  We present a derivation of a previously announced result for matrix elements
between exact eigenstates of the pairing Hamiltnonian. Our results, which
generalize the well known BCS (Bardeen-Cooper-Schrieffer) expressions for what
is known as 'coherence factors', are derived based on the Slavnov formula for
overlaps between Bethe-ansatz states, thus making use of the known connection
between the exact diagonalization of the BCS Hamiltonian, due to Richardson,
and the algebraic Bethe ansatz. The resulting formula has a compact form after
a suitable parameterization of the Energy plane. Although we apply our method
here to the pairing Hamiltonian, it may be adjusted to study what is termed the
'Sutherland limit' for exactly solvable models, namely where a macroscopic
number of rapidities form a large string.
