Statistical theory of multistep compound reactions

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Abstract
We generalize a simple version of the optical background representation for the transition amplitude to the case of well-nested doorways. Using this simple generalization of the optical background representation an alternate statistical theory of multistep compound reactions is suggested, which uses the idea of nested averaging in the case of well-nested doorways and is valid under very general conditions. Simple connections are established between the present approach of multistep compound reactions and that of Feshbach, Kerman, and Koonin, of Agassi, Weidenmüller, and Mantzouranis, and of Hussein and McVoy. The present formulation exhibits the chaining condition of Feshbach, Kerman, and Koonin in the extreme low energy limit, is time reversal symmetric, and yields the Bohr description of compound nuclei in the appropriate limit.