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DOE OSTI2022

Modeling antiphase boundary energies of Ni 3 Al-based alloys using automated density functional theory and machine learning

Antiphase boundaries (APBs) are planar defects that play a critical role in strengthening Ni-based superalloys, and their sensitivity to alloy composition offers a flexible tuning parameter for alloy design. Here, we report a computational workflow to enable the development of sufficient data to train machine-learning (ML) models to automate the study of the effect of composition on the (111) APB energy in Ni 3 Al-based alloys. We employ ML to leverage this wealth of data and identify several physical properties that are used to build predictive models for the APB energy that achieve a cross-validation error of 0.033 J m –2 . We demonstrate the transferability of these models by predicting APB energies in commercial superalloys. Moreover, our use of physically motivated features such as the ordering energy and stoichiometry-based features opens the way to using existing materials properties databases to guide superalloy design strategies to maximize the APB energy.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Electron correlation and relativistic effects in the excited states of radium monofluoride

Highly accurate and precise electronic structure calculations of heavy radioactive atoms and their molecules are important for several research areas, including chemical, nuclear, and particle physics. Ab initio quantum chemistry can elucidate structural details in these systems that emerge from the interplay of relativistic and electron correlation effects, but the large number of electrons complicates the calculations, and the scarcity of experiments prevents insightful theory-experiment comparisons. Here we report the spectroscopy of the 14 lowest excited electronic states in the radioactive molecule radium monofluoride (RaF), which is proposed as a sensitive probe for searches of new physics. The observed excitation energies are compared with state-of-the-art relativistic Fock-space coupled cluster calculations, which achieve an agreement of ≥99.64% (within ~12 meV) with experiment for all states. Guided by theory, a firm assignment of the angular momentum and term symbol is made for 10 states and a tentative assignment for 4 states. The role of high-order electron correlation and quantum electrodynamics effects in the excitation energies is studied and found to be important for all states.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Predicting Metabolic Reaction Networks with Perturbation-Theory Machine Learning (PTML) Models

Background: Checking the connectivity (structure) of complex Metabolic Reaction Networks(MRNs) models proposed for new microorganisms with promising properties is an importantgoal for chemical biology. Objective: In principle, we can perform a hand-on checking (Manual Curation). However, this is achallenging task due to the high number of combinations of pairs of nodes (possible metabolic reactions). Results: The CPTML linear model obtained using the LDA algorithm is able to discriminate nodes(metabolites) with the correct assignation of reactions from incorrect nodes with values of accuracy,specificity, and sensitivity in the range of 85-100% in both training and external validation dataseries. Methods: In this work, we used Combinatorial Perturbation Theory and Machine Learning techniquesto seek a CPTML model for MRNs >40 organisms compiled by Barabasis’ group. First, wequantified the local structure of a very large set of nodes in each MRN using a new class of node indexcalled Markov linear indices fk. Next, we calculated CPT operators for 150000 combinationsof query and reference nodes of MRNs. Last, we used these CPT operators as inputs of differentML algorithms. Conclusion: Meanwhile, PTML models based on Bayesian network, J48-Decision Tree and RandomForest algorithms were identified as the three best non-linear models with accuracy greaterthan 97.5%. The present work opens the door to the study of MRNs of multiple organisms usingPTML models.

Pharmacology & Pharmacy↗

DOE OSTI2022

Development of efficient solar cells using combination of QSPR and DFT approaches

The awarded research project aimed to design and determine the effective organic dye-sensitizers from the ensemble of chromophores for the dye-sensitized solar cell (DSSC) and fullerene-derivatives (FDs) as acceptor for polymer solar cell (PSC) followed by explore the electron transfer mechanism using the combined quantitative structure-property relationship (QSPR) analysis in conjunction with density functional theory (DFT) and time-dependent DFT (TDDFT)-based calculations. Based on our proposal we have employed different in silico approaches to design photo-efficient organic dye-sensitizers for DSSCs and FDs as acceptor for PSCs with exhaustive screening methodology.

14 SOLAR ENERGY↗

DOE OSTI2024

Investigation of Benchmark $k$ eff Sensitivity and Uncertainty for 239 Pu fission in Specific Energy Ranges

Nuclear data at intermediate energies (from 1 to 100s of keV) are evaluated based on scarce differential data and theory unable to capture physics’ expected structure. There is also a lack of integral data. This is a known deficiency and is challenging to address. Calculated effective multiplication factor, k eff , values for intermediate energy experiments are ~25× further from experiment than for fast energies and are often well outside the experimental uncertainties. The goal of the PARADIGM (PARallel Approach of Differential and InteGral Measurements) project is to significantly re duce the uncertainties of intermediate energy nuclear data for 239 Pu. To this end, PARADIGM simultaneously optimizes experiments at both the Los Alamos Neutron Science Center (LANSCE) and National Criticality Experiments Research Center (NCERC). The combined set of data will inform new intermediate-energy nuclear data. By execution of differential and integral experiments, establishment of new theory, and undertaking nuclear data evaluation in parallel, the timeline to deliver improved nuclear data to users will be reduced significantly that is to three years. For the PARADIGM project, it was decided to optimize an integral experiment for two neutron energy ranges, within the full intermediate energy range. The low energy range goes from 1 to 30 keV, while the higher energy range goes from 30 to 600 keV. This work focuses on nuclear data sensitivities and uncertainties for 239 Pu fission for existing experiments in the International Criticality Safety Benchmark Evaluation Project (ICSBEP). When designing new experiments, it is important to understand what benchmarks currently exist. For a more traditional experiment design (in which a specific application model(s) exists), comparisons would be made between the application model(s) and existing benchmarks. For PARADIGM, there is no specific application model, but instead the specific nuclear data reaction and energy ranges of interest can be explored for existing benchmarks.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

White paper on light sterile neutrino searches and related phenomenology

This white paper provides a comprehensive review of our present understanding of experimental neutrino anomalies that remain unresolved, charting the progress achieved over the last decade at the experimental and phenomenological level, and sets the stage for future programmatic prospects in addressing those anomalies. It is purposed to serve as a guiding and motivational "encyclopedic" reference, with emphasis on needs and options for future exploration that may lead to the ultimate resolution of the anomalies. We see the main experimental, analysis, and theory-driven thrusts that will be essential to achieving this goal being: 1) Cover all anomaly sectors -- given the unresolved nature of all four canonical anomalies, it is imperative to support all pillars of a diverse experimental portfolio, source, reactor, decay-at-rest, decay-in-flight, and other methods/sources, to provide complementary probes of and increased precision for new physics explanations; 2) Pursue diverse signatures -- it is imperative that experiments make design and analysis choices that maximize sensitivity to as broad an array of these potential new physics signatures as possible; 3) Deepen theoretical engagement -- priority in the theory community should be placed on development of standard and beyond standard models relevant to all four short-baseline anomalies and the development of tools for efficient tests of these models with existing and future experimental datasets; 4) Openly share data -- Fluid communication between the experimental and theory communities will be required, which implies that both experimental data releases and theoretical calculations should be publicly available; and 5) Apply robust analysis techniques -- Appropriate statistical treatment is crucial to assess the compatibility of data sets within the context of any given model.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Experimental observation of nonlinear relation between pressure and water flux is consistent with the solution-diffusion model

In several recent studies, it has been proposed that the fundamental understanding of penetrant transport in dense polymer membranes occurring via the solution-diffusion model, which has been the generally accepted theoretical framework for describing penetrant transport in such materials for the past several decades, is flawed. An alternate mechanistic framework based on the idea of two-phase flow in a porous medium (i.e., pore-flow) has been broadly advanced instead, with proponents of this approach claiming that the pore-flow theoretical framework provides the necessary mechanistic insight to design novel polymeric membrane materials for emerging applications. In this study, we show experimental results for hydraulic permeation of water that are entirely consistent with the solution-diffusion theory, without modification, for three dense polymeric membranes: crosslinked poly(ethylene glycol diacrylate) (XLPEGDA), Nafion 117 ionomer in the sodium counterion form (Nafion 117-Na), and cellulose acetate (CA). By measuring water flux at transmembrane pressures up to 240 bar, we observe a nonlinear relationship between the transmembrane pressure (TMP) and water flux, J w , for XLPEGDA and Nafion 117-Na, while this relationship is linear for CA. We demonstrate that the behavior of these three materials is described via the solution-diffusion model. According to the solution-diffusion model, flux is, to a good approximation, proportional to the transmembrane concentration difference induced by the pressure difference across the membrane, rather than to TMP itself. Water sorption isotherms are reported for all three materials. They further justify the nonlinear relationship between TMP and J w observed in XLPEGDA and Nafion 117-Na, emphasizing that the nonlinearity in the flux/TMP relationship stems from nonlinearities in the sorption isotherm with pressure. Additionally, the relationship between water flux and TMP can be predicted, a priori, with no adjustable parameters when a predictive model for the diffusion coefficient of water is employed in conjunction with the experimental water sorption isotherms in the solution-diffusion model. Furthermore, our results demonstrate the validity of the solution-diffusion model to describe transport of penetrants in dense polymer membranes, while highlighting the sensitivity of the solution-diffusion model to the many physical and mathematical simplifications commonly applied to the theory in literature.

materials↗

DOE OSTI2023

A tail of eternal inflation

Non-trivial inflaton self-interactions can yield calculable signatures of primordial non-Gaussianity that are measurable in cosmic surveys. We calculate the non-Gaussian corrections to Stochastic Inflation within the framework of Soft de Sitter Effective Theory, from which we derive the associated probability distribution for the scalar fluctuations. As a consequence of this new result, we show that the phase transition to slow-roll eternal inflation is often incalculable in these models. Instead, this transition is sensitive to the non-Gaussian tail of the distribution of scalar fluctuations, which probes physics inside the horizon, potentially beyond the cutoff scale of the Effective Field Theory of Inflation. We delineate the parameter space consistent with current observations and weak coupling at horizon crossing in which the large fluctuations relevant for eternal inflation can only be determined by appealing to a UV completion. We also argue that this breakdown of the perturbative description is required for the de Sitter entropy to reflect the number of de Sitter microstates.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Validation of Jezebel Reactivity Coefficients and Sensitivity Analysis

Nuclear data validation is often performed today using criticality measurements. The gold standard for criticality measurements is the International Criticality Safety Benchmark Experiment Project (ICSBEP). The validation specifically focuses on the effective multiplication factor ($k_{eff}$). $K_{eff}$ is a relatively easy parameter to infer and has reduced uncertainty due to being at or above critical. However, while $k_{eff}$ is the most documented parameter and its uncertainties and sensitivities have been evaluated in great detail, it cannot be used as a standalone metric to determine inaccuracies in nuclear data (e.g., cross section data, PFNS, nu), which is based on theory, physics, and differential measurements. The Experiments Underpinned by Computational Learning for Improvements in nuclear Data (EUCLID) project aims to identify compensating errors in specific isotope nuclear data by optimally designing experiments that are, or are not sensitive to a suite of measurement parameters beyond $k_{eff}$. By identifying parameters that are sensitive to each other, oppositely sensitive, or have substantial magnitude differences in sensitivity, experiments can be designed to constrain questionable nuclear data. One sensitivity that is of particular interest to this project includes the sensitivity of reactivity coefficients. Reactivity coefficients compare reactivity, which is related to $k_{eff}$ at two different states therefore being sensitive to small changes in the system. The most common type of reactivity coefficient measurements is comparison to void for a small sample within the assembly. It is key that the sample sizes are small enough to not affect the flux of the full system. Reactivity coefficients were evaluated for many early experiments to better understand transport corrected cross sections. In fact, ICSBEP includes reactivity coefficient results as “Supplemental Measurements” in appendices for a handful of older benchmarks. One of those benchmarks is Jezebel, the bare Pu critical assembly. This paper compares new simulations of reactivity coefficients for Jezebel, and explores the sensitivity of reactivity coefficients to small changes in nuclear data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Extended Fayans energy density functional: optimization and analysis

The Fayans energy density functional (EDF) has been very successful in describing global nuclear properties (binding energies, charge radii, and especially differences of radii) within nuclear density functional theory. In a recent study, supervised machine learning methods were used to calibrate the Fayans EDF. Building on this experience, in this work we explore the effect of adding isovector pairing terms, which are responsible for different proton and neutron pairing fields, by comparing a 13D model without the isovector pairing term against the extended 14D model. At the heart of the calibration is a carefully selected heterogeneous dataset of experimental observables representing ground-state properties of spherical even–even nuclei. To quantify the impact of the calibration dataset on model parameters and the importance of the new terms, we carry out advanced sensitivity and correlation analysis on both models. The extension to 14D improves the overall quality of the model by about 30%. The enhanced degrees of freedom of the 14D model reduce correlations between model parameters and enhance sensitivity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Machine‐Learning Spectral Indicators of Topology

Abstract Topological materials discovery has emerged as an important frontier in condensed matter physics. While theoretical classification frameworks have been used to identify thousands of candidate topological materials, experimental determination of materials’ topology often poses significant technical challenges. X‐ray absorption spectroscopy (XAS) is a widely used materials characterization technique sensitive to atoms’ local symmetry and chemical bonding, which are intimately linked to band topology by the theory of topological quantum chemistry (TQC). Moreover, as a local structural probe, XAS is known to have high quantitative agreement between experiment and calculation, suggesting that insights from computational spectra can effectively inform experiments. In this work, computed X‐ray absorption near‐edge structure (XANES) spectra of more than 10 000 inorganic materials to train a neural network (NN) classifier that predicts topological class directly from XANES signatures, achieving F 1 scores of 89% and 93% for topological and trivial classes, respectively is leveraged. Given the simplicity of the XAS setup and its compatibility with multimodal sample environments, the proposed machine‐learning‐augmented XAS topological indicator has the potential to discover broader categories of topological materials, such as non‐cleavable compounds and amorphous materials, and may further inform field‐driven phenomena in situ, such as magnetic field‐driven topological phase transitions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Atomic Layer Deposition of Pt on the Surface Deactivated by Fluorocarbon Implantation: Investigation of the Growth Mechanism

Selective atomic layer deposition (ALD) using surface-controlled reactivity is attracting a great deal of attention as a simple bottom-up patterning process that can provide both continued dimensional scaling and accurate pattern placement for next-generation nanoelectronics. Previously, we reported topographically selective deposition through Pt ALD using a MeCpPtMe 3 precursor and an O 2 counter reactant on fluorocarbon (CF x )-modified surfaces; however, gradual loss of selectivity in the CF x -modified regions was observed during the Pt ALD process. This work develops a fundamental understanding of the microscopic growth mechanisms of Pt ALD on the CF x -modified surface using a combination of experimental analyses and theoretical methods. The Pt growth characteristics on the CF x surface are investigated within a temperature window from 225 to 350 °C, and the results show a sharp sensitivity to growth temperature, with significant Pt growth occurring at temperatures above 300 °C. Through density functional theory (DFT) calculations, the reaction energies for adsorption of oxygen and the MeCpPtMe 3 precursor as well as formation of reaction products of CF x degradation are determined. Based on experimental results in conjunction with the DFT calculations, we show that while lower temperature Pt ALD (<300 °C) on CF x -modified surfaces can be significantly retarded because of a lack of MeCpPtMe 3 chemisorption, the surface reaction pathways for Pt ALD on CF x -modified surfaces at temperatures above 300 °C can proceed through oxygen adsorption and CF 4 desorption followed by Pt nucleation in CF x -degraded regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Optical Absorption Spectroscopy Probes Water Wire and Its Ordering in a Hydrogen-Bond Network

Water wires, quasi-one-dimensional chains composed of hydrogen-bonded (H-bonded) water molecules, play a fundamental role in numerous chemical, physical, and physiological processes. Yet direct experimental detection of water wires has been elusive so far. Based on advanced many-body theory that includes electron-hole interactions, we report that optical absorption spectroscopy can serve as a sensitive probe of water wires and their ordering. In both liquid and solid water, the main peak of the spectrum is discovered to be a charge-transfer exciton. In water, the charge-transfer exciton is strongly coupled to the H-bonding environment where the exciton is excited between H-bonded water molecules with a large spectral intensity. In regular ice, the spectral weight of the charge-transfer exciton is enhanced by a collective excitation occurring on proton-ordered water wires, whose spectral intensity scales with the ordering length of water wire. The spectral intensity and excitonic interaction strength reaches its maximum in ice XI, where the long-range ordering length yields the most pronounced spectral signal. Our findings suggest that water wires, which widely exist in important physiological and biological systems and other phases of ice, can be directly probed by this approach. Published by the American Physical Society 2025

Tang, Fujie (ORCID:0000000197615359)↗

DOE OSTI2024

Adapting CLUTCH methodology to multigroup TSUNAMI-3D for eigenvalue sensitivity calculations

The sensitivity of the eigenvalue to uncertainties in nuclear data and its evaluation are important for nuclear criticality safety. TSUNAMI-3D sequences within the SCALE code system offer several options to the user community for calculating eigenvalue sensitivity coefficients with multigroup (MG) and continuous energy (CE) 3D transport capabilities. TSUNAMI-3D sequences implement the adjoint-based perturbation theory with MG KENO code, the Contributon Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method with CE KENO code, and the Iterated Fission Probability (IFP) method with CE KENO and Shift codes. Each method has benefits and limitations depending on the problem that is run. The work presented here aims to adapt the CLUTCH method, which enables the Contributon method's mesh-free, memory-efficient approach for calculating adjoint-weighted tallies for sensitivity calculations, to the MG TSUNAMI-3D sequence. This application would eliminate the explicit adjoint KENO calculation, as well as the memory-consuming mesh flux moment tallies required by the conventional MG TSUNAMI-3D. Smaller memory footprints in the CLUTCH methodology and relatively shorter runtimes in MG KENO transport can make MG TSUNAMI-3D a viable method for some complex problems. Moreover, this adaptation allows MG sensitivity calculations with Shift, ORNL's next-generation high-performance Monte Carlo transport code, which currently does not offer any sensitivity capabilities with MG particle transport simulations. Initial implementation of the new MG TSUNAMI-3D sequence and its preliminary results with a selected critical benchmark experiment in the Verified, Archived Library of Inputs and Data (VALID) are presented in this study.

KENO↗

DOE OSTI2022

Electroweak $\mathrm{ALP}$ searches at a muon collider

A high-energy muon collider with center-of-mass energy around and above 10 TeV is also a vector boson fusion (VBF) machine, due to the significant virtual electroweak (EW) gauge boson content of high-energy muon beams. This feature, together with the clean environment, makes it an ideal collider to search for TeV-scale axion-like particles (ALP) coupling to Standard Model EW gauge bosons, which current and other future colliders have limited sensitivities to. We present detailed analyses of heavy ALP searches in both the VBF and associated production channels at a muon collider with different running benchmarks. We also show projected constraints on the ALP couplings in the effective field theory, including an operator with its coefficient not determined by the mixed Peccei-Quinn anomaly. We demonstrate that a muon collider could probe new ALP parameter space and push the sensitivities of the couplings between the ALP and EW gauge bosons by one order of magnitude compared to HL-LHC. The projected limits and search strategies for ALPs could also be applied to other types of resonances coupling to EW gauge bosons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Thermo-acoustoelastic effect of Rayleigh wave: Theory and experimental verification

Previous studies showed that the thermally-induced ultrasonic bulk wave velocity change could be used to measure acoustoelastic coefficients and third-order elastic constants of elastic materials. This method is naturally immune from the ambient temperature effect and has improved sensitivity and a simpler test setup than the conventional acoustoelastic test. However, Rayleigh wave is preferred for thick components or structures with only one accessible surface. In this work, the thermo-hyperelastic constitutive equation, along with acoustoelastic theory, is used to derive the expression of the thermo-acoustoelastic coefficient (TAEC) of Rayleigh wave. The numerical relationship between the TAEC of Rayleigh wave and Murnaghan constants ( l, m and n ) are given for common metals. Further, the TAEC expressions for Rayleigh wave and shear wave are similar, and both are dominated by the constant m . The TAEC of Rayleigh wave was measured on an aluminum 6061 specimen using the thermal modulation experiment in a temperature range of 22 ~ 35°C. The measured TAEC shows good agreement with the theoretical calculation. Then the third-order elastic constants were calculated based on TAECs of bulk waves and Rayleigh wave.

42 ENGINEERING↗

DOE OSTI2022

Sensitivity to dark sector scales from gravitational wave signatures

We consider gravitational sound wave signals produced by a first-order phase transition in a theory with a generic renormalizable thermal effective potential of power law form. We find the frequency and amplitude of the gravitational wave signal can be related in a straightforward manner to the parameters of the thermal effective potential. This leads to a general conclusion; if the mass of the dark Higgs is less than 1% of the dark Higgs vacuum expectation value, then the gravitational wave signal will be unobservable at all upcoming and planned gravitational wave observatories. Although the understanding of gravitational wave production at cosmological phase transitions is still evolving, we expect this result to be robust.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗