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DOE OSTI2018

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: In this study, we seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei, and the fission barrier of 240 Pu . Quantitatively, they perform noticeably better than the more phenomenological Skyrme functionals. Conclusions: The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies while the impact on other observables is not really significant. In conclusion, this result is especially promising since all the fits have been performed at the single-reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction, rotational correction, or zero-point vibrational energies have not been taken into account yet.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Spallation process with simultaneous multi-particle emission in nuclear evaporation

High energy probes have been used currently to explore nuclear reaction mechanism and nuclear structure. The spallation process governs the reaction process around 1 GeV energy regime. A new aspect introduced here to describe the nuclear reaction is the in-medium nucleonnucleon collision framework. The nucleon-nucleon scattering is kinematically treated by using an effective mass to represent the nuclear binding. In respect to the evaporation phase of the reaction, we introduce the simultaneous particles emission decay. This process becomes important due to the rise of new channels at high excitation energy regime of the compound nucleus. As results, the particles yields in the rapid and evaporation phases are obtained and compared to experimental data. The effect and relevance of these simultaneous emission processes in the evaporation chain is also discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Nuclear Theory from First Principles to Forefront Experiments (Final Report for DE-SC0018638)

The Lee research group is a part of the Nuclear Lattice Effective Field Theory Collaboration, which has developed and performed ab initio lattice simulations of nuclear structure, scattering, reactions, and many-body systems. The other senior members of the collaboration include Ulf-G. Meißner at Bonn/Julich, Evgeny Epelbaum and Hermann Krebs at Bochum, Timo Lahde and Thomas Luu at Julich, and Gautam Rupak at Mississippi State. Our letter “Ab initio alpha-alpha scattering” was featured in a Nature News and Views article. Another letter “Nuclear binding near a quantum phase transition” was highlighted in a Viewpoint article in the online APS journal Physics as well as a news article in the IOP publication Physics World (September 21, 2016). Our letter “Eigenvector continuation with subspace learning” was also highlighted a Synopsis article in Physics. There are many promising ab initio approaches being used to calculate the properties of few-and many-nucleon systems. This includes the no-core shell model, symmetry-adapted no-core shell model quantum Monte Carlo, auxiliary-field diffusion Monte Carlo, self-consistent Green’s functions, many-body perturbation theory, in-medium similarity renormalization group, and coupled cluster methods. Lattice effective field theory is another ab initio approach which combines the framework of effective field theory with lattice Monte Carlo methods to allow favorable scaling from few- to many-body systems. Perhaps the most important aspect of lattice effective field theory is that its strengths and weaknesses are orthogonal to that of other ab initio methods. For example, lattice effective field theory has little difficulty in probing cluster structures and collectivity, while such features are much more difficult using other methods. Furthermore it can be used to compute superfluid condensate fractions as well as the phase diagram of strongly matter and the density and temperature dependence of clustering. Lattice effective field theory was first used in simulations of infinite nuclear matter and infinite neutron matter with pions and without pions. In addition to the efforts by our collaboration, there have been recent efforts by other groups as well.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Q-value (MeV/fission) Determination for the Advanced Test Reactor

This report documents a step-by-step procedure that can be used to calculate a Q-value for the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL). The Q-value calculation here is an estimate of the total energy released per fission event in the ATR driver fuel in units of MeV/fission and is recognized as a reactor-specific Q-value for the ATR. Such a Q-value is needed INL ATR reactor physicists to normalize calculated fluxes and reaction rates to measured ATR total core and lobe powers. The calculated ATR Q-value and the procedure used to calculate this value are presented in a detailed manner so as to establish a credible basis, such that this single Q-value can be used consistently among all ATR reactor physicists. A Q-value is essentially the summation of all the kinetic energy from all radiation components released from a single fission event that ends up as heat in the reactor coolant. Estimation of a Q-value for a given reactor can theoretically be very complex because it is dependent on several variables, which include (1) the materials in the reactor core, (2) the neutron energy spectrum, and (3) the mix of actinide isotopes that are being simultaneously fissioned. Since these three variables can potentially change over time or with reactor burnup, this potentially makes the Q-value a time-dependent quantity. However, for ATR, we will invoke some simplifying assumptions, based on the unique features of the ATR core and supported by neutronic calculations, which will reduce the complexity of the problem and lead to a single time-independent Q-value. Of the three variables, the materials in the core have the greatest impact on the ATR Q-value. Since the materials in the core are most important, an array of components (materials) have been carefully selected to compose a typical ATR core configuration. It should be noted that the step-by-step procedure here for calculating a reactor-specific Q-value can be applied to any nuclear reactor. In a more general procedure, if one needed to include time-dependent spectral and actinide composition changes as a function of burnup for a specific reactor, this procedure can still be used, but at discrete time steps throughout the burnup. The result will be a set of discrete Q-values as a function of burnup. However, here we will apply the procedure to the ATR, as an example, and obtain a single Q-value that is valid for the ATR reactor as a function of burnup. In the evaluated nuclear data file (ENDF), Q-values for specific actinides are known for a reasonably high degree of accuracy, especially the major uranium and plutonium isotopes. The isotopic Q-values are composed of the kinetic energy of the fission fragments and the energies of the various radiation components emitted from the fission event. One complication is the fact that some of these energy components are dependent on the incident neutron energy (EINC) that induces the fission event (neutron energy spectrum dependence). For ATR, we will estimate an average neutron energy based on the neutron energy flux weighted by the fission cross sections and use this average neutron energy value in the ENDF formulas. This neutron energy dependence is one of two dependencies that make the final ATR Q-value a reactor-specific value. The second dependency, and the most important variable for ATR, involves the materials in the core and the de-excitation radiations produced from neutron radiative capture radiation; radiation energy that becomes heat in the reactor coolant. This important dependency is discussed in detail below. The third dependency, or the mix of fissioning actinides as a function of ATR burnup, is ignored because the bulk of the fissions over a cycle are always due to U-235 in the high-enriched ATR core. In a fission event, the fission energy is partitioned between the fission fragments and the radiation components that include neutrons, gamma rays, and beta particles. The main variable that makes the calculated Q-value reactor-specific is the amount of radiative capture energy produced in the core due to prompt and delayed neutron capture in the reactor core materials and the subsequent release of nuclear binding energy in the form of de-excitation gamma radiation energy in the reactor core. This energy component, neutron radiative capture energy, is not in the ENDF, because it depends on the reactor and its core materials. The radiative capture gamma energy release can be significant, or approximately 3–12 MeV/fission depending on the materials in the reactor core (fuel materials, cladding, structural components, coolant, targets, reflector, etc.). For the ATR, the energy released from radiative capture gamma radiation is calculated to be near the middle of the 3–12 MeV range. This makes the radiative capture radiation component an important and significant contribution to the total ATR Q-value. The ATR has unique reactor features that will allow us to simplify the complex procedure for determining an ATR reactor-specific Q-value. For example, the ATR is a thermal reactor and contains high-enriched fuel (93.15 wt% U-235). Consequently, the bulk of the fissions in the ATR core from beginning-of-cycle (BOC) to end-of-cycle are from U-235. Even though U-238 makes up approximately 7% of the uranium atoms in the fuel, the number of fissions relative to U-235 is insignificant, since U-238 is fertile and ATR is a thermal reactor. The same is true for U-234 and U-236 (both fertile). The ATR’s high-enriched uranium fuel also inhibits the buildup of large quantities of plutonium isotopes. So, even though there is some buildup of U-236, Np-237, and Pu-239 in the ATR driver fuel, the impact or contribution of these isotopes fissions on the ATR Q-value is minor compared to U-235. Nonetheless, we will include fission contributions from all the major uranium isotopes (U-234, U-235, U-236, and U-238) in the determination of an average isotopic Q-value that is used in the ATR Q-value determination. Although the ATR Q-value calculated here is based on BOC conditions (fresh fuel with no higher order actinide buildup), it is believed that the ATR Q-value is relatively constant with burnup or during any given ATR power cycle (14–60 days). The reason is that the vast majority of the core driver fuel fissions are always from U-235 during the cycle. Also, since we effectively assume instantaneous energy release for the fission product gammas and beta particles and delayed neutrons from a fission event, this corresponds to equilibrium conditions for all fission product concentrations in the ATR driver fuel too. The goal of this effort was to determine a specific numerical and core-average Q-value for the recoverable energy released by a single fission event (MeV/fission) for the ATR. This calculated value has the potential to help standardize and add credibility to not only the Monte Carlo tally normalization process used by many ATR core physics analysts, but also to the normalization process for all reactor physics calculation methods involving ATR analyses. Currently, the ATR core physics analysts use slightly different Q-values. Some values are known to be conservative for specific applications. However, sometimes a more accurate Q-value is needed for the calculation in which ATR test specimens require non-conservative and as-accurate-as-possible Q-values to estimate burnups, heat rates, neutron fluxes, nuclear reaction rates, etc., where corresponding measured post-irradiation examination data provides the ultimate validation for the calculated results. A detailed Q-value procedure was developed and is outlined in this document along with numerical values calculated specifically for the determination of the ATR Q-value. This report attempts to document in some detail the calculation methodology, nuclear data, computer code, computer model, code calculated results, hand calculations, assumptions, and logic that went into the determination of the ATR Q-value.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Chameleon sequences in neurodegenerative diseases

Chameleon sequences can adopt either alpha helix sheet or a coil conformation. Defining chameleon sequences in PDB (Protein Data Bank) may yield to an insight on defining peptides and proteins responsible in neurodegeneration. In this research, we benefitted from the large PDB and performed a sequence analysis on Chameleons, where we developed an algorithm to extract peptide segments with identical sequences, but different structures. In order to find new chameleon sequences, we extracted a set of 8315 non-redundant protein sequences from the PDB with an identity less than 25%. Our data was classified to “helix to strand (HE)”, “helix to coil (HC)” and “strand to coil (CE)” alterations. We also analyzed the occurrence of singlet and doublet amino acids and the solvent accessibility in the chameleon sequences; we then sorted out the proteins with the most number of chameleon sequences and named them Chameleon Flexible Proteins (CFPs) in our dataset. Our data revealed that Gly, Val, Ile, Tyr and Phe, are the major amino acids in Chameleons. We also found that there are proteins such as Insulin Degrading Enzyme IDE and GTP-binding nuclear protein Ran (RAN) with the most number of chameleons (640 and 405 respectively). These proteins have known roles in neurodegenerative diseases. Therefore it can be inferred that other CFP's can serve as key proteins in neurodegeneration, and a study on them can shed light on curing and preventing neurodegenerative diseases.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Discriminating binding mechanisms of an intrinsically disordered protein via a multi-state coarse-grained model

Many proteins undergo a conformational transition upon binding to their cognate binding partner, with intrinsically disordered proteins (IDPs) providing an extreme example in which a folding transition occurs. However, it is often not clear whether this occurs via an “induced fit” or “conformational selection” mechanism, or via some intermediate scenario. In the first case, transient encounters with the binding partner favour transitions to the bound structure before the two proteins dissociate, while in the second the bound structure must be selected from a subset of unbound structures which are in the correct state for binding, because transient encounters of the incorrect conformation with the binding partner are most likely to result in dissociation. A particularly interesting situation involves those intrinsically disordered proteins which can bind to different binding partners in different conformations. We have devised a multi-state coarse-grained simulation model which is able to capture the binding of IDPs in alternate conformations, and by applying it to the binding of nuclear coactivator binding domain (NCBD) to either ACTR or IRF-3 we are able to determine the binding mechanism. By all measures, the binding of NCBD to either binding partner appears to occur via an induced fit mechanism. Nonetheless, we also show how a scenario closer to conformational selection could arise by choosing an alternative non-binding structure for NCBD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Lamb Shift of n = 1 and n = 2 States of Hydrogen-like Atoms, 1 ≤ Z ≤ 110

Theoretical energy levels of the n = 1 and n = 2 states of hydrogen-like atoms with the nuclear charge numbers 1 ≤ Z ≤ 110 are tabulated. The tabulation is based on ab initio quantum electrodynamics calculations performed to all orders in the nuclear binding strength parameter Zα, where α is the fine structure constant. Theoretical errors due to various effects are critically examined and estimated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Computational schemes for the Magnus expansion of the in-medium similarity renormalization group

The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schrödinger equation through a continuous unitary transformation of the many-body Hamiltonian. The IMSRG transformation is typically truncated at the normal-ordered two-body level, the IMSRG(2), but recently several approaches have been developed to capture the effects of normal-ordered three-body operators, the IMSRG(3). In particular, a factorized approximation to the IMSRG(3) proposes to capture the leading effects of three-body operators at the same computational cost as the IMSRG(2) approximation. This approach often employs an approximate scheme for solving the IMSRG equations, the so-called hunter-gatherer scheme. In this work, I study the uncertainty associated with this scheme. I find that the hunter-gatherer scheme differs by up to 7MeV for ground-state energies and 0.5MeV for excitation energies from standard IMSRG(2) approaches. These differences are in some cases comparable to the expected size of IMSRG(3) corrections.

39 ≤ A ≤ 58↗
DOE OSTI2020

Landscape of pear-shaped even-even nuclei

The phenomenon of reflection-asymmetric nuclear shapes is relevant to nuclear stability, nuclear spectroscopy, nuclear decays and fission, and the search for new physics beyond the standard model. Global surveys of ground-state octupole deformation, performed with a limited number of models, suggest that the number of pear-shaped isotopes is fairly limited across the nuclear landscape. Here, we carry out a global analysis of ground-state octupole deformations for particle-bound even-even nuclei with Z ≤ 110 and N ≤ 210 using nuclear density functional theory (DFT) with several nonrelativistic and covariant energy density functionals. In this way, we can identify the best candidates for reflection-asymmetric shapes. The calculations are performed in the frameworks of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory and relativistic Hartree-Bogoliubov theory using DFT solvers employing harmonic oscillator basis expansion. We consider five Skyrme and four covariant energy density functionals. We predict several regions of ground-state octupole deformation. In addition to the “traditional” regions of neutron-deficient actinide nuclei around 224 Ra and neutron-rich lanthanides around 146 Ba, we identified vast regions of reflection-asymmetric shapes in very neutron-rich nuclei around 200 Gd and 288 Pu, as well as in several nuclei around 112 Ba. Our analysis suggests several promising candidates with stable ground-state octupole deformation, primarily in the neutron-deficient actinide region, that can be reached experimentally. Detailed comparison between Skyrme and covariant models is performed. Octupole shapes predicted in this study are consistent with the current experimental information. This work can serve as the starting point of a systematic search for parity doublets in odd-mass and odd-odd nuclei, which will be of interest in the context of new physics searches.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Ab initio benchmarks of neutrinoless double- β decay in light nuclei with a chiral Hamiltonian

Here, we report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-β (0νββ) decays in light nuclei with mass numbers ranging from A = 6 to A = 22. We use the transition operator derived from light-Majorana neutrino exchange and evaluate the NME with three different methods: two variants of in-medium similarity renormalization group (IMSRG) and importance-truncated no-core shell model (IT-NCSM). The same two plus three nucleon interaction from chiral effective field theory is employed, and both isospin-conserving (ΔT = 0) and isospin-changing (ΔT = 2) transitions are studied. We compare our resulting ground-state energies and NMEs to those of recent ab initio no-core shell model and coupled-cluster calculations, also with the same inputs. We show that the NMEs of ΔT = 0 transitions are in good agreement among all calculations, at the level of 10%. For ΔT = 2, relative deviations are more significant in some nuclei. The comparison with the exact IT-NCSM result allows us to analyze these cases in detail, and indicates the next steps toward improving the IMSRG-based approaches. The present study clearly demonstrates the power of consistent cross checks that are made possible by ab initio methodology. This capability is crucial for providing meaningful many-body uncertainties in the NMEs for the 0νββ decays in heavier candidate nuclei, where quasiexact benchmarks are not available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Unbound spectra of neutron-rich oxygen isotopes predicted by the Gamow shell model

The Gamow shell model has shown to efficiently describe weakly bound and unbound nuclear systems, as internucleon correlations and continuum coupling are both taken into account in this model. In the present work, we study neutron-dripline oxygen isotopes. It is hereby demonstrated that the presence of continuum coupling is important for the description of oxygen isotopes at dripline, and especially to assess the eventual bound or unbound character of 28 O. Our results suggest that the ground state of 28 O is weakly unbound and is similar to the narrow resonant 26 O ground state. Predictions of weakly bound and resonance excited states in 24–26 O are also provided. The asymptotes of the studied many-body states are analyzed via one-body densities, whereby the different radial properties of well bound, loosely bound, resonance states are clearly depicted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Ground-state properties of light 4 n self-conjugate nuclei in ab initio no-core Monte Carlo shell model calculations with nonlocal N N interactions

We report J π = 0 + ground-state energies and point-proton radii of 4 He, 8 Be, 12 C, 16 O, and 20 Ne nuclei calculated by the ab initio no-core Monte Carlo shell model with the JISP16 and Daejeon16 nonlocal NN interactions. Ground-state energies are obtained in the basis spaces up to seven oscillator shells (N shell =7) with several oscillator energies (ℏω) around the optimal oscillator energy for the convergence of ground-state energies. These energy eigenvalues are extrapolated to obtain estimates of converged ground-state energies in each basis space using energy variances of computed energy eigenvalues. We further extrapolate these energy-variance-extrapolated energies obtained in the finite basis spaces to infinite basis-space results with an empirical exponential form. This form features a dependence on the basis-space size but is independent of the value of ℏω used for the harmonic-oscillator basis functions. Point-proton radii for these states of atomic nuclei are also calculated following techniques employed for the energies. From these results, it is found that the Daejeon16 NN interaction provides good agreement with experimental data up to approximately 16 O, while the JISP16 NN interaction provides good agreement with experimental data up to approximately 12 C. Beyond these nuclei, the interactions produce overbinding accompanied by radii that are too small. These findings suggest and encourage further revisions of nonlocal NN interactions towards the investigation of nuclear structure in heavier-mass regions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Theoretical description of fission yields: Toward a fast and efficient global model

A recently proposed approach to global modeling of fission fragment distributions is extended to account for odd-even staggering in charge yields and for neutron evaporation. We show that the proposed hybrid model can reproduce experimental mass and charge fragment yields, including the odd-even staggering for a wide range of fissioning nuclei. Experimental isotopic yields can be described within a simple neutron evaporation scheme. Here, we also explore fission fragment distributions of exotic neutron-rich and superheavy systems and compare our predictions with other state-of-the art global calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

In-medium similarity renormalization group with flowing 3-body operators, and approximations thereof

Here, we explore the impact of retaining three-body operators within the in-medium similarity renormalization group (IMSRG), as well as various approximations schemes. After studying two toy problems, identical fermions with a contact interaction and the Lipkin-Meshkov-Glick model, we employ the valence-space formulation of the IMSRG to investigate the even- A carbon isotopes with a chiral two-body potential. We find that retaining only those commutators expressions that scale as N 7 provides an excellent approximation of the full three-body treatment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Measurement of the structure function of the nearly free neutron using spectator tagging in inelastic H 2 ( e , e ' p s ) X scattering with CLAS

In this study, much less is known about neutron structure than that of the proton due to the absence of free neutron targets. Neutron information is usually extracted from data on nuclear targets such as deuterium, requiring corrections for nuclear binding and nucleon off-shell effects. These corrections are model dependent and have significant uncertainties, especially for large values of the Bjorken scaling variable x. As a consequence, the same data can lead to different conclusions, for example, about the behavior of the d quark distribution in the proton at large x.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗