Microscopic calculation of the pinning energy of a vortex in the inner crust of a neutron star

The inner crust of a cold, nonaccreting neutron star is composed of a lattice of nuclei coexisting with a sea of superfluid neutrons. The interaction between one of the nuclei and a vortex induced by the rotation of a pulsar is calculated microscopically, based on the axially deformed Hartree-Fock-Bogolyubov framework, using effective interactions. The present work extends and improves previous studies in four ways: (i) it allows for the axial deformation of protons induced by the large deformation of neutrons due to the appearance of vortices; (ii) it includes the effect of Coulomb exchange; (iii) it considers the possible effects of the screening of the pairing interaction; and (iv) it improves the numerical treatment. We also demonstrate that the binding energy of the nucleus-vortex system can be used as a proxy to the pinning energy of a vortex and discuss in which conditions this applies. From our results, we can estimate the mesoscopic pinning forces per unit length acting on vortices. We obtain values ranging between 1014 to 1016 dyn/cm, consistent with previous findings.