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 to 8 pi and with 'fixed' boundary conditions.