Effect of the vortex core on the magnetic field in hard superconductors

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.