The inner crust of neutron stars is supposed to be inhomogeneous and composed
of dense structures (clusters) that are immersed in a dilute gas of unbound
neutrons. Here we consider spherical clusters forming a BCC crystal and
cylindrical rods arranged in a hexagonal lattice. We study the relative motion
of these dense structures and the neutron gas using superfluid hydrodynamics.
Within this approach, which relies on the assumption that Cooper pairs are
small compared to the crystalline structures, we find that the entrainment of
neutrons by the clusters is very weak since neutrons of the gas can flow
through the clusters. Consequently, we obtain a low effective mass of the
clusters and a superfluid density that is even higher than the density of
unbound neutrons. Consequences for the constraints from glitch observations are
discussed.Comment: 13 pages, 12 figures, figures and discussions added. Accepted in
Phys. Rev.
