Scattering in the Presence of a Reflecting and Transmitting Impurity
  We investigate factorized scattering from a reflecting and transmitting impurity. Bulk scattering is non trivial, provided that the bulk scattering matrix depends separately on the spectral parameters of the colliding particles, and not only on their difference. We show that a specific extension of a boundary algebra encodes the underlying scattering theory. The total scattering operator is constructed in this framework and shown to be unitary. 
M. Mintchev, E. Ragoucy, P. Sorba