Validity of the (Z+1) ion-core approximation for deep and shallow levels as studied by the extended energy-loss fine-structure technique

We compare the extended energy-loss fine structures of the 2p with the 3p core level on a cobalt film. The radial distribution functions F(R), obtained by Fourier transforming the fine structures observed above the $L_{23}$(2p) and $M_{23}$(3p) edges, respectively, give different lattice parameters once they are corrected with the same phase shift computed within the (Z+1) ion-core approximation. While for the $L_{23}$ fine-structure analysis the lattice parameter coincides with the crystallographic value within ±0.03 Å, for the $M_{23}$ edge we find a difference which amounts to 0.23 Å. This observation clearly shows that the (Z+1) approximation holds only for deep levels but it fails for shallow levels, suggesting an important relaxation effect from the conduction electrons even in the extended fine-structure regime.