The structure of a vortex in the inner crust of neutron stars is calculated up to density equal to one fourth of the nuclear saturation density, within the framework of quantum mean field theory, taking into account the interaction with the nuclei composing the Coulomb lattice. Vortices are associated with Coopers pairs formed out of single-particle levels of opposite parity and, due to (quantal-size) shell effects, their formation is hindered within the nuclear volume, by an amount that depends on the Fermi energy and on the effective mass associated with the adopted nuclear two-body interaction. When the vortex axis goes through the center of a nucleus, the typical linear rise of the pairing gap away from the vortex axis is delayed by about 8 fm, as compared to the case of a vortex in uniform matter. Also the velocity field is suppressed in a large region close to the interface between the nucleus and the neutron gas. As a consequence, pinning of a vortex on a nucleus leads to a loss of condensation energy, contrary to the predictions of all previous models. This result strongly influences the density dependence of the pinning energy, relevant in the study of glitches. We find that pinning of vortices on nuclei is favoured at low density.
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