Search NASA⌕ Search

SEARCH · Search NASA

Results for “user interface”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

The Hydropower Game: An Interactive Learning Tool for the Future Hydropower Workforce

This report documents a Seedling project supported by the U.S. Department of Energy (DOE) Water Power Technologies Office (WPTO), conducted by Argonne National Laboratory (ANL) and the National Laboratory of the Rockies (NLR). The Seedling and Sapling Program provides small grants over short duration to enable early-stage research at national laboratories. This funding mechanism is intended to cultivate innovative ideas and expand research road maps in hydropower and marine energy technologies. Under this Seedling award, the project team developed an educational outreach tool, or “serious game”, built in Python and powered by the Pygame library, aimed at teaching fundamental hydropower concepts through an engaging, interactive learning experience. The game features multiple lessons covering several hydropower topics while allowing for expansion and customization in the instance of future funding availability: • Hydropower Plant Types: Players explore and compare the mechanics and applications of run-of-river, dam hydropower, and pumped-storage hydropower. • Flow Dynamics and Power Generation: Interactive tasks demonstrate how release rate and hydraulic head combine to determine power output. • Grid Operations and Load Following: Simulations illustrate how hydropower facilities respond to fluctuating electricity demand to balance the grid. • Market Integration: Levels scaffold understanding of how hydropower interfaces with the broader energy market, including operational and economic considerations. The tool was showcased at several science, technology, engineering, and mathematics (STEM) outreach events, where it was demoed to students, educators, and the general public. These events provided valuable opportunities to collect feedback on the gameplay, storyline, and educational objectives from a wide audience. The game was presented at STEMapalooza, Introduce a Girl to Engineering Day, STEMCON, and Clean Currents 2025. Insights gathered during these demonstrations informed refinements to the game’s user experience and strengthened its effectiveness as an educational tool for teaching hydropower concepts. This report outlines the game’s design philosophy, educational objectives, technical implementation, user experience insights, and potential for broader deployment within educational and workforce development contexts. It emphasizes how gamified learning can demystify complex hydropower science and inspire interest in water-power technologies. The project’s success demonstrates the value of Seedling funding in fostering creative, lowcost educational tools that support DOE’s mission to advance energy literacy and innovation. The report concludes with recommendations for expanding the tool by adding new levels, integrating assessment metrics, and exploring commercialization or deployment pathways through future Sapling funding. The official webpage of the Hydropower Game, which includes a link to the educational tool, can be accessed at www.anl.gov/hydropower/hydropower-game.

13 HYDRO ENERGY↗

Implementing a unified solver for nonlinearly constrained optimization

SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno’s software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at https://github.com/cvanaret/Uno and via its C, Julia, Python, Fortran, and AMPL interfaces.

97 MATHEMATICS AND COMPUTING↗

Web-Based Tools for Data-Informed Remedy Optimization: Software Theory and User Guide

This report documents the development and application of two web-based decision-support tools for pump-and-treat (P&T) groundwater remediation systems: PTOLEMY (Pump-and-Treat Optimized Location Evaluation to Maximize Yields) and OPTIMA (Optimization for Pump-and-Treat Implementation, Management, & Assessment). These tools enhance remedy design and management by leveraging advanced computational methods – specifically deep learning and multi-objective optimization – within a user-friendly platform. By integrating data-driven models with established hydrogeological knowledge, PTOLEMY and OPTIMA enable more efficient evaluation of well placement and operational strategies, helping site managers balance multiple remediation objectives under complex conditions. Both tools are implemented as modules within the SOCRATES (Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites) web platform, which provides data access, visualization, and analytics to support remedy optimization across sites in the U.S. Department of Energy Office of Environmental Management complex. PTOLEMY is a rapid screening module designed to identify promising locations for new extraction wells. It employs a multi-channel three-dimensional convolutional neural network (MC3D-CNN) trained on high-fidelity simulation data to predict the relative performance (in terms of contaminant mass recovery) of potential well sites. Through an interactive web interface, PTOLEMY visualizes the probability of high performance across a site, highlighting areas where an extraction well is likely to yield above-threshold contaminant removal over a multi-year period. PTOLEMY’s map-based displays and exportable results support transparent communication of screening analyses. By focusing attention on the most favorable candidate locations, the tool augments traditional engineering judgment and physics-based modeling, providing a data informed basis for subsequent detailed evaluations. OPTIMA is a multi objective optimization module designed to find wellfield layouts and operating schedules that meet various cleanup goals. It quickly evaluates thousands of candidate setups – combinations of well locations, timing, and rates – and returns a small set of best trade-off options for comparison. At its core, OPTIMA uses a U-Net-based surrogate model – a deep-learning emulator of a groundwater flow and transport simulator – to dramatically accelerate scenario evaluations. Coupling this fast surrogate with the NSGA-II (Non-dominated Sorting Genetic Algorithm II) evolutionary algorithm, OPTIMA explores a wide decision space of well locations and schedules to identify Pareto-optimal solutions that trade off key objectives (e.g., minimizing cleanup time, maximizing contaminant mass removal, and minimizing plume extent). The tool outputs a family of optimal configurations and visualizes their trade-offs (Pareto frontiers of cleanup metrics and maps of optimized well placements). Site managers can use these results to understand the range of viable strategies and to select candidate designs for more detailed verification. OPTIMA is currently under active development and not yet fully released; this guide provides early documentation to support planning and gather user feedback.

54 ENVIRONMENTAL SCIENCES↗

Energy Systems Integration Facility (ESIF): World-Class Systems Integration Capabilities and Research

The Energy Systems Integration Facility (ESIF), located at the National Renewable Energy Laboratory (NREL) South Table Mountain campus, is a world-renowned user facility for research and development of modern, advanced, and clean energy technologies. ESIF is distinguished by its continuously evolving, highly integrated systems that span throughout the building, connecting research capabilities across multiple laboratories and test areas. The primary ESIF research systems include: [1] data, cyber, and control networks, [2] research electrical distribution buses (REDB), [3] thermal integration infrastructure, and [4] hydrogen systems. The data, cyber, and control networks provide monitoring, control, communication, automation, visualization, and time series data storage and tagging capabilities for research projects and ESIF systems, including facility safety functions. The REDB system consists of four dedicated AC and DC electrical power networks that can connect devices located across the facility through versatile, automatic circuit configuration to support complex power electronics experiments up to the megawatt-scale. The thermal integration infrastructure consists of three temperature-conditioned water loops that provide heating and cooling interfaces and capabilities for thermal energy research. The hydrogen systems provide megawatt-scale hydrogen production, drying, compression, high-pressure storage, and delivery to laboratory end uses, including hydrogen fuel cell vehicle fueling. The ESIF research systems interconnect and extend throughout the various lab areas of the facility to create elaborate networks composed of diverse technologies for cutting-edge research. The ESIF capabilities are operated and stewarded by the ESIF Research Operations group, who also actively upgrade and advance the systems to ensure they remain ahead of anticipated research - enabling the success of many pioneering energy integration projects. The poster, created by members of the ESIF Research Operations team, highlights and summarizes the four core integrated systems at ESIF. The poster was first presented at the internal NREL Energize Forum on May 13th, 2024, and received the "Best Poster" award.

capabilities↗

A new database website for nuclear level densities

We introduce a new open-access, web-based database (http://nld.ascsn.net), Current Archive of Nuclear Density of Levels (CANDL), that hosts experimental nuclear level density (NLD) datasets from a variety of techniques and energy ranges. Built using the Dash framework in Python, the database is designed to be interactive and user-friendly, allowing researchers to search, visualize, fit, and export NLD data with minimal effort. This resource includes data extracted from evaporation spectra, Oslo method variants, and other experimental techniques that cover excitation energies beyond the neutron resonance region. The database supports on-the-fly fitting with two widely-used phenomenological models—the Constant Temperature (CT) model and the Back-Shifted Fermi Gas (BSFG) model—selected for their simplicity and computational efficiency. Future versions aim to include additional datasets and model types, as well as easy-to-use interfaces to data science techniques. Here, this platform offers a vital tool for the nuclear physics, astrophysics, medicine, and reactor design communities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

ERF: Energy Research and Forecasting Model

High performance computing (HPC) architectures have undergone rapid development in recent years. As a result, established software suites face an ever increasing challenge to remain performant on and portable across modern systems. Many of the widely adopted atmospheric modeling codes cannot fully (or in some cases, at all) leverage the acceleration provided by General-Purpose Graphics Processing Units, leaving users of those codes constrained to increasingly limited HPC resources. Energy Research and Forecasting (ERF) is a regional atmospheric modeling code that leverages the latest HPC architectures, whether composed of only Central Processing Units (CPUs) or incorporating GPUs. ERF contains many of the standard discretizations and basic features needed to model general atmospheric dynamics. The modular design of ERF provides a flexible platform for exploring different physics parameterizations and numerical strategies. ERF is built on a state-of-the-art, well-supported, software framework (AMReX) that provides a performance portable interface and ensures ERF's long-term sustainability on next generation computing systems. This paper details the numerical methodology of ERF, presents results for a series of verification/validation cases, and documents ERF's performance on current HPC systems. The roughly 5× speed up of ERF (using GPUs) over Weather Research and Forecasting (CPUs only) for a 3D squall line test case highlights the significance of leveraging GPU acceleration.

17 WIND ENERGY↗

BioSiting Tool (BioSiting) v2

The BioSiting Tool provides a geospatial interface for analyzing bioeconomy resources and infrastructure across the continental U.S. The tool integrates empirical and modeled data from a broad range of sources. Bioeconomy resources mapped in the tool include agricultural residues, forest residues, municipal solid waste streams, food waste, manure, fats, oils and greases and potential yields of energy crops. Infrastructure mapped in the tool includes biorefineries, material recovery facilities, anaerobic digesters, wastewater treatment plants, combustion plants, district energy systems, crude oil pipelines, petroleum pipelines, natural gas pipelines, railways and freight terminals. Additional data layers include environmental justice indicators at the census tract level and carbon dioxide geologic storage potential. Users can select a location on the map, define a buffer radius in kilometers and generate an inventory of all bioecomony resources within the buffer zone. Data from the tool can be downloaded from individual buffer zones, or at the state or national level.

Huntington, Tyler↗

The Viskores User's Guide (V.1.0)

High-performance computing relies on ever finer threading. Advances in processor technology include ever greater numbers of cores, hyperthreading, accelerators with integrated blocks of cores, and special vectorized instructions, all of which require more software parallelism to achieve peak performance. Traditional visualization solutions cannot support this extreme level of concurrency. Extreme scale systems require a new programming model and a fundamental change in how we design algorithms. To address these issues we created Viskores: the visualization toolkit for multi-/many-core architectures. Viskores supports a number of algorithms and the ability to design further algorithms through a top-down design with an emphasis on extreme parallelism. Viskores also provides support for finding and building links across topologies, making it possible to perform operations that determine manifold surfaces, interpolate generated values, and find adjacencies. Although Viskores provides a simplified high-level interface for programming, its template-based code removes the overhead of abstraction.

97 MATHEMATICS AND COMPUTING↗

The Viskores User's Guide, Release 1.1

High-performance computing relies on ever finer threading. Advances in processor technology include ever greater numbers of cores, hyperthreading, accelerators with integrated blocks of cores, and special vectorized instructions, all of which require more software parallelism to achieve peak performance. Traditional visualization solutions cannot support this extreme level of concurrency. Extreme scale systems require a new programming model and a fundamental change in how we design algorithms. To address these issues we created Viskores: the visualization toolkit for multi/many-core architectures. Viskores supports a number of algorithms and the ability to design further algorithms through a top-down design with an emphasis on extreme parallelism. Viskores also provides support for finding and building links across topologies, making it possible to perform operations that determine manifold surfaces, interpolate generated values, and find adjacencies. Although Viskores provides a simplified high-level interface for programming, its template-based code removes the overhead of abstraction.

97 MATHEMATICS AND COMPUTING↗

The VTK-m User's Guide (V. 2.2)

High-performance computing relies on ever finer threading. Advances in processor technology include ever greater numbers of cores, hyperthreading, accelerators with integrated blocks of cores, and special vectorized instructions, all of which require more software parallelism to achieve peak performance. Traditional visualization solutions cannot support this extreme level of concurrency. Extreme scale systems require a new programming model and a fundamental change in how we design algorithms. To address these issues we created VTK-m: the visualization toolkit for multi-/many-core architectures. VTK-m supports a number of algorithms and the ability to design further algorithms through a top-down design with an emphasis on extreme parallelism. VTK-m also provides support for finding and building links across topologies, making it possible to perform operations that determine manifold surfaces, interpolate generated values, and find adjacencies. Although VTK-m provides a simplified high-level interface for programming, its template-based code removes the overhead of abstraction.

97 MATHEMATICS AND COMPUTING↗

VirJenDB: a FAIR (meta)data and bioinformatics platform for all viruses

High-throughput sequencing has generated an unprecedented volume of data. However, researcher-submitted data in repositories requires extensive curation and quality control for reuse. These tasks are hindered by the multiplicity of repositories, the sheer volume of the data, and the complexity of virus (meta)data curation. To address these challenges, VirJenDB offers a user-friendly platform to facilitate versioned, community-driven curation, and ontology development. Virus sequences were ingested from 16 sources, including ~200 fields of metadata or standards, covering taxonomy, sample, and host information. Up to 85 metadata fields have undergone at least one round of curation, and are linked to 15.4 million virus sequences, with 88 % from those infecting eukaryotes and the remaining infecting prokaryotes. Subsets were created, including a novel collection of 0.91 million viral operational taxonomic unit (vOTU) sequences across all viruses, while keeping the original sequences from each vOTU to facilitate downstream analyses, e.g. sequence variation. The VirJenDB web portal (https://www.virjendb.org) provides HTTPS and Application Programming Interface (API) access to the sequence datasets and metadata, offering a search engine, filtering, download, visualizations, and documentation. VirJenDB aims to connect the phage and eukaryotic virus research communities by supporting webtool integration, meta-analyses, and metadata schema extensions.

Saghaei, Shahram↗

From Obsolete to Optimal (ATR Demineralized Water System)

My project was migrating a Human-Machine Interface (HMI) and Programmable Logic Controller (PLC) program from legacy software to a modern platform, enhancing operational efficiency and eliminating unsupported, obsolete equipment. Initially, I used a migration tool to transfer the programs to the new software, then manually updated variables to align with the new PLC. I optimized the PLC code by leveraging new scaling features in the I/O cards, removing over 45 obsolete rungs, and enhancing clarity with functional tag aliases. Next, I modernized the HMI's visuals with an updated color scheme and 3D buttons. I developed multiple interface versions iteratively refining them based on operator feedback. I also designed and created a dedicated "Rounds" screen incorporating insights from a previous intern’s project to streamline daily rounds. To improve clarity, consistency, and efficiency I redesigned the entire interface. Adding visual indicators to enhance operational awareness: red is used for values outside normal specifications, green for normal operating modes, yellow for manual mode, and grey for offline units. Additionally, I added a dynamic visual representation of tank levels, creating PLC logic to show the level in inches as well as inches and feet. I then incorporated a navigation sidebar to facilitate efficient screen transitions. Risk of human error was mitigated by defining narrow input ranges for tank level shutoff and password protecting setpoint changes. I also fixed issues with datatypes that caused inaccuracies in the original code. Overall, this comprehensive upgrade significantly enhanced the HMI's functionality, user experience, and operational reliability.

47 - OTHER INSTRUMENTATION↗

PRISMA: PARALLEL REFINEMENT AND INTEGRATION SYSTEM FOR MULTI-AZIMUTHAL ANALYSIS

The Parallel Refinement and Integration System for Multi-azimuthal Analysis (PRISMA, version 1.1.0) is a Python application for processing X-ray diffraction (XRD) image data. PRISMA wraps GSAS-II to perform azimuthally-binned peak refinement, computes per-frame strain and d-spacing from those fits, and provides three PyQt5 graphical interfaces: (1) a Recipe Builder for selecting GSAS-II control (.imctrl) files, optional mask (.immask) files or threshold-ased masking, reference and experiment image sets, peaks, zimuthal range and bin size, and an optional ceria-based auto-calibration; (2) a Batch Processor that uses Dask on local workstations and pure MPI (mpi4py.futures.MPICommExecutor) on HPC to distribute GSAS-II refinement across cores or compute nodes and write results to a 4-dimensional (peaks x frames x azimuths x measurements) Zarr dataset; and (3) a Data Analyzer that renders heatmaps of fit parameters, strain, frame-to-frame deltas, and percent-change-vs-reference, and exports user-defined subsections to CSV or Excel. The peak-refinement algorithm is deterministic. Benchmark on ALCF Crux: a 20,000-image set, single-peak fit in frame mode with 44 azimuthal bins on 128 nodes x 128 workers, 48 seconds total wall time.

Lorenzo Martin, Maria De La Cinta [Argonne Nationa↗

The U.S. Agrivoltaic Shading Tool: A National-Scale Interface for Modeling Light and Shade Patterns in Ten Common Agrivoltaic Configurations

Agrivoltaic systems are dual-use configurations that co-locate agriculture and photovoltaic (PV) infrastructure and require careful design to balance crop performance and energy generation. A critical element of agrivoltaic design is the spatial and temporal distribution of irradiance and shade within and around PV arrays. To support research, planning, and stakeholder decision-making, we introduce the U.S. Agrivoltaic Shading Tool, a novel web-based application that delivers high-resolution irradiance and photosynthetically active radiation (PAR) modeling for ten standardized PV configurations across the conterminous United States. The tool leverages the National Laboratory of the Rockies (NLR) System Advisor Model (SAM) to perform detailed irradiance simulations, using meteorological data from the National Solar Radiation Database (NSRDB). Outputs include seasonal, monthly, weekly, and diurnal patterns of available sunlight, amount of shade, irradiance, and PAR at ground level within agrivoltaic system footprints. For a user's selected location, these results are visualized through interactive visualizations, heatmaps, and time-series plots, designed to be accessible to both technical and non-technical users. In addition to facilitating rapid spatial exploration of agrivoltaic light environments, the tool will offer seamless integration with the InSPIRE Agrivoltaics Design and Analysis Model (ADAM). This optional workflow will allow users to port selected site and configuration parameters into a more advanced modeling environment for further customization of structural layouts, crop-system compatibility, power generation, and technoeconomic performance. Finally, to promote open science, the entire dataset will be hosted and available for open access through the OpenEI platform. By standardizing and disseminating high-quality irradiance data and design tools, the U.S. Agrivoltaic Shading Tool supports a wide range of users, including researchers, landowners, energy developers, and policymakers, in evaluating the agronomic and energetic feasibility of agrivoltaic systems across the United States.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

New technology for an ancient fish: A lamprey life cycle modeling tool with an R Shiny application

Lampreys (Petromyzontiformes) are an ancient group of fishes with complex life histories. We created a life cycle model that includes an R Shiny interactive web application interface to simulate abundance by life stage. This will allow scientists and managers to connect available demographic information in a framework that can be applied to questions regarding lamprey biology and conservation. We used Pacific lamprey ( Entosphenus tridentatus ) as a case study to highlight the utility of this model. We applied a global sensitivity analysis to explore the importance of individual life stage parameters to overall population size, and to better understand the implications of existing gaps in knowledge. We also provided example analyses of selected management scenarios (dam passage, fish translocations, and hatchery additions) influencing Pacific lamprey in fresh water. These applications illustrate how the model can be applied to inform conservation efforts. This tool will provide new capabilities for users to explore their own questions about lamprey biology and conservation. Simulations can hone hypotheses and predictions, which can then be empirically tested in the real world.

Gomes, Dylan G. E. (ORCID:0000000226423728)↗

How Snow Drives the Seasonal Evolution of Land and Sea Surface Albedos in the Alaskan High Arctic: Final Technical Report

The purpose of the project was to observe and quantify temporal variation in snow albedo and snow characteristics across the Arctic coastal landscape as winter transitioned into spring and snowmelt occurred, both on tundra and sea ice. This transition is bounded by fully snow-covered landscapes with broadband albedos of approximately 0.8 and snow-free landscapes with albedos of 0.15 (tundra or ponded sea ice). For these landscapes, we monitored the spring surface characteristics and radiative properties nearly daily at three locations on or near the Department of Energy ARM North Slope of Alaska (NSA) User Facility in Utqiagvik, Alaska: the central NSA Facility (hereafter called ARM), one near NSA-E12 (BEO), and one on the sea ice of Elson Lagoon (ICE) during three melt seasons (2019, 2022, and 2024). The field campaign component of this award was named SALVO ( S now AL bedo E VO lution). Typical field seasons began in mid-April and lasted until mid-June. Main measurements included snow depth (at 1-m intervals), broadband albedo (at 5-m intervals), spectral albedo (at 5- m intervals), and multiple digital images. Orthomosaics were converted into binary images to determine the snow-covered fraction over time across various landscapes. Additional measurements included basic weather data and snow-ground (or ice) interface temperatures. Sky conditions were observed and photographed to help assess albedo values.

54 ENVIRONMENTAL SCIENCES↗

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power densities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. The purpose of this work is to verify the power distribution results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

97 MATHEMATICS AND COMPUTING↗

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power desnities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. The purpose of this work is to verify the power distribution results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗