  Using approximate analytical and new numerical solutions of the conventional
Ginzburg-Landau equations we calculate the small angle neutron scattering
cross-section and the variance of the field distribution as measured by
muon-spin rotation for superconductors with large Ginzburg-Landau parameter
$\kappa$. Our results prove that a proper account of the finite size of the
vortex core is important, even at relatively low fields. This finding provides
a natural explanation for the recently observed field dependence of the CeRu_2
form factor and of the YBa_2Cu_3O_{6.95} penetration depth.
