  We analyze the ground state of the open spin-1/2 isotropic quantum spin chain
with a non-diagonal boundary term using a recently proposed Bethe ansatz
solution. As the coefficient of the non-diagonal boundary term tends to zero,
the Bethe roots split evenly into two sets: those that remain finite, and those
that become infinite. We argue that the former satisfy conventional Bethe
equations, while the latter satisfy a generalization of the Richardson-Gaudin
equations. We derive an expression for the leading correction to the boundary
energy in terms of the boundary parameters.
