  Various versions of the Bethe ansatz are suggested for evaluation of
scattering two-magnon states in 2D and 3D Heisenberg-Ising ferromagnets. It is
shown that for 2D square (3D qubic) finite-periodic or infinite lattices about
a half (3/4) of states have a correctly 2D- (3D-) generalized Bethe form. The
remaining scattering states are treated (on the infinite lattices only) within
the degenerative discrete-diffractive modification of the Bethe ansatz
previously suggested by the author.
