Windowed multipole representation of R -matrix cross sections

Journal Article · Mon Jun 14 00:00:00 EDT 2021 · Physical Review. C

DOI:https://doi.org/10.1103/physrevc.103.064610· OSTI ID:1874169

Ducru, Pablo ^[1]; Alhajri, Abdulla ^[2]; Meyer, Isaac ^[2]; Forget, Benoit ^[2]; Sobes, Vladimir ^[3]; Josey, Colin ^[4]; Liang, Jingang ^[5]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Ecole Polytechnique, Palaiseau (France); Tsinghua Univ., Beijing (China)
2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
3. Univ. of Tennessee, Knoxville, TN (United States)
4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
5. Tsinghua Univ., Beijing (China)

Nuclear cross sections are basic inputs to any nuclear computation. Campaigns of experiments are fitted with the parametric R-matrix model of quantum nuclear interactions, and the resulting cross sections are documented—both pointwise and as resonance parameters (with uncertainties)—in standard evaluated nuclear data libraries (ENDF, JEFF, BROND, JENDL, CENDL, TENDL): these constitute our common knowledge of fundamental low-energy nuclear cross sections. In the past decade, a collaborative effort has been deployed to establish a new nuclear cross-section library format—the Windowed Multipole Library—with the goal of considerably reducing the computational cost of cross-section calculations in nuclear transport simulations. This work lays the theoretical foundations underpinning these efforts. From general R-matrix scattering theory, we derive the windowed multipole representation of nuclear cross sections. Though physically and mathematically equivalent to R-matrix cross sections, the windowed multipole representation is particularly well suited for subsequent temperature treatment of angle-integrated cross sections, in particular Doppler broadening, which is the averaging of cross sections over the thermal motion of the target atoms. Doppler broadening is of critical importance in neutron transport applications, as it ensures the stability of many nuclear reactors (negative thermal reactivity). Yet, Doppler broadening of nuclear cross sections has been a considerable bottleneck for nuclear transport computations, often requiring memory-costly pretabulations. We show that the windowed multipole representation can perform accurate Doppler broadening analytically (up to the first reaction threshold), from which we derive cross-section temperature derivatives to any order—all computable on the fly (without precalculations stored in memory). Furthermore, we here establish a way of converting the R-matrix resonance parameters uncertainty (covariance matrices) into windowed multipole parameters uncertainty. We show that generating stochastic nuclear cross sections by sampling from the resulting windowed multipole covariance matrix can reproduce the cross-section uncertainty in the original nuclear data file. The windowed multipole representation is therefore a novel nuclear physics formalism able to generate Doppler broadened stochastic nuclear cross sections on the fly, unlocking breakthrough computational gains for nuclear computations. Through this foundational paper, we hope to make the windowed multipole representation accessible, reproducible, and usable for the nuclear physics community, as well as provide the theoretical basis for future research on expanding its capabilities.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: Consortium for Advanced Simulation of Light Water Reactors; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001; AC05-00OR22725
• OSTI ID: 1874169
• Report Number(s): LA-UR-20-28484
• Journal Information: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 6 Vol. 103; ISSN 2469-9985
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
models and methods for nuclear reactions
neutron physics
nuclear engineering
nuclear many-body theory
nuclear reactions
resonance reactions
thermal statistical models