  We investigate the dynamics of a quantized vortex and a nuclear impurity
immersed in a neutron superfluid within a fully microscopic time-dependent
three-dimensional approach. The magnitude and even the sign of the force
between the quantized vortex and the nuclear impurity have been a matter of
debate for over four decades. We determine that the vortex and the impurity
repel at neutron densities, 0.014 fm$^{-3}$ and 0.031 fm$^{-3}$, which are
relevant to the neutron star crust and the origin of glitches, while previous
calculations have concluded that the force changes its sign between these two
densities and predicted contradictory signs. The magnitude of the force
increases with the density of neutron superfluid, while the magnitude of the
pairing gap decreases in this density range.
