The nuclear mean field plus stare-dependent pairing problem is studied by u
sing the Bethe ansatz method. It is shown that the Hamiltonian can be expan
ded in terms of generators of the infinite-dimensional Lie algebra <(SU(2))
over cap> without central extension. Exact solutions for excited energies a
nd the corresponding eigenstates of the nuclear pairing problem are derived
through the Bethe ansatz equations.