Abstract
Distorted wave theories for a direct reaction amplitude M 12 connecting channels 1 and 2 are usually obtained from the formal theory of scattering by means of a long chain of approximations. Here we consider a version of distorted wave theory which involves just one basic assumption and which can be further approximated to yield all the currently used expressions. We show that this basic assumption, which underlies all the usual theories, leads plausibly to the relation Im M 12=M 12f 11 †+M 12 †f 22, where and f 11 are the elastic scattering amplitudes in the initial and final channels. The result is discussed by means of a simple model of nuclear reactions and also on the basis of a more general theory. The implications of this “truncated unitarity relation” were brought out in an earlier paper, where it was shown to give very stringent conditions for the validity of the distorted wave treatment.
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