A new efficient multiple-scattering theory is proposed to study XAFS s
pectra, which is based on partitioning method developed by one of the
authors. This method includes important multiple-scatterings in infini
te order, which is similar to the finite path-by-path approach. We als
o obtain some symmetric relations and recurrence formulas of free elec
tron propagators G(LL') to save the storage memory. Some illustrative
examples are shown. For small systems the partial sum convergence is e
asily attained, however the efficiency is not so remarkable compared w
ith the corresponding full multiple scattering calculation The partial
sum convergence is rather slow for large closely packed systems such
as iron crystals, however it is accelerated by use of damping effects
of photoelectron waves; the computation time is only about 5% of that
by the full multiple scattering calculation for a cluster with 27 Fe a
toms. However the damping effects play a minor role for loosely packed
system such as Si crystals.