Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R -matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R -matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R -matrix channel surface . Doorway processes are parameterized by separating the Hilbert space of the interior R -matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R -matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R -matrix parameters is extended to include doorway states. This work suggests how R -matrix formalism could be extended further by adopting the concepts from related reaction formalisms.