The Tamm-Dancoff approximation as the contraction limit of the Richardson-Gaudin equations

A connection is made between the exact eigen states of the level-independent Bardeen-Cooper-Schrieffer (BCS) Hamiltonian and its Tamm-Dancoff Approximation (TDA). This is done by means of a deformation of the quasi-spin algebra, which connects the Bethe Ansatz states with a unique multi-phonon mode of the TDA. The procedure is illustrated with a model describing neutron superfluidity in 56 Fe