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At least 1,135 records · Page 63

Implementing the donor–acceptor approach in electronically conducting copolymers via electropolymerization

Electropolymerization has become a convenient method for synthesizing and characterizing complex organic copolymers having intrinsic electronic conductivity, including the donor (D)–acceptor (A) class of electronically conducting polymers (ECPs). This review begins with an introduction to the electrosynthesis of common second-generation ECPs. The information obtainable from electroanalytical studies, charge carriers such as polarons (positive and negative) and bipolarons (positive and negative) and doping will be discussed. The evolutionary chain of ECPs is then presented. ECPs comprising electron-rich D and electron-deficient A moieties have been shown to possess intrinsic electronic conductivity and unique optical and electronic properties. They are third generation ECPs and electropolymerization of mixtures of D and A leads to stoichiometrically controlled block copolymers. These D–A type ECPs are discussed on the basis of selected representative materials. Since the discovery of electropolymerization as a powerful tool to synthesize copolymers of conjugated monomers with a pre-determined ratio of D and A repeat units present in the polymer, the field of D–A type ECPs has grown considerably and the literature available since 2004 to 2021 is summarized and tabulated. Electronic and optical properties of the materials determined by computational chemistry are presented. The data obtained from electrochemical and optical methods are compared with those obtained from computational methods and reasons for discrepancies are given. The literature on the concept of electropolymerization extended to synthesizing triblock and many-block copolymers is reviewed. Finally, applications of D–A polymers in optoelectronic devices (organic solar cells and field-effect transistors) and in bio-imaging are explained quoting appropriate examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reduced‐Order Modeling of Energetic Materials Using Physics‐Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Physics-aware deep learning (PADL) has gained popularity for use in spatiotemporal dynamics simulations, such as those in computational modeling of energetic materials (EM). We show that the challenge PADL methods face while learning complex field evolution problems can be simplified and accelerated by decoupling it into two tasks: learning complex geometric features in evolving fields and modeling dynamics over these features in a lower-dimensional feature space. We build upon our previous work on physics-aware recurrent convolutional neural networks (PARC). PARC embeds knowledge of underlying physics into its neural network architecture for more robust and accurate prediction of evolving physical fields. PARC was shown to effectively learn complex nonlinear features such as the formation of hotspots and coupled shock fronts in various initiation scenarios of EMs, as a function of microstructures, serving effectively as a microstructure-aware burn model. Here, we further accelerate PARC and reduce its computational cost by projecting the original dynamics onto a lower-dimensional invariant manifold, or “latent space.” The projected latent representation encodes the complex geometry of evolving fields (e.g., temperature and pressure) in a set of data-driven features. The reduced dimension of this latent space allows us to learn the dynamics during the initiation of EM with a lighter and more efficient model. We observe a significant decrease in training and inference time while maintaining results comparable to PARC at inference. This work takes steps towards enabling rapid prediction of EM thermomechanics at larger scales and characterization of EM structure–property–performance linkages at a full application scale.

Mathematics and Computing↗

Mathematical Models and Numerical Methods for High-Fidelity Simulation of Ignition of Reactive Mixtures by Nanosecond Plasma Discharges in Realistic Configurations

We present a newly developed framework for the numerical simulation of ignition of reactive mixtures using single or repeated nanosecond discharge pulses. The framework builds upon the AMReX library, using the existing compressible solver PeleC and low-Mach solver PeleLMeX and allowing for adaptive mesh refinement, complex geometries, and execution on next-generation high-performance computing (HPC) systems. High-fidelity elementary models are adopted for weakly-ionised plasma discharges with significant energy deposition, consistent with nanosecond discharge pulses, and then implemented in the solver. The treatment of non-thermal electrons and charged species, thermodynamics of non-equilbrium species, plasma kinetics, limiting time scales, and boundary conditions for charged species are discussed and addressed for computational efficiency. The framework is demonstrated for three relevant applications: single and multi-pulse discharges in air, single pulse ignition of an ethylene/air mixture, and a three-dimensional plasma discharge in air with temperature stratification. The successful application of the framework demonstrates the feasibility of high-fidelity simulation of ignition of air/hydrocarbon mixtures in three-dimensions with multiple discharge pulses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development and Validation of SAM Multi-dimensional Flow Model for Thermal Mixing and Stratification Modeling

Thermal mixing and stratification in large pools or enclosures are very important phenomena that are critical to nuclear reactor safety. Because of the wide ranges of time and length scales associated with such phenomena, accurate modeling and simulation of thermal mixing and stratification remain as the key unresolved, challenging problems for reactor transient analyses. In traditional system analysis codes, simplified zero-dimensional (0-D) models are widely used for their high numerical efficiency, but they generally suffer from very limited prediction accuracies or range of applicability. Like traditional system analysis codes, the current version of the SAM code has implemented such simplified 0-D and one-dimensional mixing models. On the other hand, high-resolution Computational Fluid Dynamics (CFD) tools are often used to model complex thermal mixing and stratification phenomena. They are, however, generally numerically expensive, and they require large amounts of computational resources. It is therefore desirable to implement advanced and efficient thermal mixing and stratification modeling capabilities embedded in a system analysis code. This approach will improve the accuracy of reactor safety analyses when thermal mixing and stratification are involved, and also avoid using the large computational resources needed for high-resolution CFD analysis. Currently, with the support of the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation program, an effort has been launched to develop and implement a multi-dimensional flow model in the system analysis code SAM, and demonstrate its applications to model thermal mixing and stratification phenomena in large enclosures. The main outcomes of this research and development activity are summarized in this report, which presents an attempt to include a built-in advanced multi-dimensional flow model in a system analysis code with the focus on overcoming the simulation challenges of thermal mixing and stratification phenomena. In this report, we start with the introduction of existing SAM code capabilities to simulate thermal mixing and stratification phenomena, which is followed by a short summary of the multi-dimensional model implemented in the SAM code, including both the physical model and the Finite Element Method code implementation. In this study, two options were implemented in the SAM code to model turbulent flows: a relatively simple built-in turbulence model and an interface to accept externally computed turbulent viscosities (e.g., from a high- resolution CFD simulation). Code validation studies on this newly added capability were then carried out to compare SAM simulation results with experimental data from the SUPERCAVNA facility, which was designed to study the complex flow recirculation and thermal stratification phenomena relevant to sodium fast reactor designs. In this study, one transient and two steady-state test cases were used for code validation. Different approaches have been used to model the complex turbulence flow fields in the SUPERCAVNA facility. A highly simplified zero-equation turbulence model was first used, but it was determined that it is too simple to capture the complex turbulence flow fields in these test cases. Subsequently, the code validation continued with the use of turbulent viscosity data from high-resolution STAR-CCM+ CFD simulations to improve the accuracy of the results. Using this approach, the SAM simulation results showed very good agreement with both the SUPERCAVNA experimental data and STAR-CCM+ simulation results. In this report, we demonstrate the development, implementation, and successful validation of a multi-dimensional flow model in the SAM code, which aims to improve the simulation accuracy for complex thermal mixing and stratification phenomena. Lessons have also been learned, including that in cases where the flow fields are not well predicted by the zero-equation model, the iinput of turbulent viscosities from an external source can enhance the overall predictive capabilities needed to accurately capture complex thermal-hydraulic phenomena. Therefore, future research will be needed to further improve the code’s capabilities, such as by developing a more efficient and robust approach to capture the turbulence effects in the SAM code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

FY20 ASC IC L2 Milestone 7180: Performance Portability of SIERRA Mechanics Applications to ATS-1 and ATS-2. Executive Summary

The overall goal of this work was to accelerate simulations supporting the nuclear deterrence (ND) mission through improved performance of key algorithms in the ASC IC Sierra multi-physics application suite. This work focused on porting and optimizing algorithms for the graphics processing units (GPU) on the second ASC advanced technology system (ATS-2), while maintaining or improving performance on commodity technology systems (CTS) and ATS-1. Furthermore, these algorithmic developments used the ASC developed Kokkos performance portability abstraction library to maintain high performance across platforms using identical code, and enable sustainable reduced-cost migration and performance optimization to emerging hardware.

97 MATHEMATICS AND COMPUTING↗

Second Report of the Nuclear Data Subcommittee of the Nuclear Science Advisory Committee

The central importance of the nuclear data curated by the US Nuclear Data Program (USNDP) for clean energy generation, national security, nonproliferation, medical applications, and space exploration as well as basic science was described in a prior report issued by the DOE/NSF Nuclear Science Advisory Committee subcommittee on Nuclear Data (NSAC-ND) in September 2022. In this report, we present a set of fourteen (14) recommendations that will enhance and advance DOE-NP's stewardship of nuclear data. The first three recommendations focus on the existing core USNDP capabilities, namely: 1) Support the nuclear structure evaluation workforce to improve the currency, consistency, and accessibility of the Evaluated Nuclear Structure Data File (ENSDF); 2) Enhance nuclear reaction evaluation within the USNDP in support of the Evaluated Nuclear Data File (ENDF) through expansion of the workforce and integration of high-performance computing, automation, and machine learning and; 3) Continue atomic mass evaluation in support AME and NUBASE databases. This is followed by eight (8) recommendations representing new cross-cutting initiatives involving both measurement and evaluation to address outstanding nuclear data needs. These new initiatives require a highly trained, diverse workforce that includes personnel with expertise from both inside and outside the nuclear physics community from which evaluators have traditionally been recruited. As such, many of these initiatives are accomplished via a Topical Nuclear Data Collaborations (TNDC). A TNDC is made up of domestic and international stakeholders, subject matter and nuclear data experts, and nuclear data evaluators and features a workforce development plan to ensure that nuclear data evaluators maintain currency in the relevant applications and are seen as equity partners in the endeavor. These include: 1) Establish a coordinated effort to improve evaluation and modeling in nuclear astrophysics for stellar dynamics, multi-messenger astronomy and nucleosynthesis; 2) Initiate a TNDC to develop and maintain nuclear structure evaluation beyond discrete states, including nuclear level densities, photon strength functions and photonuclear data for improved reaction modeling, and exploring nuclear structure at finite temperature; 3) Create a TNDC to perform correlated fission data evaluation, including cross sections, fragment yields, v(A), v(E n ) for nuclear energy, national security, nonproliferation and basic science; 4) From a panel of subject matter experts to establish and annually update a roster of key decay data to nurture its accelerated dissemination including both measurement and evaluation for targeted high-value nuclides for national security, nonproliferation and medical applications; 5) Comprehensive, consistent neutron-induced structure and reaction data for nuclear energy, national security, nonproliferation and planetary nuclear spectroscopy; 6) Charged-particle stopping powers for detector design, space effects and ion beam therapy; 7) High-energy reactions for space exploration and medical nuclide production, and; 8) The creation of an infrastructure for open data and data preservation for use by the entire nuclear physics community. All told, these initiatives require approximately $6.5M increase in NP support of the USNDP in fiscal year 2023 dollars and would require at least 3-5 years to carry out due to the length of time needed to recruit and train new nuclear data researchers. This relatively modest investment would help ensure that the fruits of the nuclear data research carried out by DOE-NP and its collaborators would be brought to bear to address some of the most important needs of our nation and the world. To ensure effective execution of this plan, we present an overview of recruitment, training, and retention goals for the USNDP, the centerpiece of which is a mutually agreed upon code of conduct. Finally, we identify the facility and instrumentation needed to perform the recommended experimental activities. This includes a short review of target fabrication capabilities, reactors, neutron beam, light- and heavy-stable ion, gamma-ray, high-energy and radioactive ion beam facilities. Lastly, a more complete appendix of experimental facilities previously compiled is included with new input provided for 6 facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]↗

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Huge ensembles – Part 2: Properties of a huge ensemble of hindcasts generated with spherical Fourier neural operators

Abstract. In Part 1, we created an ensemble based on spherical Fourier neural operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires orders-of-magnitude fewer computational resources. Here in Part 2, we generate a huge ensemble (HENS), with 7424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. HENS has two primary applications: (1) as a large dataset with which to study the statistics and drivers of extreme weather and (2) as a weather forecasting system. For extreme climate statistics, HENS samples events 4σ away from the ensemble mean. At each grid cell, HENS increases the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.

Mahesh, Ankur↗

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗

Computational Methods in Heterogeneous Catalysis

The unprecedented ability of computations to probe atomic-level details of catalytic systems holds immense promise for the fundamentals-based bottom-up design of novel heterogeneous catalysts, which are at the heart of the chemical and energy sectors of industry. Here, we critically analyze recent advances in computational heterogeneous catalysis. First, we will survey the progress in electronic structure methods and atomistic catalyst models employed, which have enabled the catalysis community to build increasingly intricate, realistic, and accurate models of the active sites of supported transition-metal catalysts. We then review developments in microkinetic modeling, specifically mean-field microkinetic models and kinetic Monte Carlo simulations, which bridge the gap between nanoscale computational insights and macroscale experimental kinetics data with increasing fidelity. Here, we finally review the advancements in theoretical methods for accelerating catalyst design and discovery. Throughout the review, we provide ample examples of applications, discuss remaining challenges, and provide our outlook for the near future.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory

We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by 'ideal interfaces', and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient $\nabla p = 0$. The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the $\nabla p = 0$ in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion6 101; Glasser et al 1975 Phys. Fluids18 875–88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Projection-Based Model Reduction for Coupled Conduction—Enclosure Radiation Systems

We report a projection-based reduced order model (pROM) methodology has been developed for transient heat transfer problems involving coupled conduction and enclosure radiation. The approach was demonstrated on two test problems of varying complexity. The reduced order models demonstrated substantial speedups (up to 185×) relative to the full order model with good accuracy (less than 3% L ∞ error). An attractive feature of pROMs is that there is a natural error indicator for the ROM solution: the final residual norm at each time-step of the converged ROM solution. Using example test cases, we discuss how to interpret this error indicator to assess the accuracy of the ROM solution. The approach shows promise for many-query applications, such as uncertainty quantification and optimization. The reduced computational cost of the ROM relative to the full-order model (FOM) can enable the analysis of larger and more complex systems as well as the exploration of larger parameter spaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Preliminary Assessment of Qiskit Quantum Simulator Capabilities for Development of Quantum Hopfield Neural Network for Anomaly Detection Applications (Q4 Report)

Quantum information processing offers potentially faster performance compared to the classical counterpart. The goal of this work is to investigate performance of Quantum Hopfield Neural Network for applications to anomaly detection. Preliminary study consist of assessment of computational capabilities of Qiskit quantum simulator. Eventual objective is to implement Quantum Hopfield Network algorithm for detection of weak nuisance and anomaly signal in the presence of strong and highly varying background in gamma radiation data measured during environmental screening.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Predictive Theory of Topological States of Matter (Final Report for DOE Award DE-SC0018945)

This DOE award supported the PI’s research on topological quantum materials between 2018 and 2021. The PI developed predictive theories for new classes of topological insulators and topological/unconventional superconductors and identified their material realizations in collaboration with experimentalists. The PI theorized new topological transport phenomena, including spin superfluidity in moire materials and the superconducting diode effect. Topological transport phenomena have potential applications in cryogenic computing, low-power electronics, high-frequency rectification, infrared detection, energy harvesting and thermoelectric application. By discovering new quantum materials and new functional properties, the PI’s research contributed significantly to the advancement of DOE scientific and technological base, especially in energy frontier research.

36 MATERIALS SCIENCE↗

Digital Twins for Materials

Digital twins are emerging as powerful tools for supporting innovation as well as optimizing the in-service performance of a broad range of complex physical machines, devices, and components. A digital twin is generally designed to provide accurate in-silico representation of the form (i.e., appearance) and the functional response of a specified (unique) physical twin. This paper offers a new perspective on how the emerging concept of digital twins could be applied to accelerate materials innovation efforts. Specifically, it is argued that the material itself can be considered as a highly complex multiscale physical system whose form (i.e., details of the material structure over a hierarchy of material length) and function (i.e., response to external stimuli typically characterized through suitably defined material properties) can be captured suitably in a digital twin. Accordingly, the digital twin can represent the evolution of structure, process, and performance of the material over time, with regard to both process history and in-service environment. This paper establishes the foundational concepts and frameworks needed to formulate and continuously update both the form and function of the digital twin of a selected material physical twin. The form of the proposed material digital twin can be captured effectively using the broadly applicable framework of n-point spatial correlations, while its function at the different length scales can be captured using homogenization and localization process-structure-property surrogate models calibrated to collections of available experimental and physics-based simulation data.

36 MATERIALS SCIENCE↗

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

Efficient solution of the Vlasov equation, which can be up to six-dimensional, is key to the simulation of many difficult problems in plasma physics. The discontinuous Petrov-Galerkin (DPG) finite element methodology provides a framework for the development of stable (in the sense of Ladyzhenskaya–Babuška–Brezzi conditions) finite element formulations, with built-in mechanisms for adaptivity. While DPG has been studied extensively in the context of steady-state problems and to a lesser extent with space-time discretizations of transient problems, relatively little attention has been paid to time-marching approaches. In the present work, we study a first application of time-marching DPG to the Vlasov equation, using backward Euler for a Vlasov-Poisson discretization. We demonstrate adaptive mesh refinement for two problems: the two-stream instability problem, and a cold diode problem. Furthermore, we believe the present work is novel both in its application of unstructured adaptive mesh refinement (as opposed to block-structured adaptivity, which has been studied previously) in the context of Vlasov-Poisson, as well as in its application of DPG to the Vlasov-Poisson system. We also discuss extensive additions to the Camellia library in support of both the present formulation as well as extensions to higher dimensions, Maxwell equations, and space-time formulations.

97 MATHEMATICS AND COMPUTING↗

Advances in Nuclear Data Evaluation Theory for NCSP [Slides]

The generalized form of the Bayes’ Theorem improves UQ for NCSP of differential and/or integral data evaluations and of applications. It is being implemented in an API for use by SCALE, SAMMY, etc. Extended R-matrix formalism improves evaluations of RRR including direct reactions, direct capture, and the Reich-Moore approx., doorway state reactions with applications to RPI data on lead isotopes. Extended R-Matrix formalism will be implemented into SAMMY post modernization.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗