Effective R-Matrix Parameterizations for Nuclear Data*

Abstract

We derive an effective Reich-Moore approximation (RMA) of the Wigner-Eisenbud R-matrix formalism parameterized by complex-valued resonance energies and widths; this RMA exactly reproduces the total eliminated cross section. We show that resonance parameters evaluated for a conventional *** boundary conditions (BCs), Bc = Sc(E),are approximately equal to the R-matrix parameters in Park’s formalism by employing a linear approximation of the shift function therein [T.-S. Park, Phys. Rev. C 106 (2021) 064612]. We outline a method for converting Park’s observed reduced width amplitudes (RWAs) and their covariance matrix into Brune’s alternative R-matrix RWAs and their covariance matrix [C. Brune, Phys. Rev. C 66 (2002) 044611]. We extend the Park’s R-matrix formalism into the complex plane by introducing a complex-valued basis set of eigenfunctions of a complex-symmetric (non-Hermitian) Hamiltonian in the R-matrix interior. We observe that its R-matrix resonance energies and widths are directly related to the poles and residues, respectively, of Hwang’s sum-over-poles representation of cross sections [R.N. Hwang, Nucl. Sci. Eng. 96 (1987) 192].