  The microscopic structure of an isolated vortex line in superfluid neutron
star matter is studied by solving the Bogoliubov-de Gennes equations. Our
calculation, which is the starting point for a microscopic calculation of
pinning forces in neutron stars, shows that the size of the vortex core varies
differently with density, and is in general smaller than assumed in some
earlier calculations of vortex pinning in neutron star crusts. The implications
of this result are discussed
