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DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1976

Calculations of the Electron Energy Distribution Function in a Uranium Plasma by Analytic and Monte Carlo Techniques

Electron energy distribution functions were calculated in a U235 plasma at 1 atmosphere for various plasma temperatures and neutron fluxes. The distributions are assumed to be a summation of a high energy tail and a Maxwellian distribution. The sources of energetic electrons considered are the fission-fragment induced ionization of uranium and the electron induced ionization of uranium. The calculation of the high energy tail is reduced to an electron slowing down calculation, from the most energetic source to the energy where the electron is assumed to be incorporated into the Maxwellian distribution. The pertinent collisional processes are electron-electron scattering and electron induced ionization and excitation of uranium. Two distinct methods were employed in the calculation of the distributions. One method is based upon the assumption of continuous slowing and yields a distribution inversely proportional to the stopping power. An iteration scheme is utilized to include the secondary electron avalanche. In the other method, a governing equation is derived without assuming continuous electron slowing. This equation is solved by a Monte Carlo technique.

Bathke, C. G.↗

DOE OSTI2022

{beta}- and {gamma}-spectroscopy study of {sup 119}Pd and {sup 119}Ag

Neutron-rich Pd-119 nuclei were produced in fission of natural uranium, induced by 25-MeV protons. Fission fragments swiftly extracted with the Ion Guide Isotope Separation On-Line method were mass separated using a dipole magnet and a Penning trap, providing mono-isotopic samples of Pd-119. Their beta(-) decay was measured with gamma gamma- and beta gamma-spectroscopy methods using low-energy germanium detectors and a thin plastic scintillator. Two distinct nuclear-level structures were observed in Ag-119, based on the 1/2(-) and 7/2(+) isomers reported previously. The beta(-)decay work was complemented by a prompt-gamma study of levels in Ag-119 populated in spontaneous fission of (252)cf, performed using the Gammasphere array of germanium detectors. Contrary to previous suggestions, our data show that the 1/2(-) isomer is located below the 7/2(+) isomer and is proposed as a new ground state of Ag-119 with the 7/2(+) isomer excitation energy determined to be 33.4 keV. Our data indicate that there are two beta unstable isomers in Pd-119, a proposed ground state of Pd-119 with tentative spin 1/2(-) or 3/2(+) and a half-life of 0.88 s and the other one about 350 keV above, having spin (11/2(-)) and a half-life of 0.85 s. The higher-energy isomer probably decays to the 1/2(-) or 3/2(+) ground state via a gamma cascade comprising 18.7-219.8-X-keV transitions. The unobserved isomeric transition with energy X approximate to 100 keV probably has an E3 multipolarity. Its hindrance factor is significantly lower than for analogous E3 isomeric transitions in lighter Pd isotopes, suggesting an oblate deformation of levels in Pd-119. Oblate configurations in Ag-119 are discussed also.

Kurpeta, J↗

DOE OSTI2020

Measurement of the 239 Pu$(n, f$) prompt fission neutron spectrum from 10 keV to 10 MeV induced by neutrons of energy 1–20 MeV

Although the prompt fission neutron spectrum (PFNS) is an essential component of neutron-driven systems that has been measured for decades, there are still multiple glaring unknowns regarding the PFNS of major actinides in the fission neutron incident energy range, specifically with regard to multichance fission and pre-equilibrium neutron emission processes. The only impactful experimental 239 Pu PFNS measurements included in recent nuclear data evaluations were measured over a limited outgoing neutron energy range at thermal and 1.5-MeV average incident neutron energy, while other potentially impactful measurements have been shown to contain errors that resulted in either large uncertainty increases or in complete exclusion from nuclear data evaluation. Here, we report a measurement of the 239 Pu PFNS over a wide range of incident neutron energy (1–20 MeV) and three orders of magnitude in outgoing neutron energy (0.01–10 MeV) resulting from the Chi-Nu experiment at the Los Alamos Neutron Science Center. These results are the combination of separate PFNS measurements in the same experimental area, one using a Li-glass and the other a liquid scintillator detector array. Covariances between all PFNS data points from each detector and within each incident energy range were generated between all other data in both detector arrays and within all other incident neutron energy bins, yielding a single covariance matrix for all 1300 PFNS data points reported here. These covariances are based on a thorough assessment of systematic bias and uncertainties associated with the measurement, PFNS extraction technique, combination of data from each detector type, and other aspects of the analysis. The existence of covariances between PFNS data points in different incident neutron energy ranges yielded covariances between average PFNS energy values at each incident energy to be reported here as well, which allowed for firm statements to be made regarding a shape of a purely experimental mean PFNS energy trend for the first time. Although minor PFNS shape differences exist between the results reported here and recent nuclear data evaluations, the ENDF/B-VIII.0 and JEFF-3.3 PFNS evaluations agree reasonably well with the present results from 1-to 10-MeV incident neutron energy, which spans the well-measured 1.5-MeV incident neutron energy PFNS from Lestone and Shores as well as the onset of second-chance fission. However, while the pre-equilibrium component of the PFNS above 12-MeV incident neutron energy roughly agrees in position and magnitude with ENDF/B-VIII.0 and JEFF-3.3, clear differences relating to the relative magnitude of third-chance fission PFNS features are present in the PFNS shape and in the mean PFNS energy trends.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

An integrated statistical-thermodynamic model for fission gas release and swelling in nuclear fuels

Here, we propose a new model for burst fission gas release induced by microcracking in ceramic nuclear fuels such as uranium dioxide. The model stipulates that the densities of defects in the fuel material, such as microcracks and fission gas bubbles on grain boundaries, evolve in accordance with the second law of thermodynamics. Central to the model is the notion of an effective temperature, conjugate to the configurational entropy of the fuel material, and directly linked to the burnup. The model predicts that microcracking, driven by the internal stress state of the fuel material, reduces the bubble storage capacity of grain boundaries, and accounts for burst fission gas release during rapid temperature transients that simulate power transients, reactor startup, and loss-of-coolant accident conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

239 Pu R -matrix Analysis and Neutron Multiplicities in the Neutron Energy Region up to a few keVs [Abstract]

The evaluation of 239 Pu neutron resonance parameters coupled to neutron multiplicities $\overline{v}_p$ is of particular importance to investigate the ($\mathcal{n, γf}$) reaction in which a $\mathcal{γ}$-ray emission occurs before the scission of the compound nuclear. This reaction has offered one explanation for the fluctuations in the measured values of $\overline{v}_p$ In this regard, the competition between ($\mathcal{n, γf}$) reaction and the direct fission process can be also included in the R matrix analysis of fission and capture measured data. The goal of this work is the coupled evaluation of the $\mathcal{n}$+ 239 Pu resonance parameters and related neutron multiplicities by ensuring the adoption of thermal neutron constants recently evaluated at the International Atomic Nuclear Energy as well as the recommended (thermal-neutron) induced prompt neutron fission spectrum (PFNS). Moreover, this new set of physical evaluated quantities should also guarantee the agreement for high-leakage solution benchmarks while keeping the good performance of large thermal solution assemblies.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Boson Fermion Nucleus And The Phenomenon Of Nuclear Fission (Monograph #14)

Nuclear fission can be induced by a neutron with insufficient energy to physically impact and disrupt the nucleus. A boson fermion nucleus (BFN) capturing an incident neutron at the same quantum state as a neutron in the BFN structure, or an assimilated incident neutron altering the quantum state of a neutron or proton in the structure to match another, is sufficient by the Pauli exclusion principle to disrupt the organized nuclear structure. This creates a scission point and force imbalance where the inverse radius squared (1/r 2 ) electrostatic repulsive force among protons dominates over the inverse radius exponential (1/e µr ) strong, short-range attractive Yukawa force among nucleons. The result is nuclear fission.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Manufacturing porous U10Zr fuels with controlled porosities by SPS and thermal properties

To accommodate the swelling of metallic fuels induced by the fission gas release during burnup in sodium fast reactor for a sodium-free fuel option, advanced U-10Zr fuels with controlled porosity were designed and demonstrated by spark plasma sintering. U-10Zr fuel pellets with manufactured porosities varying from 35% up to fully dense fuel pellets have been fabricated by controlling ball milling times of the starting uranium powders, sintering temperature, pressure, and duration, and the correlation among the microstructure control – porosity – sintering conditions has been established. To further mimick the pore structure in irradiated fuels, different pore formers (NaCl and NH4HCO3) have been used to control the pore size and distribution. Microstructure characterization indicates a lamellar reaction zone of U and Zr, differing from the arc-melted U-10Zr as a result of rapid consolidation of SPS at lower temperature and short durations. The thermal conductivity of U10Zr with different porosities are also measured. Here this work demonstrates the success in manufacturing new metallic fuel forms with controlled porosities and pore distribution, which can be used as model systems to investigate the thermal transfer behavior of metallic fuels in the reactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Evaluating 239 Pu(n,f) cross sections via machine learning using experimental data, covariances, and measurement features

In this paper, the neutron-induced 239 Pu fission cross section, 239 Pu(n,f), is evaluated from 1–20 MeV using experimental data and associated covariances while also considering information on the measurement, termed features here. For instance, methods to determine the background, sample backing material, or impurities in the sample, are explicitly taken into account in the evaluation process. To this end, outliers in the experimental data are identified with a modified version of the Hybrid Robust Support Vector Machine. In a second step, two machine learning methods (logistic regression with elastic net regularization and random forest regression with SHAP feature importance metric) are used to highlight measurement features that are common among many of the outlying data points. Based on this analysis, penalty uncertainties are added to the experimental covariances of outlying data points that have outlier measurement features and are put through the generalized-least-squares evaluation. The resulting evaluated mean values and covariances differ distinctly from those data evaluated without the penalty uncertainties. These results highlight that certain measurement features should be more closely examined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Design and Analysis of an Advanced Three-Point Bend Test Approach for Miniature Irradiated Disk Specimens

Candidate tungsten armor materials in a magnetic confinement fusion device must be able to withstand thermal variation that leads to internal stresses caused by the impinging heat load. In addition, the thermomechanical properties of these materials are degraded by irradiation-induced defect accumulation. Fission reactor–based irradiation data are used to predict the fusion neutron damage and property change. This study examines the motivation and design of a custom-designed three-point bend test for neutron-irradiated disk specimens that are 3 mm in diameter to be able to define the flexural strength of advanced tungsten materials, alloys, and composites—and to the extent that embrittlement occurs after neutron irradiation. The theory provided shows a calculation for the flexural deflection and shear deflection due to the small-geometry constraints. A finite element deformation analysis is performed to evaluate the mechanical stress field of disk bend specimens. The stress values above 80% of the maximum stress are concentrated in 2.4 mm of the 3.0-mm length of the centerline across the tungsten disk diameter. A bend test fixture has been designed and fabricated to enable testing of these specimens with precisely engineered tolerance and minimal machine compliance. This fixture will be able to be placed inside a universal testing frame at elevated temperatures for the mechanical property evaluation of future neutron-irradiated disk specimens.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Patchy snapshots of nuclear chain reactions

Stochastic fluctuations of the neutron population within a nuclear reactor are typically prevented by operating the core at a sufficiently high power. This regime, where the evolution of the neutron density is essentially deterministic, is key for automatic protection and safety systems to safely detect unwanted power excursions during an accident, and to rapidly initiate a reactor trip procedure in case it is needed. Recent works, supported by numerical simulations, have however reported that, for large reactors, the branching nature of the fission reactions might induce strongly non-Poissonian patterns in the neutron spatial distribution, and that stochastic fluctuations might still persist at reactor powers close to operating conditions (startup phase). An international program conducted by LANL, IRSN and CEA was therefore setup to experimentally detect and characterize such fluctuations and correlations. An experiment took place in 2017 at the Reactor Critical Facility (RCF) of the Rensselaer Polytechnic Institute (USA). In this paper we will report the main findings of this experimental program, supported by stochastic models and by the development of a dedicated high-fidelity Monte Carlo simulation code. We will in particular describe and explain the strong patchiness in neutron power distributions measured at the RCF, as well as a peculiar ‘blinking’ behavior of the core, and discuss the consequences of these findings on nuclear safety.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Updated Godiva-IV Benchmark Preview

A note of errata prepended to the Godiva-IV delayed-critical benchmark (HEU-MET-FAST- 086) identifies two corrections to be made to the model: The glory hole in the spindle should be made larger, and the height of the safety block should be made smaller (and therefore its density made larger). In addition, the safety block at its full-in position is closer to the inner subassembly plate than was modeled in the benchmark. These changes have been made to HEU-MET-FAST-086 Case 4 in order to estimate the effect on $\kappa$ eff and on the neutron flux spectrum. Using smaller separation, a smaller safety block, and a larger glory hole caused keff to increase by 453 ± 1 pcm from the benchmark. The latest nuclear data, ENDF/B-VIII.0, have also been used, causing $\kappa$ eff to increase another 37 ± 1 pcm. Flux spectra were compared in a modeled fission foil (near the center of Godiva-IV in the glory hole) and at three external (point) detectors. Within the fission foil, using ENDF/B-VIII.0 induced changes in the flux spectrum similar in size to the changes due to using smaller separation, a smaller safety block, and a larger glory hole. At the detectors, using ENDF/B- VIII.0 induced changes in the flux spectrum much larger than those due to changing the model. In other words, the corrections to the benchmark model cause a large increase in $\kappa$ eff , but the changes to the neutron flux spectrum are small compared to those caused by using the latest nuclear data. This study presents a preview of results expected during the reevaluation of the Godiva IV benchmark, but it is not a substitute for the full reevaluation.A note of errata prepended to the Godiva-IV delayed-critical benchmark (HEU-MET-FAST- 086) identifies two corrections to be made to the model: The glory hole in the spindle should be made larger, and the height of the safety block should be made smaller (and therefore its density made larger). In addition, the safety block at its full-in position is closer to the inner subassembly plate than was modeled in the benchmark. These changes have been made to HEU-MET-FAST-086 Case 4 in order to estimate the effect on $\kappa$ eff and on the neutron flux spectrum. Using smaller separation, a smaller safety block, and a larger glory hole caused $\kappa$ eff to increase by 453 ± 1 pcm from the benchmark. The latest nuclear data, ENDF/B-VIII.0, have also been used, causing $\kappa$ eff to increase another 37 ± 1 pcm. Flux spectra were compared in a modeled fission foil (near the center of Godiva-IV in the glory hole) and at three external (point) detectors. Within the fission foil, using ENDF/B-VIII.0 induced changes in the flux spectrum similar in size to the changes due to using smaller separation, a smaller safety block, and a larger glory hole. At the detectors, using ENDF/B- VIII.0 induced changes in the flux spectrum much larger than those due to changing the model. In other words, the corrections to the benchmark model cause a large increase in $\kappa$ eff , but the changes to the neutron flux spectrum are small compared to those caused by using the latest nuclear data. This study presents a preview of results expected during the reevaluation of the Godiva IV benchmark, but it is not a substitute for the full reevaluation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Measurement of the prompt fission neutron spectrum from 800 keV to 10 MeV for 240 Pu(sf) and for the 240 Pu($n,f$) reaction induced by neutrons of energy from 1–20 MeV

Here, the presence of 240 Pu in nuclear fuels for reactors has resulted in high uncertainties in the results of reactor and nuclear transmutation calculations because of deficiencies in 240 Pu-related nuclear data. Specifically for the prompt fission neutron spectrum (PFNS) of 240 Pu, there is only one neutron-induced, (n,f), measurement at 0.85 MeV incident neutron energy and only one complete spontaneous fission, (sf), measurement. This limited availability of data does not sufficiently guide nuclear data evaluations of these quantities. Here we report on a measurement of both the 240 Pu(sf) and the 240 Pu(n,f) PFNS, both over the emitted neutron energy range of 0.79–10.0 MeV, and from incident neutron energies of 1.0–20.0 MeV for the (n,f) reaction. Measurements were made with a hemispherical array of liquid scintillators at the high-energy Los Alamos Neutron Science Center white neutron source at the Weapons Neutron Research facility as part of the joint LANL-LLNL Chi-Nu experimental campaign to measure actinide fission neutron spectra. These measurements are the first of their kind, and provide clear experimental evidence for second-chance fission, third chance fission, and pre-equilibrium neutron emission processes in neutron-induced fission of 240 Pu, and are the first ever measurements above 1 MeV incident neutron energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Measurement of the Prompt Fission Neutron Spectrum from 800 keV to 10 MeV for 240 Pu($sf$) and for the 240 Pu($n,f$) Reaction Induced by Neutrons of Energy from 1-20 MeV

The presence of 240 Pu in nuclear fuels for reactors has resulted in high uncertainties in the results of reactor and nuclear transmutation calculations because of deficiencies in 240 Pu-related nuclear data. Specifically for the prompt fission neutron spectrum (PFNS) of 240 Pu, there is only one neutron-induced, ($n,f$), measurement at 0.85 MeV incident neutron energy and only one complete spontaneous fission, ($sf$), measurement. This limited availability of data does not sufficiently guide nuclear data evaluations of these quantities. Here we report on a measurement of both the 240 Pu($sf$) and the 240 Pu($n,f$) PFNS, both over the emitted neutron energy range of 0.79–10.0 MeV, and from incident neutron energies of 1.0–20.0 MeV for the ($n,f$) reaction. Measurements were made with a hemispherical array of liquid scintillators at the high-energy Los Alamos Neutron Science Center white neutron source at the Weapons Neutron Research facility as part of the joint LANL-LLNL Chi-Nu experimental campaign to measure actinide fission neutron spectra. These measurements are the first of their kind, and provide clear experimental evidence for second-chance fission, third-chance fission, and pre-equilibrium neutron emission processes in neutron-induced fission of 240 Pu, and are the first ever measurements above 1 MeV incident neutron energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Fission In R-process Elements (FY20 Q2 Quarterly Report)

The goal of the FIRE topical collaboration in nuclear theory is to determine the astrophysical conditions of the rapid neutron capture process (r-process), which is responsible for the formation of heavy elements. This will be achieved by including in r-process simulations the most advanced models of fission (spontaneous, neutron-induced, β-delayed) that have been developed at LLNL and LANL. The collaboration is composed of LLNL (lead) and LANL for fission work, BNL for nuclear data management, and the university of Notre Dame and North Carolina State University for r-process simulations. Under DOE/NNSA agreement, both universities receive funds from DOE Office of Science, while national laboratories receive funds directly from NA221.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Fission In R-process Elements (Q4 FY2020 Quarterly Report)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Fission In R-process Elements (Q1 FY2021)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Fission In R-Process Elements

The goal of the FIRE topical collaboration in nuclear theory is to determine the astrophysical conditions of the rapid neutron capture process (r-process), which is responsible for the formation of heavy elements. This will be achieved by including in r-process simulations the most advanced models of fission (spontaneous, neutron-induced, β-delayed) that have been developed at LLNL and LANL. The collaboration is composed of LLNL (lead) and LANL for fission work, BNL for nuclear data management, and the university of Notre Dame and North Carolina State University for r -process simulations. Under DOE/NNSA agreement, both universities receive funds from DOE Office of Science, while national laboratories receive funds directly from NA221.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗