  We study scattering of three equal mass particles in one dimension.
Integrable interactions are synonymous with non-diffractive scattering, meaning
that the set of incoming momenta for any scattering event coincides with the
set of outgoing momenta. A system is integrable if the two particle scattering
matrix obeys the Yang--Baxter equation. Nonintegrable interactions correspond
to diffractive scattering, where the set of outgoing momenta may take on all
values consistent with energy and momentum conservation. Such processes play a
vital role in the kinetics of one dimensional gases, where binary collisions
are unable to alter the distribution function.
  When integrability is broken weakly, the result is a small diffractive
scattering amplitude. Our main result is a simple formula for the diffractive
part of the scattering amplitude, when the violation of the Yang--Baxter
equation is small. Although the derivation is given for delta-function
interactions, the result depends only on the two-particle scattering matrix,
and should therefore also apply to finite-range interactions close to
integrable.
