkivkjdelta{E-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 and corresponding quasiparticle energy function €=E+DeltaF2 will just be to replace the Dirac distributional integrand by the smoother distribution in the formula K∝∫dkvkivkjDeltaF2/€k3. 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 p must be small enough to give 2|pvki