  We calculate the force that pins vortices in the neutron superfluid to nuclei
in the inner crust of rotating neutron stars, relying on a detailed microscopic
description of both the vortex radial profile and the inner crust nuclear
structure. The contribution to the pinning energy from pair condensation is
estimated in the local density approximation with realistic nucleon-nucleon
interactions. The kinetic contribution, not consistently included in previous
approaches, is evaluated in the same approximation, and found to be relevant.
The vortex-nucleus interaction turns out to be attractive for stellar desities
greater than $\sim 10^13 g/cm^3$. In this region, we find values for the
pinning force which are almost one order of magnitude lower than the ones
obtained so far. This has direct consequences on the critical velocity
differences for depinning.
