Fully consistent semi-classical treatment of vortex-nucleus interaction in rotating neutron stars

We present the first realistic and fully consistent model to study the vortex-nucleus interaction in the inner crust of a rotating neutron star, where a gas of unbound superfluid neutrons threaded by vortex lines coexists with a lattice of neutron-rich nuclei. Within the framework of the local density approximation, the model determines unambiguously the structure and radius of the vortex core along the crust, and takes into account all energy contributions to evaluate the vortex-nucleus configuration with lowest energy. The results show that, quite independent from the pairing interaction used, pinning of vortices on nuclei occurs only in the deepest layers of the crust and even there the average pinning forces are quite weak. If confirmed by complete quantum calculations, such a limited region of weak nuclear pinning may be relevant to the explanation of pulsar glitches.