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.

This paper presents an in-depth analysis on the accuracy and performance of the windowed multipole Doppler broadening method. The basic theory behind cross section data is described, along with the basic multipole formalism followed by the approximations leading to windowed multipole method and the algorithm used to efficiently evaluate Doppler broadened cross sections. The method is tested by simulating the BEAVRS benchmark with a windowed multipole library composed of 70 nuclides. Accuracy of the method is demonstrated on a single assembly case where total neutron production rates and 238 U capture rates compare within 0.1% to ACE format files at the same temperature. With regards to performance, clock cycle counts and cache misses were measured for single temperature ACE table lookup and for windowed multipole. The windowed multipole method was found to require 39.6% more clock cycles to evaluate, translating to a 7.9% performance loss overall. However, the algorithm has significantly better last-level cache performance, with 3 fewer misses per evaluation, or a 65% reduction in last-level misses. This is due to the small memory footprint of the windowed multipole method and better memory access pattern of the algorithm.

Application of idealized statistical methods to GRMA shows that variance among conventional RMA capture widths in extant RMA evaluations could be used to estimate variance among off-diagonal elements neglected by conventional RMA. Significant departure of capture widths from an idealized distribution may indicate the presence of underlying doorway states.

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.

This article establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j ). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature Tnamely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j ). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j ) is then undertaken so as to best reconstruct, in the L ∞ sense, the kernels over a given temperature range [T min , T max ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238 U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238 U total cross section over the temperature range [300K, 3000K] with only 9 reference temperatures.