A Unified Theory of Nuclear Reactions, II

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The effective Hamiltonian method for nuclear reactions described in an earlier paper with the same title, part I, is generalized so as to include all possible reaction types, as well as the effects arising from the identity of particles. The principal device employed, as in part I, is the projection operator which selects the open channel components of the wave function. It is found that the formal structure of part I providing a unified description for direct and compound nuclear reactions including the coupled equation description for direct reactions remains valid in this wider context. A Kapur–Peierls expansion may also be readily obtained. The concept of channel radii is not needed nor is any decomposition of the wave function for the system into angular momentum eigenstates required, so that the expressions for transition amplitudes and widths are invariant with respect to the angular momentum coupling scheme. Since the open channels can only be defined in an asymptotic sense, the corresponding projection operators are not unique. As a consequence the projection operator method has a flexibility which in the first place is consonant with the wide range of phenomena which can occur in nuclear reactions and in the second place can effectively exploit an intuitive understanding of the phenomena. Examples of projection operators are obtained including one which leads to the Wigner–Eisenbud formalism, another which is appropriate for the stripping reaction, and, finally, one which takes the Pauli exclusion principle into account. Note that explicit representations of the projection operators are not required for the development of general formal results but are necessary if, eventually, quantitative calculations are made.