Effect of BCS pairing on entrainment in neutron superfluid current in neutron star crust
Abstract
The 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^{}=K^{}p_{} in terms of a physically welldefined 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_{})γ^{}. 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^{}∝∫d^{}kvkivkjδ{E_{}μ}, 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 Δ_{} and corresponding quasiparticle energy function €_{}=E^{}+ΔF2 will just be to replace the Dirac distributional integrand by the smoother distribution in the formula K^{}∝∫d^{}kvkivkjΔF2/€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 2p_{}vki<€k2/E_{}μ 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.
 Publication:

Nuclear Physics A
 Pub Date:
 September 2005
 DOI:
 10.1016/j.nuclphysa.2005.05.151
 arXiv:
 arXiv:astroph/0406228
 Bibcode:
 2005NuPhA.759..441C
 Keywords:

 Astrophysics;
 Nuclear Theory
 EPrint:
 30 pages, revised published version