We present ab initio calculations of X-ray-absorption fine structure f
or the Re L3 and L1 edges in crystalline ReO3 based-on an exact curved
-wave multiple-scattering approach. We show that (1) the contribution
of multiple-scattering signals from linear chains, like Re - O - Re an
d O - Re - O, is very large both in the L3 and L1-edge spectra due to
the strong focussing effect caused by the middle atom; (2) the geometr
ical dependence of multiple-scattering terms on the final l state lead
s to the additional difference between signals from L3 and L1 edges, e
specially for paths forming a right angle at the absorbing atom; (3) t
he fine structure above L1-edge is a superposition of two signals from
L1 and L2 edges with a very significant contribution of this latter.