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.