  The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with
N sites have solutions containing i/2, -i/2 that are singular: both the
corresponding energy and the algebraic Bethe ansatz vector are divergent. Such
solutions must be carefully regularized. We consider a regularization involving
a parameter that can be determined using a generalization of the Bethe
equations. These generalized Bethe equations provide a practical way of
determining which singular solutions correspond to eigenvectors of the model.
