Boundary S matrix of an open XXZ spin chain with nondiagonal boundary terms

Using a recently proposed solution for an open antiferromagnetic spin-1/2 XXZ quantum spin chain with N (even) spins and two arbitrary boundary parameters at roots of unity, we compute the boundary scattering amplitudes for one-hole states. We also deduce the relations between the lattice boundary parameters appearing in the spin-chain Hamiltonian and the IR (infrared) parameters that appear in the boundary sine-Gordon S matrix.