We extend the method introduced recently by Korol for the approximate calcu
lation of the compound relativistic free-free matrix elements. The method i
s based on the accurate treatment of the diagonal singularities in the one-
photon relativistic matrix elements, which appear in the compound matrix el
ement.
For the case of relativistic projectile scattering in the field of a short-
range potential we present the evaluation of the singular parts of the free
-free single-photon matrix elements. The result is used to treat approximat
ely the amplitude of the two-photon bremsstrahlung (2BrS) process for the r
elativistic electron. This is done for the first time.