Direct Calculation of the Boundary $S$ Matrix for the Open Heisenberg   Chain
  We calculate the boundary $S$ matrix for the open antiferromagnetic spin $1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrix for the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with ``fixed'' boundary conditions. 
M. T. Grisaru, Luca Mezincescu and Rafael I. Nepomechie