Effective R-Matrix Parameterizations for Nuclear Data

• Main Authors: Arbanas, Goran, Holcomb, Andrew, Pigni, Marco, Wiarda, Dorothea, Brown, Jesse, Leal, Luiz
• Format: Conference Proceeding
• Language: English
• Subjects: Approximation; Boundary conditions; Covariance matrix; Cross-sections; Eigenvectors; Formalism; Hamiltonian functions; Mathematical analysis; Parameters; Poles; Resonance
• ISSN: 2100-014X; 2101-6275; 2100-014X
• DOI: 10.1051/epjconf/202429404007

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), B c = S c (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].