Scattering matrix pole expansions for complex wave numbers in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math>-matrix theory

Ducru, Pablo; Forget, Benoit; Sobes, Vladimir; Hale, Gerald M.; Paris, Mark W.

doi:10.1103/physrevc.103.064609

Cited by 3 publications

(25 citation statements)

References 68 publications

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“…Theorem 1 of [31] presents the branch structure of the radioactive poles E j on the Riemann surface of the energywave-number mapping (4). We also show that when solving in dimensionless wave-number space ρ c , there are N L number of solutions to the radioactive problem (32). In the case of massive neutral particles (neutrons and neutrinos) we have…”

Section: -5mentioning

confidence: 72%

“…which forms a complex multisheeted Riemann surface with branch points at (or close to) the threshold energies E T c , as discussed in Sec. II.A p. 2 of [32].…”

Section: Wave-number-energy Mappingmentioning

confidence: 98%

“…Usually, photon channels (γ "gamma capture") are eliminated, so that in practice the Reich-Moore approximation of R-matrix theory [44] consists of adding a partial eliminated capture width λ,γ to every resonance energy E λ , shifting the latter into the complex plane (see Sec. IV.A of [32]):…”

Section: Reich-moore and Breit-wigner Approximations To R-matrix Theorymentioning

confidence: 99%

“…In this paper, we use this connection to establish the windowed multipole representation, which is the meromorphic continuation of Rmatrix cross sections in z √ E space, locally expressing open channels as pole expansions. We build upon our previous work on such expansions [31,32], using the same consistent notation as reference. As such, this article closes our trilogy on pole parametrizations of R-matrix theory (see Supplemental Material of Ref.…”

Section: From R-matrix To Windowed Multipolementioning

confidence: 99%

“…This formalism was further developed into the windowed multipole representation in order to perform efficient on-the-fly computations of no-threshold neutron cross sections with a lesser computational memory footprint [26][27][28][29][30]. In this article, which follows [31] and [32], we extend the windowed multipole representation to all cross sections in the context of R-matrix theory-be they Coulomb, photon, or neutrons, with or without thresholds-thereby closing our trilogy on pole parametrizations of R-matrix theory (as described in the Supplemental Material of Ref. [31]).…”

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Windowed multipole representation of R -matrix cross sections

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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 paper 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.

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Section: -5mentioning

confidence: 72%

“…which forms a complex multisheeted Riemann surface with branch points at (or close to) the threshold energies E T c , as discussed in Sec. II.A p. 2 of [32].…”

Section: Wave-number-energy Mappingmentioning

confidence: 98%

Section: Reich-moore and Breit-wigner Approximations To R-matrix Theorymentioning

confidence: 99%

Section: From R-matrix To Windowed Multipolementioning

confidence: 99%

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Windowed multipole representation of R -matrix cross sections

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Shadow poles in the alternative parametrization of R -matrix theory

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We discover new, hitherto unknown, shadow poles in Brune's alternative parametrization of R-matrix theory [Brune, Phys. Rev. C 66, 044611 (2002)]. Where these poles are, and how many there are, depends on how one continues R-matrix operators to complex wave numbers (especially the shift S and penetration P functions). This has little consequence for the exact R-matrix formalism (past the last energy threshold), as we show one can still always fully reconstruct the scattering matrix with only the previously known alternative parameters (poles and corresponding resonance widths), for which there were as many poles as the number of levels N λ . However, we generalize the alternative parametrization to the Reich-Moore formalism and show that the choice of continuation is now critical as it changes the alternative parameters values (poles and residue widths are now complex). In order to establish nuclear libraries with alternative parameters, the nuclear community will thus have to decide what convention to adopt. We argue in favor of analytical continuation (against the legacy of Lane and Thomas approach) in the second article [P. Ducru, B. Forget, V. Sobes, G. Hale, and M. Paris, Phys. Rev. C 103, 064609 (2021)] of this trilogy on pole parametrizations of R-matrix theory, on which we build to establish the windowed multipole representation or R-matrix cross sections in the third and last article [P. Ducru, A. Alhajri, I. Meyer, B. Forget, V. Sobes, C. Josey, and J. Liang, Phys. Rev. C 103, 064610 (2021)]. We observe the first evidence of shadow poles in the alternative parametrization of R-matrix theory in the isotope 134 Xe spin-parity group J π = 1/2 (−) and show how they indeed depend on the choice of continuation to complex wave numbers.

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Definite complete invariant parametrization of R -matrix theory

Ducru

Sobes

2022

Phys. Rev. C

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Scattering matrix pole expansions for complex wave numbers inR-matrix theory

Cited by 3 publications

References 68 publications

Windowed multipole representation of R -matrix cross sections

Windowed multipole representation of R -matrix cross sections

Shadow poles in the alternative parametrization of R -matrix theory

Definite complete invariant parametrization of R -matrix theory

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