Eilenberger theory for nuclear magnetic relaxation rate in superconducting vortex lattice state

On the basis of the Eilenberger theory, spatial variation of the local NMR relaxation rate T-1(-1) is quantitatively estimated in the vortex lattice state, to clarify the differences between the s-wave and the d-wave superconductors. We study the temperature and the magnetic field dependencies of T-1(-1) inside and outside of the vortex core, including influences of nonmagnetic impurity scatterings in the Born limit and in the unitary limit. These results are helpful to detect detailed characters of local electronic structures in the vortex lattice states via site-selective NMR experiments.