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

Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field