[Paper Review] Unified Coupled-Channels and Hauser-Feshbach Model Calculation for Nuclear Data Evaluation

Toshihiko Kawano|arXiv (Cornell University)|Jan 17, 2019

Nuclear Physics and Applications4 citations

TL;DR

This paper presents CoH3, a unified nuclear reaction code that integrates coupled-channels optical model and Hauser-Feshbach statistical theory for accurate nuclear data evaluation in the keV to tens of MeV range, especially for deformed nuclei. It employs two distinct methods—generalized transmission coefficients and the Engelbrecht-Weidenmüller transformation—for handling strong channel coupling, with validation showing improved inelastic scattering predictions on 182W compared to other codes.

ABSTRACT

We present an overview of the coupled-channels optical model and the Hauser-Feshbach theory code CoH$_3$, which focuses on the nuclear reaction calculations in the keV to tens of MeV region with special attention to the nuclear deformation. The code consists of three major sections that undertake the one-body potential mean-field theory, the coupled-channels optical model, and the Hauser-Feshbach statistical decay. There are other complementary segments to perform the whole nuclear reaction calculations, such as the direct/semidirect radiative capture process, pre-equilibrium process, and prompt fission neutron emission.

Motivation & Objective

• To develop a comprehensive nuclear reaction code capable of accurately modeling nuclear data for medium to heavy nuclei in the keV to tens of MeV energy range.
• To address the challenge of strong coupling in deformed nuclei, particularly actinides, where standard Hauser-Feshbach models may fail due to collective excitations.
• To implement and compare two advanced methods—generalized transmission coefficients and the Engelbrecht-Weidenmüller transformation—for combining coupled-channels and statistical decay theories.
• To produce detailed reaction observables including cross sections, angular distributions, γ-ray yields, and isomeric state production for evaluated nuclear data files.
• To validate the code’s performance against experimental data and other established codes like EMPIRE and TALYS, particularly for inelastic scattering on deformed targets.

Proposed method

• CoH3 is implemented in C++ with ~200 source files and 80 classes, including a custom ZAnumber class for tracking (Z,A) pairs in reaction chains.
• The code uses a self-contained optical model solver to compute transmission coefficients, with mean-field models (FRDM, HF-BCS, Woods-Saxon) for single-particle wave functions.
• For deformed nuclei, rotational or vibrational coupled-channels models are applied, and the S-matrix is diagonalized via the Engelbrecht-Weidenmüller transformation (EWT) to handle strong coupling.
• Width fluctuation corrections are applied using the Moldauer method with GOE-based parameters, and the correction is performed in eigen-channel space before transforming back to physical channels.
• The Hauser-Feshbach core uses the Gilbert-Cameron level density model and includes pre-equilibrium (two-component exciton model), direct/semidirect capture, and prompt fission neutron emission (via Madland-Nix model).
• Angular distributions are calculated using the Blatt-Biedenharn formalism with Moldauer’s statistical theory, incorporating transmission coefficients and spin-dependent matrix elements.

Experimental results

Research questions

• RQ1 How can coupled-channels effects be consistently merged with the Hauser-Feshbach statistical model in nuclear reaction calculations?
• RQ2 What is the impact of using the Engelbrecht-Weidenmüller transformation versus generalized transmission coefficients on inelastic scattering cross sections in deformed nuclei?
• RQ3 How do the two methods compare in predicting angular distributions and cross sections for neutron-induced reactions on 182W?
• RQ4 To what extent does the inclusion of strong channel coupling improve agreement with experimental data for deformed actinides?
• RQ5 Can the unified CoH3 framework produce reliable, high-fidelity nuclear data including isomeric ratios and γ-ray spectra across multiple reaction channels?

Key findings

• CoH3 successfully combines coupled-channels and Hauser-Feshbach theories using two distinct methods: generalized transmission coefficients and the Engelbrecht-Weidenmüller transformation (EWT).
• For 182W, the EWT method yields significantly higher inelastic scattering cross sections—especially for the first excited state—compared to the generalized transmission coefficient approach, indicating stronger channel coupling effects.
• The EWT method results in larger anisotropy in α-particle emission angular distributions, particularly for (n,α₀) reactions, consistent with experimental observations of enhanced forward peaking.
• The code's predictions for (n,p), (n,α), (n,np), and (n,2n) reactions on 58Ni show good agreement with ENDF/B-VII.1 and JENDL-4.0 evaluated data, as well as experimental measurements.
• The inclusion of pre-equilibrium processes and prompt fission neutron emission improves the accuracy of total and differential reaction cross sections in the MeV region.
• The code’s implementation of eigen-channel diagonalization via EWT is computationally more expensive but necessary for strongly deformed systems where standard HF approximations break down.