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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 theKorepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrixfor the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with``fixed'' boundary conditions.Comment: 29 pages, plain TEX, UMTG-17

Direct calculation of the boundary S-matrix for the open Heisenberg chain