Structure of theSMatrix in the Presence of a Bound State

Abstract

It is shown that the phase factor associated with the "orthogonality phase shift" due to a bound state should be factored out of the $S$ matrix. A crucial test of this statement is found in a study of the final state interaction of an inelastic process which ends in a channel involving the bound state. If we assume that the sum of the Born series for the $S$ matrix gives a right answer after we separate the effect of the bound state in terms of the orthogonality phase shift, an agreement with Watson's result obtains only when the $S$ matrix has the factored structure.