  Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian,
Richardson-Gaudin (RG) states, are used as a variational wavefunction Ansatz
for strongly-correlated electronic systems. These states are geminal products
whose coefficients are solutions of non-linear equations. Previous results
showed un-physical behaviour but in this contribution it is shown that with
only the variational solution for the ground state, all the seniority-zero
states are quite well approximated. The difficulty is in choosing the correct
RG state. The systems studied showed a clear choice and we expect it should
always be possible to reason physically which state to choose.
