Effective R-Matrix Parameterizations for Nuclear Data∗

Goran Arbanas; Andrew Holcomb; Marco Pigni; Dorothea Wiarda; Jesse Brown; Luiz Leal

doi:10.1051/epjconf/202429404007

Effective R-Matrix Parameterizations for Nuclear Data^∗

Nuclear Data

Research output: Contribution to journal › Conference article › peer-review

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), B_c = S_c(E),^∗∗∗ are approximately equal to the Rmatrix 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.

Original language	English
Article number	04007
Journal	EPJ Web of Conferences
Volume	294
DOIs	https://doi.org/10.1051/epjconf/202429404007
State	Published - Apr 17 2024
Event	6th International Workshop on Nuclear Data Evaluation for Reactor Applications, WONDER 2023 - Aix-en-Provence, France Duration: Jun 5 2023 → Jun 9 2023

Funding

Useful discussions with Helmut Leeb, Ian J. Thompson, Mark W. Paris, Gerald M. Hale, Zhenpeng Chen, and other INDEN-LE Meeting participants are gratefully acknowledged. This work was supported by the Nuclear Criticality Safety Program, funded and managed by the National Nuclear Security Administration for the US Department of Energy.

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title = "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 Rmatrix parameters in Park{\textquoteright}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{\textquoteright}s observed reduced width amplitudes (RWAs) and their covariance matrix into Brune{\textquoteright}s alternative R-matrix RWAs and their covariance matrix [C. Brune, Phys. Rev. C 66 (2002) 044611]. We extend the Park{\textquoteright}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.",

author = "Goran Arbanas and Andrew Holcomb and Marco Pigni and Dorothea Wiarda and Jesse Brown and Luiz Leal",

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T1 - Effective R-Matrix Parameterizations for Nuclear Data∗

AU - Arbanas, Goran

AU - Holcomb, Andrew

AU - Pigni, Marco

AU - Wiarda, Dorothea

AU - Brown, Jesse

AU - Leal, Luiz

PY - 2024/4/17

Y1 - 2024/4/17

N2 - 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 Rmatrix 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.

AB - 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 Rmatrix 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.

UR - https://www.scopus.com/pages/publications/85212179113

U2 - 10.1051/epjconf/202429404007

DO - 10.1051/epjconf/202429404007

M3 - Conference article

AN - SCOPUS:85212179113

SN - 2101-6275

VL - 294

JO - EPJ Web of Conferences

JF - EPJ Web of Conferences

M1 - 04007

T2 - 6th International Workshop on Nuclear Data Evaluation for Reactor Applications, WONDER 2023

Y2 - 5 June 2023 through 9 June 2023

ER -

Effective R-Matrix Parameterizations for Nuclear Data^∗

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