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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A new HALEU isotopic certified reference material

Candidate certified reference material (CRM) U196 was prepared by gravimetrically mixing and dissolving NNSA NRMP CRM 112-A (natural uranium metal) and CRM 116-A (highly enriched 93.2% 235 U metal) to achieve a high-assay low-enriched uranium (HALEU) isotopic abundance reference material. CRM U196 will be certified for the 233 U/ 238 U, 234 U/ 238 U, 235 U/ 238 U, and 236 U/ 238 U ratios. Gravimetrically determined uranium isotope amount ratios and values derived from the isotope data were calculated from the buoyancy corrected mass data and from certified values for the metal CRMs used to create the solution. The 235 U isotope amount fraction (·100) and expanded uncertainty is 19.5846 ± 0.0028. For attribute verification, total evaporation and modified total evaporation isotope ratio measurements were performed. In conclusion, the reference material is to be distributed as a unit containing 5 mg uranium as dry uranyl nitrate.

High-assay low-enriched uranium↗
DOE OSTI2026

A lumped particle direct simulation Monte-Carlo method combined with the collisional-radiative model for simulations of non-equilibrium laser-induced plasma plumes

Collisional plasma plumes induced by laser irradiation of material targets exhibit large variations in local density as well as ionization and excitation states, making purely hydrodynamic or kinetic simulations inaccurate or infeasible. To address this challenge and capture non-equilibrium effects in laser-induced plasma plumes at arbitrary degrees of ionization, we develop a hybrid computational approach that combines the kinetic direct simulation Monte Carlo (DSMC) method with a collisional-radiative model (CRM). This ℓDSMC-CRM approach utilizes a lumped particle method to represent minor fractions of excited ions in particle-based simulations and a special coarse-graining technique for atomic spectra and photoionization rates, ensuring numerical convergence at reduced computational cost. The hybrid approach is applied to simulate spatially homogeneous relaxation as well as one- and two-dimensional expansions of plasma plumes induced by irradiation of a copper target by a nanosecond laser pulse in a vacuum or background gas. The comparison with an equilibrium model, where local Saha-Boltzmann equilibrium is enforced, shows that the non-equilibrium effects play a dominant role. The equilibrium model can fail to predict the flow structure and strongly underestimate the degree of absorption of laser radiation by the plume. The ℓDSMC-CRM approach is validated against experimental data demonstrating reasonable agreement with the experimental electron density and temperature, while the equilibrium model is found to dramatically underestimate electron density and temperature. The flexibility of the ℓDSMC-CRM approach allows for its seamless integration into existing DSMC frameworks, making it a valuable tool for high-fidelity plasma modeling in laser-material interactions, laser-based manufacturing, and beyond.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Experimental validation of a collision-radiation dataset for molecular hydrogen in plasmas

Quantitative spectroscopy of molecular hydrogen has generated substantial demand, leading to the accumulation of diverse elementary process data encompassing radiative transitions, electron-impact transitions, predissociations, and quenching. However, their rates currently available are still sparse, and there are inconsistencies among those proposed by different authors. In this study, we demonstrate an experimental validation of such a molecular dataset by composing a collisional-radiative model (CRM) for molecular hydrogen and comparing experimentally obtained vibronic populations across multiple levels. From the population kinetics of molecular hydrogen, the importance of each elementary process in various parameter space is studied. In low-density plasmas (electron density ne≲1017 m−3) the excitation rates from the ground states and radiative decay rates, both of which have been reported previously, determine the excited state population. The inconsistency in the excitation rates affects the population distribution the most significantly in this parameter space. However, in higher density plasmas (ne≳1018 m−3), the excitation rates from excited states become important, which have never been reported in the literature, and may need to be approximated in some way. In order to validate these molecular datasets and approximated rates, we carried out experimental observations for two different hydrogen plasmas; a low-density radio frequency heated plasma (ne≈1016 m−3) and the Large Helical Device (LHD) divertor plasma (ne≳1018 m−3). The visible emission lines from EF1Σg+, HH¯1Σg+, D1Πu±, GK1Σg+, I1Πg±, J1Δg±, h3Σg+, e3Σu+, d3Πu±,g3Σg+, i3Πg±, and j3Δg± states were observed simultaneously and their population distributions were obtained from their intensities. We compared the observed population distributions with the CRM prediction, in particular the CRM with the rates compiled by Janev et al., Miles et al., and those calculated with the molecular convergent close-coupling (MCCC) method. The MCCC prediction gives the best agreement with the experiment, particularly for the emission from the low-density plasma. However, the population distribution in the LHD divertor shows a worse agreement with the CRM than those from low-density plasma, indicating the necessity of the precise excitation rates from excited states. We also found that the rates for the electron attachment is inconsistent with experimental results. This requires further investigation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

US-DOE and Republic of South Africa Uranium Benchmarking: Results From Los Alamos National Laboratory (Study Report)

This report details work performed at Los Alamos National Laboratory (LANL) in support of an interlaboratory uranium (U) benchmarking collaboration between LANL, Lawrence Livermore National Laboratory (LLNL), and South African Nuclear Energy Corporation (Necsa). The goal of this interlaboratory benchmarking exercise is to compare analytical methods and data obtained on uranium reference materials CUP-2 and New Brunswick Laboratory (NBL) certified reference material (CRM) 124-2. The LANL commitments for this project include performing microwave digestion of fresh CUP-2 and CRM 124-2 powders, measuring the U isotope composition of CUP-2 and CRM 124-2 by both single-collector and multi-collector inductively coupled plasma mass spectrometry (SC-ICP-MS and MC-ICP-MS, respectively), and determining trace-element abundances in CUP-2 and CRM 124-2 by inductively coupled plasma mass spectrometry (ICP-MS). This report details the methods employed by LANL in support of these objectives and presents the data obtained during this collaborative exercise.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2024

Fast and Flexible Inference Framework for Continuum Reverberation Mapping Using Simulation-based Inference with Deep Learning

Continuum reverberation mapping (CRM) of active galactic nuclei (AGN) monitors multiwavelength variability signatures to constrain accretion disk structure and supermassive black hole (SMBH) properties. The upcoming Vera Rubin Observatory’s Legacy Survey of Space and Time will survey tens of millions of AGN over the next decade, with thousands of AGN monitored with almost daily cadence in the deep drilling fields. However, existing CRM methodologies often require long computation time and are not designed to handle such large amounts of data. In this paper, we present a fast and flexible inference framework for CRM using simulation-based inference (SBI) with deep learning to estimate SMBH properties from AGN light curves. We use a long short-term memory summary network to reduce the high dimensionality of the light curve data and then use a neural density estimator to estimate the posterior of SMBH parameters. Using simulated light curves, we find SBI can produce more accurate SMBH parameter estimation with 10 3 –10 5 times speed up in inference efficiency compared to traditional methods. The SBI framework is particularly suitable for wide-field CRM surveys as the light curves will have identical observing patterns, which can be incorporated into the SBI simulation. We explore the performance of our SBI model on light curves with irregular-sampled, realistic observing cadence and alternative variability characteristics to demonstrate the flexibility and limitation of the SBI framework.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Upcycling Metal(loid) Contaminants to Produce Critical Raw Materials: The Nexus of Water Treatment and Material Criticality

The Critical Raw Materials Act adopted by the European Commission in 2024 signals a growing shift in the societal value of many elements, which has important implications for the water treatment sector. This legislation partly aims to increase production of Critical Raw Materials (CRMs) from waste streams, with many CRMs being elements with which the water sector has decades of experience, such as the notorious contaminant and newly classified CRM, arsenic. In this Perspective, we use arsenic as a case study to explore how water treatment waste can be repurposed to contribute to CRM supply chain requirements. Combining arsenic mass balances for indicative groundwater treatment plants and EU statistics of water use and arsenic compound consumption, we propose that arsenic upcycling integrated with water treatment can help offset imports of arsenic compounds. However, research is now needed to develop more holistic treatment systems that integrate CRM upcycling with contaminant removal and to better understand the political, institutional, and social drivers that can accelerate adoption of such systems at water utilities. With this work, we intend to stimulate a discussion of water treatment as a discipline that can both improve water quality by removing metal(loid) contaminants and generate local sources of CRMs.

Arsenic↗
DOE OSTI2021

Spatiotemporal distribution of chemical signatures exhibited by Myxococcus xanthus in response to metabolic conditions

Myxococcus xanthus is a common soil bacterium with a complex life cycle, which is known for production of secondary metabolites. However, little is known about the effects of nutrient availability on M. xanthus metabolite production. In this study, we utilize confocal Raman microscopy (CRM) to examine the spatiotemporal distribution of chemical signatures secreted by M. xanthus and their response to varied nutrient availability. Here, ten distinct spectral features are observed by CRM from M. xanthus grown on nutrient-rich medium. However, when M. xanthus is constrained to grow under nutrient-limited conditions, by starving it of casitone, it develops fruiting bodies, and the accompanying Raman microspectra are dramatically altered. The reduced metabolic state engendered by the absence of casitone in the medium is associated with reduced, or completely eliminated, features at 1140 cm –1 , 1560 cm –1 , and 1648 cm –1 . In their place, a feature at 1537 cm –1 is observed, this feature being tentatively assigned to a transitional phase important for cellular adaptation to varying environmental conditions. In addition, correlating principal component analysis heat maps with optical images illustrates how fruiting bodies in the center co-exist with motile cells at the colony edge. While the metabolites responsible for these Raman features are not completely identified, three M. xanthus peaks at 1004, 1151, and 1510 cm –1 are consistent with the production of lycopene. Thus, a combination of CRM imaging and PCA enables the spatial mapping of spectral signatures of secreted factors from M. xanthus and their correlation with metabolic conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

An interlaboratory collaboration to determine consensus 231 Pa/ 235 U model ages of a uranium certified reference material for nuclear forensics

Application of the 231 Pa/ 235 U radiochronometer for nuclear forensic investigations is challenged by a lack of certified reference materials with 231 Pa/ 235 U model purification dates. The Japan Atomic Energy Agency, Los Alamos National Laboratory, and Lawrence Livermore National Laboratory completed an interlaboratory study measuring 231 Pa/ 235 U model ages of New Brunswick Laboratory CRM U100. Results from independent laboratories were combined to calculate a consensus 231 Pa/ 235 U model purification date for CRM U100 of March 26, 1959 ± 237 days. This 231 Pa/ 235 U consensus date for CRM U100 may be used by the nuclear forensic community for quality control of 231 Pa/ 235 U radiochronometry measurements of unknown materials.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Reinforcement Learning for feedback-enabled cyber resilience

The rapid growth in the number of devices and their connectivity has enlarged the attack surface and made cyber systems more vulnerable. As attackers become increasingly sophisticated and resourceful, mere reliance on traditional cyber protection, such as intrusion detection, firewalls, and encryption, is insufficient to secure the cyber systems. Cyber resilience provides a new security paradigm that complements inadequate protection with resilience mechanisms. A Cyber-Resilient Mechanism (CRM) adapts to the known or zero-day threats and uncertainties in real-time and strategically responds to them to maintain the critical functions of the cyber systems in the event of successful attacks. Feedback architectures play a pivotal role in enabling the online sensing, reasoning, and actuation process of the CRM. Reinforcement Learning (RL) is an important gathering of algorithms that epitomize the feedback architectures for cyber resilience. It allows the CRM to provide dynamic and sequential responses to attacks with limited or without prior knowledge of the environment and the attacker. In this work, we review the literature on RL for cyber resilience and discuss the cyber-resilient defenses against three major types of vulnerabilities, i.e., posture-related, information-related, and human-related vulnerabilities. Here we introduce moving target defense, defensive cyber deception, and assistive human security technologies as three application domains of CRMs to elaborate on their designs. The RL algorithms also have vulnerabilities themselves. We explain the major vulnerabilities of RL and present develop several attack models where the attacker target the information exchanged between the environment and the agent: the rewards, the state observations, and the action commands. We show that the attacker can trick the RL agent into learning a nefarious policy with minimum attacking effort. The paper introduces several defense methods to secure the RL-enabled systems from these attacks. However, there is still a lack of works that focuses on the defensive mechanisms for RL-enabled systems. Last but not least, we discuss the future challenges of RL for cyber security and resilience and emerging applications of RL-based CRMs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Evaluating and Improving Scale–Awareness of a Convective Parameterization Closure Using Cloud–Resolving Model Simulations of Convection

This study aims to evaluate a revised closure of the Zhang-McFarlane (ZM) scheme for deep convection and to further improve its scale awareness. Output from two cloud-resolving model (CRM) simulations of both midlatitude organized (MC3E) and tropical unorganized (TWP-ICE) convection are used for the evaluation. By averaging the CRM output over different subdomain sizes from 64 km to 4 km, convection-associated fields are obtained to represent the fields at different horizontal resolutions of global climate models (GCMs). The convection parameterization closure is then tested using these fields. Results show that the cloud base mass flux M b determined from the closure has a relatively good relationship with CRM-simulated convection at coarse resolutions for both MC3E and TWP-ICE, but their correlation degrades at higher resolutions, especially when approaching the gray zone scale under 10 km. The fluctuation of CAPE consumption rate per unit cloud base mass flux for different convective events is found to be an important factor affecting the correlation. When averaged over the base domain, the cloud base mass flux determined by the closure is found to increase with decreasing subdomain size, implying that the closure is not scale-aware. To improve its scale-awareness, a modified closure is designed to alleviate the overprediction of convection at high GCM resolutions. Furthermore, results show that the modified closure has the scale-aware ability to suppress the overprediction problem at high GCM resolutions for both MC3E and TWP-ICE.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Understanding Precipitation Bias Sensitivities in E3SM-Multi-Scale Modeling Framework From a Dilution Framework

We investigate a set of Energy Exascale Earth System Model Multi-scale modeling framework (MMF) (E3SM-MMF) simulations that vary the dimensionality and momentum transport configurations of the embedded cloud-resolving models (CRMs), including unusually ambitious 3D configurations. Issues endemic to all MMF simulations include too much Intertropical Convergence Zone rainfall and too little over the Amazon. Systematic MMF improvements include more on-equatorial rainfall across the Warm Pool. Interesting sensitivities to the CRM domain are found in the regional time-mean precipitation pattern over the tropics. The 2D E3SM-MMF produces an unrealistically rainy region over the northwestern tropical Pacific; this is reduced in computationally ambitious 3D configurations that use 1,024 embedded CRM grid columns per host cell. Trajectory analysis indicates that these regional improvements are associated with desirably fewer tropical cyclones and less extreme precipitation rates. To understand why and how the representation of precipitation improved in 3D, we propose a framework that dilution is stronger in 3D. This viewpoint is supported by multiple indirect lines of evidence, including a delayed moisture-precipitation pickup, smaller precipitation efficiency, and amplified convective mass flux profiles and more high clouds. We also demonstrate that the effects of varying embedded CRM dimensionality and momentum transport on precipitation can be identified during the first few simulated days, providing an opportunity for rapid model tuning without high computational cost. Meanwhile the results imply that other less computationally intensive ways to enhance dilution within MMF CRMs may also be strategic tuning targets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Validation of 2D Te and ne measurements made with Helium imaging spectroscopy in the volume of the TCV divertor

Abstract Multi-spectral imaging of helium atomic emission (HeMSI) has been used to create 2D poloidal maps of T e and n e in TCV’s divertor. To achieve these measurements, TCV’s MANTIS multispectral cameras (Perek et al 2019 Rev. Sci. Instrum. 90 123514) simultaneously imaged four He I lines (two singlet and two triplet) and a He II line (468 nm) from passively present He and He + . The images, which were absolutely calibrated and covered the whole divertor region, were inverted through the assumption of toroidal symmetry to create emissivity profiles and, consequently, line-ratio profiles. A collisional-radiative model (CRM) was applied to the line-ratio profiles to produce 2D poloidal maps of T e and n e . The collisional-radiative modeling was accomplished with the Goto helium CRM code (Zholobenko et al 2018 Nucl. Fusion 58 126006, Zholobenko et al 2018 Technical Report , Goto 2003 J. Quant. Spectrosc. Radiat. Transfer 76 331–44) which accounts for electron-impact excitation (EIE) and deexcitation, and electron–ion recombination (EIR) with He + . The HeMSI T e and n e measurements were compared with co-local Thomson scattering measurements. The two sets of measurements exhibited good agreement for ionizing plasmas: ( 5 eV ⩽ T e ⩽ 60 eV , and 2 × 10 18 m − 3 ⩽ n e ⩽ 3 × 10 19 m − 3 ) in the case of majority helium plasmas, and ( 10 eV ⩽ T e ⩽ 40 eV , 2 × 10 18 m − 3 ⩽ n e ⩽ 3 × 10 19 m − 3 ) in the case of majority deuterium plasmas. However, there were instances where HeMSI measurements diverged from Thomson scattering. When T e ⩽ 10 eV in majority deuterium plasmas, HeMSI deduced inaccurately high values of T e . This disagreement cannot be rectified within the CRM’s EIE and EIR framework. Second, on sporadic occasions within the private flux region, HeMSI produced erroneously high measurements of n e . Multi-spectral imaging of Helium emission has been demonstrated to produce accurate 2D poloidal maps of T e and n e within the divertor of a tokamak for plasma conditions relevant to contemporary divertor studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Model Intercomparison of the Impacts of Varying Cloud Droplet–Nucleating Aerosols on the Life Cycle and Microphysics of Isolated Deep Convection

The microphysical impacts of aerosol particles on scattered isolated deep convective cells near Houston, Texas, on 19 June 2013, are examined using multiple cloud-resolving model (CRM) simulations initialized with vertical profiles of low and high concentrations of cloud droplet–nucleating aerosols. These simulations formed part of the Model Intercomparison Project (MIP) conducted by the Deep Convective Working Group of the Aerosol, Cloud, Precipitation and Climate (ACPC) initiative. Each CRM generated a field of convective cells representing those observed during the case study with varying degrees of accuracy. The Tracking and Object-Based Analysis of Clouds (tobac) cell-tracking algorithm was applied to each MIP CRM simulation to track relatively long-lived convective cells (20–60 min). Most of the CRMs produced similar aerosol loading impacts on the warm phase of tracked cell properties with reduced autoconversion and accretion growth of rain, increased cloud water, reduced rainfall, and reduced near-surface evaporation of rain. The sign of aerosol impacts on the warm-phase properties of the convective cells was also quite consistent over cell lifetimes with the greatest magnitude of influence in the first half of the life cycle in most CRMs. In contrast, the ice-phase response to aerosol loading was highly variable among CRMs and included increases or decreases in ice amounts at inconsistent stages of the cell life cycle and midlevel versus upper-level changes in ice. This intermodel variability in ice is indicative both of the complex indirect interactions between aerosols and ice-phase processes in deep convection and their associated parameterizations.

Aerosol-cloud interaction↗
DOE OSTI2026

Position Operators in Terms of Converging Finite-Dimensional Matrices and Their Intertwining with Geometry, Transport, and Gauge

The position operator 𝑟̂ appears as 𝑖∂ 𝑝 in wave mechanics, while its matrix form (e.g., under a Bloch basis) is well known diverging in diagonals, causing difficulties in basis transformation, observable yielding, etc. We aim to find a convergent r-matrix (CRM) to improve the existing divergent r-matrix (DRM), and investigate its influence at both the conceptual and the application levels. A key modification is increasing the familiar substitution of 𝑟̂ by 𝑖∂ 𝑝 to 𝑖∑ 𝑗 ∂ 𝑘 𝑗 , namely the N-th Weyl algebra. Resolving the divergence makes r-matrix rigorously defined, and we are able to show r-matrix is distinct from a spin matrix in terms of its defining principles, transformation behavior, and the observable it yields. Conceptually, the CRM fills the logical gap between the r-matrix and the Berry connection (this unremarked vagueness has caused the diagonal divergence). In application, we focus on transport, and discover that the Hermitian matrix is not identical with the associative Hermitian operator, i.e., 𝑟 𝑚,𝑛 = 𝑟$^∗_{𝑛,𝑚}$ ⇎ 𝑟̂ = 𝑟̂ † , which subtly affects the celebrated Berry curvature formula for adiabatic current. We also discuss how such a non-representation CRM can contribute to building a unified transport theory.

Weyl algebras↗
DOE OSTI2022

A method for transporting cloud-resolving model variance in a multiscale modeling framework

Abstract. An unphysical checkerboard pattern has recently been identified in the multiscale modeling framework configuration of the Energy Exascale Earth System Model (E3SM-MMF) that is hypothesized to be associated with the inability of large-scale dynamics to transport fluctuations within the embedded cloud-resolving model (CRM) on the global grid. To address this issue, a method is presented to facilitate the large-scale transport of CRM variance in E3SM-MMF. Simulation results show that the method is effective at reducing the occurrence of unphysical checkerboard patterns on a range of timescales from days to years. This result is confirmed both subjectively through visual inspection and quantitatively with a previously developed pattern categorization technique. The CRM variance transport does not significantly alter the model climate, although it does tend to reduce temporal variance on fields associated with convection on the global grid.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Update on the High Precision Titration Method for Uranium Assay Supported by NBL Program Office

The NBL Program Office (NBL PO) has coordinated with Oak Ridge National Laboratory (ORNL) to implement the High Precision Titration (HPT) method for uranium assay measurements. The measurement method has been successfully developed and qualified, therefore ORNL has progressed to performing analyzes critical to the mission of the NBL PO. The HPT method is vital to producing the next generation of certified reference materials for uranium assay and isotopic abundance. The work described here focused on establishing traceability of the method to the NIST SRM 136 potassium dichromate series, and focused on investigating small differences between SRM 136e and 136f. The NBL PO evaluated the history of all of its primary uranium reference materials, including CRM 112A natural uranium metal, and worked with NIST in investigating the small differences in the dichromate SRM’s. ORNL performed comparative experiments on SRM 136e and 136f using CRM 112A. The results of the experiment will be presented here, along with NBL PO’s plans to re-evaluate the CRM 112A certified uncertainty to comply with JCGM 100, “Guide to the expression of uncertainty in measurement.”

Rogers, Kayron↗
DOE OSTI2025

On the Dependence of Simulated Convection on Domain Size in CRMs

Abstract We present a heuristic model to explain the suppression of deep convection in convection‐resolving models (CRMs) with a small number of grid columns, such as those used in super‐parameterized or multi‐scale modeling framework (MMF) general circulation models (GCM) of the atmosphere. Domains with few grid columns require greater instability to sustain convection because they force a large convective fraction, driving strong compensating subsidence warming. Updraft dilution, which is stronger for reduced horizontal grid spacing, enhances this effect. Thus, suppression of deep convection in CRMs with few grid columns can be reduced by increasing grid spacing. Radiative‐convective equilibrium simulations using standalone CRM simulations with the System for Atmospheric Modeling (SAM) and using GCM‐coupled CRM simulations with the Energy Exascale Earth System Model (E3SM)‐MMF confirm the heuristic model results.

CRM↗
DOE OSTI2020

International cooperation in age-dating uranium standards for nuclear forensics using the 231 Pa/ 235 U radiochronometer

During 2017–2018 Los Alamos National Laboratory, Lawrence Livermore National Laboratory and the China Institute of Atomic Energy collaborated in an interlaboratory 231 Pa/ 235 U radiochronometry exercise. The laboratories used different analytical methods to obtain a consensus model purification date for CRM U010 of December 28, 1958 ± 198 days and for CRM U850 of May 20, 1958 ± 363 days. These results agree with previously reported model dates using the 230 Th/ 234 U radiochronometer as well as the production histories of these materials. The concordance of interlaboratory data here confirms the ability of laboratories to make reproducible radiochronometry measurements using distinct analytical approaches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗