Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “optimization of nuclear systems”

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 253 records · Page 14

Noise Optimization for MKIDs with Different Design Geometries and Material Selections

The separation and optimization of noise components is critical to microwave-kinetic inductance detector (MKID) development. We analyze the effect of several changes to the lumped-element inductor and interdigitated capacitor geometry on the noise performance of a series of MKIDs intended for millimeter-wavelength experiments. We extract the contributions from two-level system noise in the dielectric layer, the generation-recombination noise intrinsic to the superconducting thin-film, and system white noise from each detector noise power spectrum and characterize how these noise components depend on detector geometry, material, and measurement conditions such as driving power and temperature. We observe a reduction in the amplitude of two-level system noise with both an elevated sample temperature and an increased gap between the fingers within the interdigitated capacitors for both aluminum and niobium detectors. We also verify the expected reduction of the generation-recombination noise and associated quasiparticle lifetime with reduced inductor volume. This study also iterates over different materials, including aluminum, niobium, and aluminum manganese, and compares the results with an underlying physical model.

generation-recombination noise↗

Selected Uses of TSUNAMI in Critical Experiment Design and Analysis

Validation in criticality safety is performed by comparing the results of critical experiments with the calculated results from models of the experiments using the computational method to be validated. Laboratory critical experiments are controlled systems that achieve a k eff of approximately 1 and enable investigation of the parameters at which such a critical condition is achieved. For the critical experiments used in a validation to capture the biases of the materials and neutron energy spectra of interest, those materials must be included in the experiment such that they influence k eff or another observable parameter with statistical significance. This paper discusses the use of sensitivity uncertainty (S/U) methods to develop critical experiments for various purposes. S/U techniques are useful for understanding the underlying components of nuclear data which affect the k eff or another parameter of a given configuration. S/U calculations are most commonly used to compare existing experiments to applications of interest; however, S/U techniques can also be used to identify, optimize, or assess features of proposed experiments so that they can better test specific portions of nuclear data or match an application of interest. The S/U techniques discussed here are from the TSUNAMI code system. The two primary codes discussed in this work are TSUNAMI-3D, which implements the KENO criticality code to calculate the sensitivity of k eff to nuclear data, and TSAR, which calculates the sensitivity of a reactivity difference between two configurations based on their TSUNAMI-3D generated sensitivity profiles. The methods used in these tools are discussed in more detail in the SCALE manual. This paper is one of a series on the development and use of TSUNAMI tools. The other papers address development of TSUNAMI methods and a review of TSUNAMI applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Fully Distributed Acoustic and Magnetic Field Monitoring Via a Single Fiber Line for Optimized Production of Unconventional Resource Plays

This is the final technical report for the Virginia Tech Center for Photonics Technology (VT-CPT) research project entitled “Fully Distributed Acoustic and Magnetic Field Monitoring Via a Single Fiber Line for Optimized Production of Unconventional Resource Plays”. In the the four-year effort, VT-CPT collaborated with the Departments of Mathmatics at VT and Sentek Instrument, LLC (Sentek) to develop a fiber-optic sensing system capable of real-time simultaneous distributed measurement of multiple subsurface, drilling, and production parameters. The ultra-sensitive fiber optic distributed acoustic sensing technology, picoDAS, developed by Sentek was integrated with a novel multi-material optical sensing fiber fabricated by CPT-VT to obtain distributed acoustic and magnetic field measurements with ultrahigh sensitivity and high spatial resolution. The sensing technology successfully developed and demonstrated under this research program is truly unique has application beyond subsurface imaging to include carbon storage and electrical grid monitoring, as well as healthcare and nuclear fusion. The project, sponsored by the Advanced Technology Program, began in 2019 and had the original goal of developing the next generation of harsh environment sensing systems. Exhaustive theoretical modeling was performed to optimize the multi-material optical fiber design. VT developed the processing techniques employed to successfully fabricate single mode fibers with metal cladding wires. Sensing fibers with nickel and Metglas cladding wires were fully characterized, inscribed with sensors, and fully integrated with the picoDAS system. Laboratory scale testing was performed to demonstrate performance upon exposure to lateral and transverse magnetic fields. Preliminary field trials were performed for prototype magnetic and acoustic sensing systems upon near surface deployment at VT. The distributed acoustic and magnetic field sensing system was advanced from a (Technology Readiness Level) TRL=2 to a TRL=5 via laboratory scale system validation in relevant environments. The truly one-of-its kind distributed magnetic and acoustic sensing system is expected to find immediate applications that require subsurface monitoring, to include carbon storage site monitoring, and has the potential to be a distributive technology in healthcare and electric grid markets. The technologies developed by Virginia Tech’s Center for Photonics Technology will support the mission of the National Energy Technology Laboratory (NETL) to drive innovation and deliver solutions for an environmentally sustainable and prosperous energy future by ensuring affordable, abundant, and reliable energy that drives a robust economy and national security. Technical accomplishments during the program are summarized briefly here and described in detail in the remainder of the report.

02 PETROLEUM↗

Impact of Higher Fidelity Design Iterations on Critical System Criteria

Nuclear criticality experiments are effective at informing the performance of nuclear data libraries across many applications. This work explores the implications of refining critical experiment MCNP models from their low fidelity optimization phase to penultimate neutronic models. Specifically, this work is focused on two series of plutonium fueled experiments funded through internal programs at Los Alamos National Laboratory building off previous efforts under the EUCLID (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) collaboration. Thales, the first of the two collaborations, is a fast spectrum Ta-reflected plutonium experiment to support operations at PF-4. The second experiment are twin configurations designed to target the intermediate energy cross sections in 239 Pu. Motivation for this experiment stems from the PARallel Approach of Differential and InteGral Measurements (PARADIGM) collaboration which hopes to achieve a significant reduction in 239 Pu cross section uncertainties in the intermediate region.

97 MATHEMATICS AND COMPUTING↗

Investigation of the temperature-dependent failure processes in PVD Cr-coated ZIRLO nuclear fuel cladding using in situ X-ray micro-tomography imaging

In this work, an accident tolerant fuel cladding system with Cr coating deposited using physical vapour deposition (PVD) method onto commercial Optimized ZIRLO™ was studied. The cladding tubes were machined into C-rings and loaded to failure under compression with real-time synchrotron micro-X-ray computed tomography (XCT) imaging at room temperature (RT), 345 °C, 650 °C and 950 °C in argon (Ar) atmosphere. The mechanical behaviour and failure processes were found strongly temperature-dependent where the Cr coating showed brittle fracture at RT and 345 °C, ductile fracture at 650 °C and a reversion to brittle fracture at 950 °C. Nanoindentation measurements and scanning electron microscopy (SEM) imaging were conducted on the materials after high temperature testing. It was found that recrystallisation of the Cr coating occurred at elevated temperatures, which significantly affected its local properties hence the failure behaviour at different temperatures. This work represents the first in situ 3D XCT observation of progressive failure processes in PVD Cr-coated ZIRLO claddings up to 950 °C providing critical insights into its brittle-to-ductile transition (BDTT) behaviour and subsequent ductile-to-brittle reversion with the increase in temperature. Moreover, results are compared with other PVD Cr-coated Zircaloy materials from open literature; the influences of the coating microstructure and local properties on the failure stress/strain and fracture processes are discussed.

Yuan, Guanjie↗

Testing in Support of Space Fission System Development and Qualification

Extensive data would be required for the qualification of a fission surface power (FSP) system. The strategy for qualifying a FSP system could have a significant programmatic impact. This paper explores potential options that could be used for qualifying FSP systems, including cost-effective means for obtaining required data. three methods for obtaining qualification data are analysis, non-nuclear testing, and nuclear testing. It has been over 40 years since the US qualified a space reactor for launch. During that time, advances have been made related to all three methods. Perhaps the greatest advancement has occurred in the area of computational tools for design and analysis. Tools that have been developed, coupled with modem computers, would have a significant impact on a FSP qualification. This would be especially true for systems with materials and fuels operating well within temperature, irradiation damage, and burnup limits. The ability to perform highly realistic non-nuclear testing has also advanced throughout the past four decades. Instrumented thermal simulators were developed during the 1970s and 1980s to assist in the development, operation, and assessment of terrestrial fission systems. Instrumented thermal simulators optimized for assisting in the development, operation, and assessment of modem FSP systems have been under development (and utilized) since 1998. These thermal simulators enable heat from fission to be closely mimicked (axial power profile, radial power profile, temperature, heat flux, etc.} and extensive data to be taken from the core region. Both steady-state and transient operation can be tested. For transient testing, reactivity feedback is calculated (or measured in cold/warm criticals) based on reactor temperature and/or dimensional changes. Pin power during a transient is then calculated based on the reactivity feedback that would occur given measured values of temperature and/or dimensional change. In this way nonnuclear testing can be used to provide very realistic information related to nuclear operation. Non-nuclear testing can be used at all levels, including component, subsystem, and integrated system testing. Realistic non-nuclear testing is most useful for systems operating within known temperature, irradiation damage, and burnup capabilities.

Houts, Mike↗

Laser-Based Means for Accelerating Nuclear Decay Rate

This project aims to replicate and build upon a reported series of results whereby nuclear decay of unstable species has been accelerated under laser irradiation in the presence of resonantly excited plasmonic nanoparticles. We are currently utilizing a laser system similar to that used within these reports as well as optimizing nanoparticle solution environments in an attempt to replicate reported results or provide alternative pathways that may explain some perceived discrepancies. The current work is being performed with equipment and techniques currently available at SRNL, including nanoparticle synthesis and pulsed lasers for plasmon excitation. The results of these experiments could provide quantitative data that can be used to resolve the discrepancies in the calculations and better estimate the ultimate utility of the process. If verified, this would represent a pathway for using readily available and scalable technology to reduce the long-term radiological storage requirements of certain forms of nuclear waste.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Distinguishing fissile uranium isotopes using an active well neutron coincidence counter

Proposed thorium-based nuclear fuel cycles are likely to require quantification and verification of 233 U within nuclear material. Because of their similar fission cross sections, active neutron nondestructive assay (NDA) systems may respond similarly to 233 U and 235 U. Traditional safeguards equipment has been optimized for 235 U and 238 U quantification associated with conventional uranium/plutonium fuel cycles and may not be directly applicable to 233 U quantification when mixed with other actinides. This work used models of the large volume active well coincidence counter (LV-AWCC) at Oak Ridge National Laboratory to evaluate the performance of this neutron NDA system to differentiate fissile uranium isotopes. The models were developed to simulate NDA system performance in response to a number of triangular radiation signature training device sources within the central cavity or well. This work predicted that the LV-AWCC can effectively differentiate 233 U from 235 U in certain modes of operation. In active mode, the LV-AWCC with the cadmium liner results in different doubles count rates between the fissile isotopes for a given fissile uranium mass. Without the cadmium liner, the uranium isotopes provide a statistically indistinguishable doubles count rate response for the fissile masses considered in this work (up to approximately 150 g). The cadmium liner serves to harden the neutron interrogation spectrum, which better exploits the notable difference in the 233 U and 235 U fission cross sections at approximately 1 eV. In passive mode, the two fissile isotopes exhibit different doubles and singles count rates regardless of liner presence because the passive source strength of 233 U is approximately 2 orders of magnitude stronger than that of 235 U due to the shorter half-life and correspondingly higher (α, n) yield. We conclude that using neutron interrogation in the LV-AWCC, two measurements are needed to quantify 233 U content in mixed uranium items. The first measurement is used to determine the total fissile uranium mass using a mode that cannot distinguish fissile isotopes (i.e., where a similar response is observed for both fissile uranium isotopes such as active doubles without cadmium or using a thermal neutron interrogation source). In conclusion, the second measurement is used to determine the 233 U content by using a differentiating technique (e.g., passive doubles, passive doubles to singles ratio, active doubles with cadmium).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

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↗

Design and optimization of flexible decoupled high-temperature gas-cooled reactor plants with thermal energy storage

Advanced nuclear power plants are well-positioned for future zero-carbon grids, however, the need for flexible power generation will be required over the traditional emphasis on baseload generation for meeting historical demands. To achieve such flexibility, this work examines viable configurations for coupling nuclear energy production with thermal energy storage. Previous designs on nuclear-thermal energy storage configurations for advanced reactor designs, which utilized reactor steam as the heat source for charging the thermal energy storage, are restricted by the heat diversion ratio and efficiency losses, thus their impacts can be limited. In this context, this study proposes configurations for fully decoupling the nuclear reactor from the power cycle and positioning the storage as an intermediate loop, thereby achieving an unconstrained heat diversion ratio and improved efficiency. Compared with a standard high-temperature gas-cooled reactor’s power cycle, steady-state thermodynamic modeling and dispatch optimizations quantify the benefits of a steam reheat cycle within the fully decoupled thermal energy system to separate the plant cycle from the high-pressure primary side. These benefits are further detailed, compatible with required high-temperature and high-pressure conditions, through (1) open-source dynamic transient models that examine the impact of off-design operation on the systems, (2) the investigation of components design and costing and finally (3) sizing and dispatch optimization. The fully-decoupled design achieves a cycle efficiency of 43.1%, an enhancement over the vendor’s standard efficiency of 42.2% (Xe-100 design). Here, the proposed design offers strengthened physical barriers from the nuclear island as well as superior operational flexibility and power boosting. Dispatch optimization and market analysis reveal that thermal energy storage size is highly dependent on the peak patterns of electricity prices and the minimum generation level constraint imposed on the balance of plant. Evaluation of off-design operation demonstrates that the full decoupling design with the suggested fail-safe control mechanisms ensures a minimal impact on reactor parameters, even during rapid power ramping.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Evaluation of Hybrid FPOG Applications in Regulated and Deregulated Markets Using HERON

Recent changes in the U.S. energy market, such as low natural gas prices and increased electricity production for variable renewable energy (VRE) sources, have led to an economic crisis for existing light-water reactor (LWR) nuclear power plants (NPP). Many owners and operators of LWRs have elected to decommission these plants rather than continue using them as consistent sources of clean baseload power. This has led to exploration of various possibilities to increase the economic viability of these units, including market restructuring to monetize benefits LWRs already provide to the grid through ancillary markets, load following and economic dispatch, and possible integration of secondary systems directly to the NPP for production of additional products through technologies such as hydrogen electrolysis or water desalination. Previous studies have considered the technologies associated with these Integrated Energy Systems (IES) activities, and the analysis of markets for these secondary products. To analyze the economic viability of various system configurations including IES, especially given the uncertainty surrounding load demand, electricity prices, and the availability of VRE resources, the stochastic technoeconomic analysis package HERON (Heuristic Energy Resource Optimization Network) was released earlier this year as an extension of the risk analysis framework RAVEN (Risk Analysis Virtual Environment). HERON focuses foremost on making the complex uncertainty quantification analysis tools approachable for energy systems analysts, also providing general dispatch optimization algorithms for those workflows. HERON continues to be improved and tested as a significant part of the IES viability analyses performed in this work. HERON is not a capacity expansion model. To consider market and grid energy system development in a variety of scenarios, HERON is best used in coupling with modelling tools such as US-REGEN, which sacrifice some of the uncertainty analysis and resolution of HERON's modelling for the ability to efficiently predict the change in the grid energy system's profile due to economic drivers over decades. HERON can then use this information to explore the economic viability of introducing changes to the predicted outcomes, such as the introduction of an IES. In this work, experts at EPRI using US-REGEN provide six projection scenarios for use in HERON stochastic technoeconomic analysis (STEA) in considering the options available for increasing LWR economic viability through introduction of a hydrogen-centric IES using a high-temperature steam electrolysis plant (HTSE), hydrogen storage, and a constant-rate contracted hydrogen consumer. The results obtained are differential in nature; they do not report expected profits for any configuration, but rather report on the possible increase in the NPV of a configuration with respect to a baseline no-IES configuration. Due to the uncertainty captured in the variable net load of the systems, there is likewise uncertainty in the mean values reported. We consider this viability both in terms of a regulated market, where the energy producers and IES are owned and operated by single entity, as well as a deregulated market, where the IES chooses its bid for electricity generation and is then dispatched by the grid system operator. Results indicate that for deregulated markets, the inclusion of the IES is often statistically beneficial. This is especially true in policies that are not favorable towards nuclear, as nuclear is less often dispatched and is forced to deal with frequent idle capacity. In the nominal case as well as the case of carbon tax policies, inclusion of the IES clearly benefited the economic performance of the NPP. In the regulated case, however, there was a trend towards minimizing the IES, likely due to the optimal sizing performed by US-REGEN of the NPP within the system as well as the lack of penalty for idle capacity at the NPP in the regulated market analyses.

99 GENERAL AND MISCELLANEOUS↗

Nuclear electric propulsion

We investigate the feasibility of using nuclear electric propulsion (NEP) for slow "freighter" ships traveling from a 500 km low Earth orbit {LEO) to the Moon's orbit about the Earth, and on to Mars. NEP is also shown to be feasible for transporting people to Mars on long conjunction-class missions lasting about nine months one way, and on short "sprint" missions lasting four months one way. Generally, we have not attempted to optimize ion exhaust velocities, but rather we have chosen suitable parameters to demonstrate NEP feasibility. Various combinations of missions are compared with chemical and nuclear thermal propulsion (NTR) systems. Typically, NEP and NTR can accomplish the same lifting task with similar mass in LEO. When compared to chemical propulsion, NEP was found to accomplish the same missions with 40% less mass in LEO. These findings are sufficiently encouraging as to merit further studies with optimum systems.

Paul W Keaton↗

Evaluation of the Reconstruction Accuracy of the Ultrasound Model–Based Image Reconstruction (U-MBIR) Method for Concrete to Optimize Damage Detection

Reinforced concrete is a critical structural material used to construct nuclear power plants (NPPs). As such, its safety and performance must be thoroughly examined throughout the life cycle of the NPP infrastructure system. Ultrasonic measurements have been an industry standard for both surface and subsurface inspections. To support the development of these techniques, Oak Ridge National Laboratory (ORNL) has researched and developed advanced image reconstruction algorithms to capture internal damage. The results and discussion presented herein summarize the current state of the ultrasonic model–based iterative reconstruction (U-MBIR) algorithm developed at ORNL. In the work documented in this report, the U-MBIR methodology was applied to four sets of ultrasonic data collected from concrete specimens. The results demonstrate that the U-MBIR algorithm can successfully detect defects within the four concrete samples. The reconstruction images help identify the specimen thickness, regions of delamination, and location of rebar embedded within the concrete. The reconstruction images allow engineers and technicians to characterize the internal defects within concrete specimens and structural members. Ultimately, this knowledge can guide engineers in making informed decisions regarding the performance, safety, and reliability of structural materials (i.e., reinforced concrete) throughout the life cycle of NPPs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Plasma facing components with capillary porous system and liquid metal coolant flow

Liquid metal can create a renewable protective surface on plasma facing components (PFC), with an additional advantage of deuterium pumping and the prospect of tritium extraction if liquid lithium (LL) is used and maintained below 450 °C, the temperature above which LL vapor pressure begins to contaminate the plasma. LM can also be utilized as an efficient coolant, driven by the Lorentz force created with the help of the magnetic field in fusion devices. Capillary porous systems can serve as a conduit of LM and simultaneously provide stabilization of the LM flow, protecting against spills into the plasma. Recently, a combination of a fast-flowing LM cooling system with a porous plasma facing wall (CPSF) was investigated [A. Khodak and R. Maingi, Nucl. Mater. Energy 26, 100935 (2021)]. The system takes an advantage of a magnetohydrodynamics velocity profile as well as attractive LM properties to promote efficient heat transfer from the plasma to the LL at low pumping energy cost, relative to the incident heat flux on the PFC. In the case of a disruption leading to excessive heat flux from the plasma to the LM PFCs, LL evaporation can stabilize the PFC surface temperature, due to high evaporation heat and apparent vapor shielding. The proposed CPSF was optimized analytically for the conditions of a fusion nuclear science facility [Kessel et al., Fusion Sci. Technol. 75, 886 (2019)]: 10 T toroidal field and 10 MW/m 2 peak incident heat flux. Finally, computational fluid dynamics analysis confirmed that a CPSF system with 2.5 mm square channels can pump enough LL so that no additional coolant is needed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Cold Moderator For Sub-Thermal Neutron Flux Enhancement at the RPI-LINAC

The importance of high-quality thermal neutron scattering kernels coupled with a lack of accurate sub-thermal total cross section data prompted researchers at Rensselaer Polytechnic Institute (RPI) to design a cold moderation system to enhance sub-thermal neutron flux (defined as flux below 5 meV), for nuclear data measurements at the RPI Gaerttner LINAC facility. Using a series of neutronic and heat transfer simulations obtained with MCNP and COMSOL, an optimized final design was produced. The final design exceeded current target sub-thermal neutron producing capabilities by a factor of 8 in the sub-thermal region and is easily configurable with existing neutron producing targets.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

FORCE Development Status Update: Vertical Integration and Benchmarking of System Dynamics

Recent efforts to establish effective models for grid energy analysis, especially given the increase in variable renewable energy (VRE) sources and the economic challenges faced by traditional nuclear energy, have generated new technological considerations. One effort to improve the economic viability of nuclear power involves investigating integrated energy systems (IES) which include secondary energy systems that introduce flexibility and secondary market possibilities to existing and perceived future nuclear energy generation technologies. To analyze the technical and economic potential of IES, the Framework for Optimization of Resources and Economics (FORCE) tool suite was developed through a collaboration among national laboratories. Within the FORCE tool suite, the Holistic Energy Resource Optimization Network (HERON) provides algorithms for analyzing the long-term viability of potential IES technologies, while HYBRID provides algorithms and models to achieve high-resolution analysis of coupling physics over a short time period. Continued maturing of the FORCE tool suite requires further interconnections between the various tools in the suite in order to ensure consistent analysis. Analyses performed by applying HYBRID to transient process modeling should be easily harvestable as inputs to HERON analyses. The first item in this status update is a demonstration of an automated data pipeline for loading data from HYBRID into HERON analyses. Application of HYBRID results to HERON, as part of using the FORCE tool suite, relies on robust modeling assumptions for the various models included in HYBRID. The second result of this status update is the benchmarking and validation of cost and operational data, with a particular focus on natural gas energy generators. These generators are benchmarked with a focus on contrasting them with proposed thermal energy storage (TES) technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. Further, the method is demonstrated through calculations of the binding energies of nuclei with atomic number A ϵ {2,3,4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and infinite-volume effective field theory calculations of A ϵ {2,3,4,5,6} systems based on this matching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗