  Richardson-Gaudin states provide a basis of the Hilbert space for strongly
correlated electrons. In this study, optimal expressions for the transition
density matrix elements between Richardson-Gaudin states are obtained with a
cost comparable with the corresponding reduced density matrix elements.
Analogues of the Slater-Condon rules are identified based on the number of
near-zero singular values of the RG state overlap matrix. Finally, a
perturbative approach is shown to be close in quality to a configuration
interaction of Richardson-Gaudin states while being feasible to compute.
