  In this note the notion of infinitesimal scattering matrix is introduced. It
is shown that under certain assumption, the scattering operator of a pair of
trace compatible operators is equal to the chronological exponential of the
infinitesimal scattering matrix and that the trace of the infinitesimal
scattering matrix is equal to the absolutely continuous part of the
infinitesimal spectral flow. As a corollary, a variant of the Birman-Krein
formula is derived. An interpretation of Pushnitski's $\mu$-invariant is given.
