Parameterization of Direct and Doorway Processes in R-Matrix Formalism

¹ Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, TN 37831, USA
² OECD Nuclear Energy Agency, Paris, France
³ Rensselaer Polytechnic Institute, Troy, NY 12180, USA
⁴ Naval Nuclear Laboratory, Schenectady, New York 12301-1072, USA

^* e-mail: arbanasg@ornl.gov

Published online: 26 May 2023

Abstract

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.