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The i?-matrix theory of nuclear reactions is modified so that (a) the collision matrix can be constructed from the Hamiltonian eigenfunctions and eigenvalues provided by any nuclear-structure calculation for the compound nucleus, (b) the results of an optical-model or coupled-channel-model calculation can be incorporated into the expression for the collision matrix to represent the nonresonant background scattering, and (c) the direct-reaction contribution to the reaction can be separated from the resonant part. The resonance contribution to the R matrix can be evaluated from the compound-nucleus eigenstates on the basis of a truncation approximation or of a projection-operator approximation.

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