Biomimetic Reductive Cleavage of Keto Aryl Ether Bonds by Small-Molecule Thiols
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Chemistry↗
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Understanding the Electronic Structure of 4d Metal Complexes: From Molecular Spinors to L-Edge Spectra of a di-Ru Catalyst
L{sub 2,3}-edge X-ray absorption spectroscopy (XAS) has demonstrated unique capabilities for the analysis of the electronic structure of di-Ru complexes such as the blue dimer cis,cis-[Ru{sub 2}{sup III}O(H{sub 2}O){sub 2}(bpy){sub 4}]{sup 4+} water oxidation catalyst. Spectra of the blue dimer and the monomeric [Ru(NH{sub 3}){sub 6}]{sup 3+} model complex show considerably different splitting of the Ru L{sub 2,3} absorption edge, which reflects changes in the relative energies of the Ru 4d orbitals caused by hybridization with a bridging ligand and spin-orbit coupling effects. To aid the interpretation of spectroscopic data, we developed a new approach, which computes L{sub 2,3}-edges XAS spectra as dipole transitions between molecular spinors of 4d transition metal complexes. This allows for careful inclusion of the spin-orbit coupling effects and the hybridization of the Ru 4d and ligand orbitals. The obtained theoretical Ru L{sub 2,3}-edge spectra are in close agreement with experiment. Critically, existing single-electron methods (FEFF, FDMNES) broadly used to simulate XAS could not reproduce the experimental Ru L-edge spectra for the [Ru(NH{sub 3}){sub 6}]{sup 3+} model complex nor for the blue dimer, while charge transfer multiplet (CTM) calculations were not applicable due to the complexity and low symmetry of the blue dimer water oxidation catalyst. We demonstrated that L-edge spectroscopy is informative for analysis of bridging metal complexes. The developed computational approach enhances L-edge spectroscopy as a tool for analysis of the electronic structures of complexes, materials, catalysts, and reactive intermediates with 4d transition metals.
Alperovich, Igor↗
Critical insights into the steam electrolysis electrode in protonic ceramic cells for hydrogen production
Intermediate-temperature protonic ceramic electrolysis cells (PCECs), which combine the benefits of both lower- and higher-temperature electrolysis, are among the most efficient technologies for the production of green hydrogen. To ensure economic competitiveness and broad adoption, ongoing innovations in cell materials are essential to improve durability and reduce costs. The water oxidation half-reaction at the anode is a key area for improvement as it is a major contributor to performance degradation and efficiency loss in PCECs. Current anode designs, which are largely derived from solid oxide electrolysis cells, fail to address the specific requirements for PCECs under realistic operating conditions. Here, this Perspective highlights the unique challenges faced by PCEC anodes, focusing on the impact of high steam concentrations and the critical role of proton-coupled electron-transfer mechanisms—factors that are absent in solid oxide electrolysis cells. Furthermore, we explore design principles for advancing anodes tailored for PCECs, offering guidance for future research and development in this promising field.
Electrocatalysis↗
Evaluation of the coordination preferences and catalytic pathways of heteroaxial cobalt oximes towards hydrogen generation
Three new heteroaxial cobalt oxime catalysts, namely [Co III (prdioxH)( 4tBu py)(Cl)]PF 6 (1), [Co III (prdioxH)( 4Pyr py)(Cl)]PF 6 (2), and [Co III (prdioxH)( 4Bz py)(Cl)]PF 6 (3) have been studied. These species contain chloro and substituted tert-butyl/pyrrolidine/benzoyl-pyridino ligands axially coordinated to a trivalent cobalt ion bound to the N 4 -oxime macrocycle (2 E ,2' E ,3 E ,3' E )-3,3'-(propane-1,3-diylbis(azanylylidene))bis(butan-2-one)dioxime, abbreviated (prdioxH)– in its monoprotonated form. Emphasis was given to the spectroscopic investigation of the coordination preferences and spin configurations among the different 3d 6 Co III , 3d 7 Co II , and 3d 8 Co I oxidation states of the metal, and to the catalytic proton reduction with an evaluation of the pathways for the generation of H 2 via Co III –H – or Co II –H – intermediates by mono and bimetallic routes. The strong field imposed by the (prdioxH)– ligand precludes the existence of high-spin configurations, and 6-coordinate geometry is favored by the LS Co III species. Species 1 and 3 show a split Co III /Co II electrochemical wave associated with partial chemical conversion to a [Co III (prdioxH)Cl 2 ] species, whereas 2 shows a single event. The reduction of these Co III complexes yields LS Co II and LS Co I species in which the pyridine acts as the dominant axial ligand. In the presence of protons, the catalytically active Co I species generates a Co III –H – hydride species that reacts heterolytically with another proton to generate dihydrogen. The intermediacy of a trifluoroacetate-bound Co III /Co II couple in the catalytic mechanism is proposed. Finally, these results allow for a generalization of the behavior of heteroaxial cobalt macrocycles and serve as guidelines for the development of new catalysts based on macrocyclic frameworks.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Planar defect-driven electrocatalysis of CO 2 -to-C 2 H 4 conversion
The selectivity towards a specific C 2+ product, such as ethylene (C 2 H 4 ), is sensitive to the surface structure of copper (Cu) catalysts in carbon dioxide (CO 2 ) electro-reduction. The fundamental understanding of such sensitivity can guide the development of advanced electrocatalysts, although it remains challenging at the atomic level. In this work, we demonstrated that planar defects, such as stacking faults, could drive the electrocatalysis of CO 2 -to-C 2 H 4 conversion with higher selectivity and productivity than Cu(100) facets in the intermediate potential region (–0.50 ~ –0.65 V vs. RHE). The unique right bipyramidal Cu nanocrystals containing a combination of (100) facets and a set of parallel planar defects delivered 67% faradaic efficiency (FE) for C 2 H 4 and a partial current density of 217 mA cm –2 at –0.63 V vs. RHE. In contrast, Cu nanocubes with exclusive (100) facets exhibited only 46% FE for C 2 H 4 and a partial current density of 87 mA cm –2 at an identical potential. Both ex situ CO temperature-programmed desorption and in situ Raman spectroscopy analysis implied that the stronger *CO adsorption on planar defect sites facilitates CO generation kinetics, which contributes to a higher surface coverage of *CO and in turn an enhanced reaction rate of C–C coupling towards C 2+ products, especially C 2 H 4 .
36 MATERIALS SCIENCE↗
COLLISIONLESS SHOCKS IN A PARTIALLY IONIZED MEDIUM. II. BALMER EMISSION
Strong shocks propagating into a partially ionized medium are often associated with optical Balmer lines. This emission is due to impact excitation of neutral hydrogen by hot protons and electrons in the shocked gas. The structure of such Balmer-dominated shocks has been computed in a previous paper, where the distribution function of neutral particles was derived from the appropriate Boltzmann equation including coupling with ions and electrons through charge exchange and ionization. This calculation showed how the presence of neutrals can significantly modify the shock structure through the formation of a neutral-induced precursor ahead of the shock. Here we follow up on our previous work and investigate the properties of the resulting Balmer emission, with the aim of using the observed radiation as a diagnostic tool for shock parameters. Our main focus is on supernova remnant shocks, and we find that, for typical parameters, the H{alpha} emission typically has a three-component spectral profile, where (1) a narrow component originates from upstream cold hydrogen atoms, (2) a broad component comes from hydrogen atoms that have undergone charge exchange with shocked protons downstream of the shock, and (3) an intermediate component is due to hydrogen atoms that have undergone charge exchange with warm protons in the neutral-induced precursor. The relative importance of these three components depends on the shock velocity, on the original degree of ionization, and on the electron-ion temperature equilibration level. The intermediate component, which is the main signature of the presence of a neutral-induced precursor, becomes negligible for shock velocities {approx}< 1500 km s{sup -1}. The width of the intermediate line reflects the temperature in the precursor, while the width of the narrow one is left unaltered by the precursor. In addition, we show that the profiles of both the intermediate and broad components generally depart from a thermal distribution, as a consequence of the non-equilibrium distribution of neutral hydrogen. Finally, we show that a significant amount of Balmer emission can be produced in the precursor region if efficient electron heating takes place.
79 ASTRONOMY AND ASTROPHYSICS↗
Metabolic profiling reveals altered sugar and secondary metabolism in response to UGPase overexpression in Populus
Background: UDP-glucose pyrophopharylase (UGPase) is a sugar metabolizing enzyme (E.C. 2.7.7.9) that catalyzes a reversible reaction of UDP-glucose and pyrophosphate from glucose-1-phosphate and uridine triphosphate glucose. UDP-glucose is a key intermediate sugar that is channeled to multiple metabolic pathways. The functional role of UGPase in woody plants such as Populus is poorly understood. Results: We characterized the functional role of UGPase in Populus deltoides by overexpressing a native gene. Overexpression of the native gene resulted in increased leaf area and leaf-to-shoot biomass ratio but decreased shoot and root growth. Metabolomic analyses showed that manipulation of UGPase results in perturbations in primary as well as secondary metabolism resulting in reduced sugar and starch levels and increased phenolics such as caffeoyl- and feruloyl conjugates. While cellulose and lignin levels in the cell walls were not significantly altered, the syringyl-to-guaiacyl ratio was significantly reduced. Conclusions: These results demonstrate that UGPase plays a key role in the tightly coupled primary and secondary metabolic pathways and perturbation in its function results in pronounced effects on growth and metabolism outside of cell wall biosynthesis of Populus.
09 BIOMASS FUELS↗
Thin films of the spin ice compound Ho{sub 2}Ti{sub 2}O{sub 7}
The pyrochlore compounds Ho{sub 2}Ti{sub 2}O{sub 7} and Dy{sub 2}Ti{sub 2}O{sub 7} show an exotic form of magnetism called the spin ice state, resulting from the interplay between geometrical frustration and ferromagnetic coupling. A fascinating feature of this state is the appearance of magnetic monopoles as emergent excitations above the degenerate ground state. Over the past years, strong effort has been devoted to the investigation of these monopoles and other properties of the spin ice state in bulk crystals. Here, we report the fabrication of Ho{sub 2}Ti{sub 2}O{sub 7} thin films using pulsed laser deposition on yttria-stabilized ZrO{sub 2} substrates. We investigated the structural properties of these films by X-ray diffraction, scanning transmission electron microscopy, and atomic force microscopy, and the magnetic properties by vibrating sample magnetometry at 2 K. The films not only show a high crystalline quality, but also exhibit the hallmarks of a spin ice: a pronounced magnetic anisotropy and an intermediate plateau in the magnetization along the [111] crystal direction.
36 MATERIALS SCIENCE↗
Overview of the Predictive Simulation Capability Element of the Plume Surface Interaction Project
As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The GCD PSI Project, planned to be completed over a four year period, contains a Predictive Simulation Capability (PSC) Element focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the PSC Element, the GCD Program also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper describes the PSC Element of the PSI Project as well as providing descriptions of recent accomplishments and remaining work. The overall structure of the PSC Element is broken down into four areas of focus. The first area is the Prediction of Plume Flow in low pressure environments. The development approach taken is the augmentation of the existing production-mode computational fluid dynamics (CFD) tool Loci/Chem, with targeted extensions necessary to accurately model rarefied conditions found in both Martian and Lunar applications. Production readiness and validation of predictive capability are the major objectives of this task. The second area is the effect of mixed continuum/rarefied flow on crater development and ejecta sheets. A new CFD application, Loci/GGFS (Gas Granular Flow Solver), is being developed which implements an Eulerian/Eulerian two-phase model of gas- and soil-phases in order to simulate the soil erosion, crater formation, and soil ejecta transport in a fully coupled simulation. This task seeks to verify Loci/GGFS is production-ready as well as perform validation studies to determine the degree of predictive capability achieved by Loci/GGFS. The third area is focused on the details and extension of particle phase modeling of soil. In this task, Discrete Element Modeling (DEM) techniques are used to perform direct simulations of complex soil particles under the action of forcing similar to that to be cause by PSI. The simulation results are then used to construct closures to the Eulerian model of the soil phase used by Loci/GGFS. The fourth area is gas-particle interaction modeling. In this task, experiments are being conducted as well as detailed simulation results are being studied to further understand the complexities of gas-particle interactions in dilute, intermediate, and high soil volume fraction regimes. Improved models of particle drag and the particle turbulent kinetic energy (PTKE) resulting from the interaction of gas flows within particle clouds are the objective of this task.
Jeff West↗
Prediction of Feasibility of Polaronic OER on (110) Surface of Rutile TiO 2
The polaronic effects at the atomic level hold paramount significance for advancing the efficacy of transition metal oxides in applications pertinent to renewable energy. The lattice–distortion mediated localization of photoexcited carriers in the form of polarons plays a pivotal role in the photocatalysis. This investigation focuses on rutile TiO 2 , an important material extensively explored for solar energy conversion in artificial photosynthesis, specifically targeting the generation of green H 2 through photoelectrochemical (PEC) H 2 O splitting. By employing Hubbard-U corrected and hybrid density functional theory (DFT) methods, we systematically probe the polaronic effects in the catalysis of oxygen evolution reaction (OER) on the (110) surface of rutile TiO 2 . Theoretical understanding of polarons within the surface, coupled with simulations of OER at distinct titanium (Ti) and oxygen (O) active sites, reveals diverse polaron formation energies within the lattice sites with strong preference for bulk and surface bridge (O b ) oxygen sites. Moreover, we provide the evidence for the facilitative role of polarons in OER. Here, we find that hole polarons situated at the equatorial oxygen sites near the Ti–active site, along with bridge site hole polarons distal from the O b active site yield a small reduction in OER overpotential by ~0.06 eV and ~0.12 eV, respectively. However, subsurface, equatorial, and bridge site hole polarons significantly reduce the Ti-active site OER overpotential by ~0.4 eV through the peroxo–type oxygen pathway. We also observe that the presence of hole polarons stabilizes the *OH, *O, and *OOH intermediate species compared to the scenario without hole polarons. Overall, this study provides a detailed mechanistic insight into polaron–mediated OER, offering a promising avenue for improving the catalytic activity of transition metal oxide-based photocatalysts catering to renewable energy requisites.
14 SOLAR ENERGY↗
Weakly-interacting massive particles in non-supersymmetric SO(10) grand unified models
Here, non-supersymmetric SO(10) grand unified theories provide a framework in which the stability of dark matter is explained while gauge coupling unification is realized. In this work, we systematically study this possibility by classifying weakly interacting dark matter candidates in terms of their quantum numbers of SU(2) L Ⓧ U(1) Y , B – L, and SU(2) R . We consider both scalar and fermion candidates. We show that the requirement of a sufficiently high unification scale to ensure a proton lifetime compatible with experimental constraints plays a strong role in selecting viable candidates. Among the scalar candidates originating from either a 16 or 144 of SO(10), only SU(2) L singlets with zero hypercharge or doublets with Y = 1/2 satisfy all constraints for SU(4) C Ⓧ SU(2) L Ⓧ SU(2) R and SU(3) C Ⓧ SU(2) L Ⓧ SU(2) R Ⓧ U(1) B–L intermediate scale gauge groups. Among fermion triplets with zero hypercharge, only a triplet in the 45 with intermediate group SU(4) C Ⓧ SU(2) L Ⓧ SU(2) R leads to solutions with M GUT > M int and a long proton lifetime. We find three models with weak doublets and Y = 1/2 as dark matter candidates for the SU(4) C Ⓧ SU(2) L Ⓧ SU(2) R and SU(4) C Ⓧ SU(2) L Ⓧ U(1) R intermediate scale gauge groups assuming a minimal Higgs content. We also discuss how these models may be tested at accelerators and in dark matter detection experiments.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Isolation and Study of Ruthenium–Cobalt Oxo Cubanes Bearing a High-Valent, Terminal Ru V –Oxo with Significant Oxyl Radical Character
High-valent Ru V -oxo intermediates have long been proposed in catalytic oxidation chemistry, but investigations into their electronic and chemical properties have been limited due to their reactive nature and rarity. The incorporation of Ru into the [Co 3 O 4 ] subcluster via the single-step assembly reaction of Co II (OAc) 2 (H 2 O) 4 (OAc = acetate), perruthenate (RuO 4 - ), and pyridine (py) yielded an unprecedented Ru(O)Co 3 (μ 3 -O) 4 (OAc) 4 (py) 3 cubane featuring an isolable, yet reactive, RuV-oxo moiety. EPR, ENDOR, and DFT studies reveal a valence-localized [Ru V (S = 1/2)Co III 3(S = 0)O 4 ] configuration and non-negligible covalency in the cubane core. Significant oxyl radical character in the Ru V -oxo unit is experimentally demonstrated by radical coupling reactions between the oxo cubane and both 2,4,6-tri-tert-butylphenoxyl and trityl radicals. The oxo cubane oxidizes organic substrates and, notably, reacts with water to form an isolable μ-oxo bis-cubane complex [(py) 3 (OAc) 4 Co 3 (μ 3 -O) 4 Ru]-O-[RuCo 3 (μ 3 -O) 4 (OAc) 4 (py) 3 ]. Redox activity of the Ru V -oxo fragment is easily tuned by the electron-donating ability of the distal pyridyl ligand set at the Co sites demonstrating strong electronic communication throughout the entire cubane cluster. Natural bond orbital calculations reveal cooperative orbital interactions of the [Co 3 O 4 ] unit in supporting the Ru V -oxo moiety via a strong π-electron donation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Conceptual design of BabyIAXO, the intermediate stage towards the International Axion Observatory
This article describes BabyIAXO, an intermediate experimental stage of the International Axion Observatory (IAXO), proposed to be sited at DESY. IAXO is a large-scale axion helioscope that will look for axions and axion-like particles (ALPs), produced in the Sun, with unprecedented sensitivity. BabyIAXO is conceived to test all IAXO subsystems (magnet, optics and detectors) at a relevant scale for the final system and thus serve as prototype for IAXO, but at the same time as a fully-fledged helioscope with relevant physics reach itself, and with potential for discovery. The BabyIAXO magnet will feature two 10 m long, 70 cm diameter bores, and will host two detection lines (optics and detector) of dimensions similar to the final ones foreseen for IAXO. BabyIAXO will detect or reject solar axions or ALPs with axion-photon couplings down to g aγ ~ 1 . 5 × 10 -11 GeV -1 , and masses up to m a ~ 0.25 eV. BabyIAXO will offer additional opportunities for axion research in view of IAXO, like the development of precision x-ray detectors to identify particular spectral features in the solar axion spectrum, and the implementation of radiofrequency-cavity-based axion dark matter setups.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration
Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field is electrostatic, this yields a set of 10 strongly coupled and non-linear conservation equations that exhibit multiscale and anisotropy features. The computational domain is a torus of complex geometrical section, that corresponds to the divertor configuration, i.e. with an “X-point” in the magnetic surfaces. To capture the complex physics that is involved, high order methods are used: The time-discretization is based on a Strang splitting, that combines implicit and explicit high order Runge–Kutta schemes, and the space discretization makes use of the spectral element method in the poloidal plane together with Fourier expansions in the toroidal direction. The paper thoroughly describes the algorithms that have been developed, provides some numerical validations of the key algorithms and exhibits the results of preliminary numerical experiments. In particular, we point out that the highest frequency of the system is intermediate between the ion and electron cyclotron frequencies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Energy spectra of finite temperature superfluid helium-4 turbulence
A mesoscopic model of finite temperature superfluid helium-4 based on coupled Langevin-Navier-Stokes dynamics is proposed. Drawing upon scaling arguments and available numerical results, a numerical method for designing well resolved, mesoscopic calculations of finite temperature superfluid turbulence is developed. The application of model and numerical method to the problem of fully developed turbulence decay in helium II, indicates that the spectral structure of normal-fluid and superfluid turbulence is significantly more complex than that of turbulence in simple-fluids. Analysis based on a forced flow of helium-4 at 1.3 K, where viscous dissipation in the normal-fluid is compensated by the Lundgren force, indicate three scaling regimes in the normal-fluid, that include the inertial, low wavenumber, Kolmogorov k{sup −5/3} regime, a sub-turbulence, low Reynolds number, fluctuating k{sup −2.2} regime, and an intermediate, viscous k{sup −6} range that connects the two. The k{sup −2.2} regime is due to normal-fluid forcing by superfluid vortices at high wavenumbers. There are also three scaling regimes in the superfluid, that include a k{sup −3} range that corresponds to the growth of superfluid vortex instabilities due to mutual-friction action, and an adjacent, low wavenumber, k{sup −5/3} regime that emerges during the termination of this growth, as superfluid vortices agglomerate between intense normal-fluid vorticity regions, and weakly polarized bundles are formed. There is also evidence of a high wavenumber k{sup −1} range that corresponds to the probing of individual-vortex velocity fields. The Kelvin waves cascade (the main dynamical effect in zero temperature superfluids) appears to be damped at the intervortex space scale.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Dark matter annihilations into two light fermions and one gauge boson: general analysis and antiproton constraints
We study in this paper the scenario where the dark matter is constituted by Majorana particles which couple to a light Standard Model fermion and an extra scalar via a Yukawa coupling. In this scenario, the annihilation rate into the light fermions with the mediation of the scalar particle is strongly suppressed by the mass of the fermion. Nevertheless, the helicity suppression is lifted by the associated emission of a gauge boson, yielding annihilation rates which could be large enough to allow the indirect detection of the dark matter particles. We perform a general analysis of this scenario, calculating the annihilation cross section of the processes χχ→f f-bar V when the dark matter particle is a SU(2){sub L} singlet or doublet, f is a lepton or a quark, and V is a photon, a weak gauge boson or a gluon. We point out that the annihilation rate is particularly enhanced when the dark matter particle is degenerate in mass to the intermediate scalar particle, which is a scenario barely constrained by collider searches of exotic charged or colored particles. Lastly, we derive upper limits on the relevant cross sections from the non-observation of an excess in the cosmic antiproton-to-proton ratio measured by PAMELA.
79 ASTRONOMY AND ASTROPHYSICS↗
Microscopic study of the string breaking in QCD
Theory of strong decays defines in addition to decay widths also the channel coupling and the mass shifts of the levels above the decay thresholds. In the standard decay models of the {sup 3}P{sub 0} type the decay vertex is taken to be a phenomenological constant {gamma} and such a choice leads to large mass shifts of all meson levels due to real and virtual decays, the latter giving a divergent contribution. Here we show that taking the microscopic details of decay vertex into account, one obtains new string width effect coefficient, which strongly suppresses virtual decay contribution. In addition for a realistic space structure of the decay vertex of highly excited states, the decay matrix elements appear to be strongly different from those, where the constant {gamma} is used. From our analysis also follows that so-called flattening potential can imitate the effects of intermediate decay channels.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Electron-Hydrogen Elastic Scattering
Scattering by single-electron systems is always of interest because the wave function of the target is known exactly. Various approximations have been employed to take into account distortion produced in the target. Among them are the method of polarized orbitals and the close coupling approximation. Recently, e-H and e-He+ S-wave scattering in the elastic region has been studied using the Feshbach projection operator formalism. In this approach, the usual Hartree-Fock and exchange potentials are augmented by an optical potential and the resulting phase shifts have rigorous lower bounds. Now this method is being applied to the e-H P-wave scattering in the elastic region. The number of terms in the Hylleraas-type wave function for the 1,3 P phase shifts is 84 and the resulting phase shifts (preliminary) are given. The results have been given up to five digits because to that accuracy they are rigorous lower bounds. They are in general agreement with the variational (VAR) results of Armstead, and those obtained from the intermediate energy R-matrix method (RM) of Scholz et al., and the finite element method (FEM) of Botero and Shertzer. The later two methods do not provide any bounds on phase shifts.
Bhatia, A. K.↗