  The magnetic field dependence of the vortex core size in the multi-band
superconductor NbSe2 has been determined from muon spin rotation measurements.
The spatially extended nature of the quasiparticle core states associated with
the smaller gap leads to a rapid field-induced shrinkage of the core size at
low fields, while the more tightly bound nature of the states associated with
the larger gap leads to a field-independent core size for fields greater than 4
kOe. A simple model is proposed for the density of delocalized core states that
establishes a direct relationship between the field-induced reduction of the
vortex core size and the corresponding enhancement of the electronic thermal
conductivity. We show that this model accurately describes both NbSe2 and the
single-band superconductor V3Si.
