Shadow poles in the alternative parametrization of 
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-matrix theory

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

doi:10.1103/physrevc.103.064608

Cited by 6 publications

(134 citation statements)

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“…The Reich-Moore approximation -widely used in nuclear data libraries -introduces complex Reich Moore Brune parameters (61), and their values depend on which convention -analytic continuation definition (43) v/s branch-point definition (41) -is chosen to continue the Rmatrix operators to complex wavenumbers. Deciding on this convention (for mathematical and physical reasons the authors are arguing in favor of analytic continuation in a follow-up article [13]) is thus a necessary prerequisite to converting nuclear data libraries to Brune parameters.…”

Section: Discussionmentioning

confidence: 99%

“…This means that in order to convert nuclear data libraries to Brune parameters, the nuclear physics community must first agree on how to continue the R-matrix operators to complex wavenumbers. We argue in favor of analytic continuation in a follow-up article [13].…”

Section: Introductionmentioning

confidence: 90%

“…This elegant closure of channels comes at the cost of loosing the mathematical properties of the scattering matrix U (k): it is no longer analytic for complex wavenumbers k c ∈ C (we will also show in a follow-up article [13] that this introduces non-physical spurious poles to the scattering matrix and brakes the generalized unitarity of Eden & Taylor [15]). In this Lane & Thomas approach (41), the function calculated for S changes from S(E) S c (E) above threshold (E ≥ E Tc ), to S(E) L c (E) below threshold (E < E Tc ), because of (42).…”

Section: B Ambiguity In Shift and Penetration Factors Definition For ...mentioning

confidence: 99%

“…If instead the analytic continuation definition ( 43) is chosen, we now show in theorem 2 that this unfolds the Riemann surface for the shift function S c (E) so that no branch points are required to define the Brune parameters. We argue in a follow-up article that the analytic continuation approach (44) is the physically correct one [13], as it conserves the meromorphic properties of the Kapur-Peierls operator, which preserves general unitarity, cancels non-physical poles out of the scattering ma-trix U (E) otherwise spuriously introduced by the Lane & Thomas approach (41), allows for parameters transform under change of channel radius, and still should close cross sections below channel thresholds. Though there is no absolute consensus yet amongst the community as to which approach ought to be valid, both yield identical results for real energies above threshold (real wavenumbers k c ∈ R).…”

Section: Number Of Brune Poles: Existence Of Shadow Polesmentioning

confidence: 99%

“…Thus, in order to convert nuclear data libraries from Wigner-Eisenbud to Brune parameters, the nuclear scientists community must convene on a convention -either branch-point definition (41) or analytic continuation definition (43) -to compute R-matrix operators for complex wavenumbers. The authors are publishing a follow-up article arguing in favor of analytic continuation [13].…”

Section: Generalized Brune Parameters For Reich-moore Approximationmentioning

confidence: 99%

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Shadow poles in Brune parametrization of R-matrix theory

Ducru,

Sobes,

Forget

et al. 2020

Preprint

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Our collective knowledge of nuclear cross sections is recorded as resonance parameters in nuclear data libraries. To evaluate these parameters, campaigns of measurements are fitted with a parametric model of nuclear cross sections called R-matrix theory. R-matrix theory can parametrize the energy dependence of nuclear cross sections in different ways. Historically, the Wigner-Eisenbud parametrization has been used, because its resonance parameters are real-valued and there is a one-to-one correspondance between each cross-section resonance (called levels) and the Wigner-Eisenbud resonance energies (the poles of the R-matrix). This means that for each level, every nuclear interaction channel has one resonance width and one resonance energy. The drawback of the Wigner-Eisenbud parametrization is that it introduces in each channel an arbitrary boundary parameter upon which all other resonance parameters depend. Thus, if two evaluations of the same experiments are done with different boundary parameters, both will yield the same fit, but a different set of resonance parameters. This is a challenge for nuclear data libraries.To overcome such arbitrarity, Brune proposed an alternative parametrization preserving most benefits of the Wigner-Eisenbud parameters while eliminating the arbitrary boundary parameter. Consequently, the community is considering converting all nuclear data libraries to Brune resonance parameters. The Brune resonance energies are the poles of the Brune alternative level matrix, and Brune proved that, above the channel threshold energy, there is one pole per level (or resonance).In this article, we unveil the existence of more Brune parameters than previously thought. Below the channel threshold, we prove the theoretical existence of two types of additional shadow polesbranch shadow poles and analytic shadow poles -depending on what convention is chosen to continue the R-matrix operators to complex wavenumbers (to do so we establish the first derivations of the Mittag-Leffler expansions of external region R-matrix operators). This entails there are more Brune poles (or Brune resonance energies) than levels. Importantly, we also prove that choosing any subset of Brune poles will yield the same cross sections than using the entire set of Brune poles, as long it is bigger or equal the number of levels (resonances). In practice, this means that shadow Brune poles can safely be discarded from the new nuclear data libraries.Many isotopes in nuclear cross section libraries are evaluated under the Reich-Moore approximation, which introduces complex resonance energies to eliminate certain channels. We generalize Brune's parameterization to encompass both the Reich-Moore approximation and the addional shadow poles. In the process, we show that all Brune parameters values depend on what convention we choose to continue the R-matrix operators to complex wavenumbers. To convert nuclear data libraries to Brune parameters, the nuclear scientists community must thus first decide on such a convention. The authors a...

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%

Section: B Ambiguity In Shift and Penetration Factors Definition For ...mentioning

confidence: 99%

Section: Number Of Brune Poles: Existence Of Shadow Polesmentioning

confidence: 99%

Section: Generalized Brune Parameters For Reich-moore Approximationmentioning

confidence: 99%

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Shadow poles in Brune parametrization of R-matrix theory

Ducru,

Sobes,

Forget

et al. 2020

Preprint

Self Cite

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Effective R-Matrix Parameterizations for Nuclear Data

Arbanas,

Holcomb,

Pigni

et al. 2024

EPJ Web of Conf.

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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 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].

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

et al. 2021

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In this follow-up article to [1], we establish new results on scattering matrix pole expansions for complex wavenumbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory, and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wavenumbers [1]. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift S and penetration P functions: the legacy Lane & Thomas "force closure" approach, versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF [2].In this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and unveil new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii ac. We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix -cancelling spurious poles and guaranteeing generalized unitarity -while still being able to close channels below thresholds.

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Shadow poles in the alternative parametrization of R -matrix theory

Cited by 6 publications

References 58 publications

Shadow poles in Brune parametrization of R-matrix theory

Shadow poles in Brune parametrization of R-matrix theory

Effective R-Matrix Parameterizations for Nuclear Data

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

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