  Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer
Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a
wavefunction ansatz for strong correlation. This wavefunction physically
represents a mean-field of pairs of electrons (geminals) with a constant
pairing strength. To move beyond the mean-field, one must develop the
wavefunction in the basis of all the RG states. This requires both practical
expressions for transition density matrices and an idea of which states are
most important in the expansion. In this contribution, we present expressions
for the transition density matrix elements and calculate them numerically for
half-filled picket fence models. There are no Slater-Condon rules for RG
states, though an analogue of the aufbau principle proves to be useful in
choosing which states are important.
