Search NASA⌕ Search

SEARCH · Search NASA

Results for “nuclear energy density functional”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Examining the justification for the introduction of a fermion localization function

Becke and Edgecombe suggested in 1990 a theoretical tool to describe electron localization in atoms and molecules, an idea which was borrowed by a large number of nuclear theorists since 2011 to describe nucleon localization in nuclear systems. I argue here that these arguments are highly questionable and cannot be used in interacting systems where effects beyond the naive mean field or the simple Hartree-Fock framework are important and the inclusion of correlations induced by particle interactions is necessary in order to introduce such a localization function. Furthermore, I also describe several aspects of the exchange and irreducible two-body density matrices, which depend on the character and strength of the two-particle interaction and which can be useful in justifying the derivation of an appropriate energy density functional.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Global optimization of harmonic oscillator basis in covariant density functional theory

The present investigation focuses on the improvement of the accuracy of the description of binding energies within moderately sized fermionic basis. Using the solutions corresponding to infinite fermionic basis it was shown that in the case of meson exchange (ME) covariant energy density functionals (CEDFs) the global accuracy of the description of binding energies in the finite $N_F$ = 16 - 20 bases can be drastically (by a factor ranging from ~3 up to ~9 dependent on the functional and $N_F$) improved by a global optimization of oscillator frequency of the basis. This is a consequence of the unique feature of the ME functionals in which with increasing fermionic basis size fermionic and mesonic energies approach the exact (infinite basis) solution from above and below, respectively. As a consequence, an optimal oscillator frequency $\hbar\omega_0$ of the basis can be defined which provides an accurate reproduction of exact total binding energies by the ones calculated in truncated basis. This leads to a very high accuracy of the calculations in moderately sized $N_F=20$ basis when mass dependent oscillator frequency is used: global rms differences $\delta B_{rms}$ between the binding energies calculated in infinite and truncated bases are only 0.025 MeV and 0.031 MeV for the NL5(Z) and DD-MEZ functionals, respectively. Optimized values of the oscillator frequency $\hbar\omega_0$ are provided for three major classes of CEDFs, i.e. for density dependent meson exchange functionals, nonlinear meson exchange ones and point coupling functionals.

Binding energy & masses↗
DOE OSTI2023

Influence of the symmetry energy on the nuclear binding energies and the neutron drip line position

A clear connection can be established between properties of nuclear matter and finite-nuclei observables, such as the correlation between the slope of the symmetry energy and the dipole polarizability, or between compressibility and the isoscalar monopole giant resonance excitation energy. Establishing a connection between realistic atomic nuclei and an idealized infinite nuclear matter leads to a better understanding of underlying physical mechanisms that govern nuclear dynamics. In this work, we aim to study the dependence of the binding energies and related quantities (e.g., location of drip lines, the total number of bound even-even nuclei) on the symmetry energy S 2 (ρ). The properties of finite nuclei are calculated by employing the relativistic Hartree-Bogoliubov model, assuming even-even axial and reflection symmetric nuclei. Calculations are performed by employing two families of relativistic energy density functionals, based on different effective Lagrangians, constrained to a specific symmetry energy at the saturation density J within the interval of 30–36 MeV. Nuclear binding energies and related quantities of bound nuclei are calculated between 8 ≤ Z ≤ 104 from the two-proton to the two-neutron drip line. As the neutron drip line is approached, the interactions with stiffer J tend to predict more bound nuclei, resulting in a systematic shift of the two-neutron drip line towards more neutron-rich nuclei. Consequentially, a correlation between the number of bound nuclei N nucl and S 2 (ρ) is established for a set of functionals constrained using the similar optimization procedures. Furthermore the direction of the relationship between the number of bound nuclei and the symmetry energy highly depends on the density under consideration.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Propagation of statistical uncertainties of Skyrme mass models to simulations of r -process nucleosynthesis

Uncertainties in nuclear models have a major impact on simulations that aim at understanding the origin of heavy elements in the universe through the rapid neutron capture process ( r process) of nucleosynthesis. Within the framework of the nuclear density functional theory, we use results of Bayesian statistical analysis to propagate uncertainties in the parameters of energy density functionals to the predicted r -process abundance pattern, by way not only of the nuclear masses but also through the influence of the masses on β -decay and neutron capture rates. We point out the importance of the nonequilibrium end stage of the r process in determining the width of the resulting abundance pattern uncertainty bands. We additionally make the first identifications of specific parameters of Skyrme-like energy density functionals which show tentative correlations with particular aspects of the r -process abundance pattern. While previous studies have explored the reduction in the abundance pattern uncertainties due to anticipated new measurements of neutron-rich nuclei, here we point out that an even larger reduction will occur when these new measurements are used to reduce the uncertainty of model predictions of masses, which are then propagated through to the abundance pattern. We make a quantitative prediction for how large this reduction will be.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Comparing different density-matrix expansions for long-range pion exchange

Empirical energy density functionals (EDFs) are generally successful in describing nuclear properties across the table of nuclides. But their limitations motivate using the density-matrix expansion (DME) to embed long-range pion interactions into a Skyrme functional. Recent results on the impact of the pion were both encouraging and puzzling, necessitating a careful re-examination of the DME implementation. In this study, we take the first steps, focusing on two-body scalar terms in the DME. Exchange energies with long-range one-pion contributions are well approximated by all DME implementations considered, with preference for variants that do not truncate at two derivatives in every EDF term. The use of the DME for chiral pion contributions is therefore supported by this investigation. For scalar-isovector energies it is important to treat neutrons and protons separately. The results are found to apply under broad conditions, although self-consistency is not yet tested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Three-dimensional Skyrme Hartree-Fock-Bogoliubov solver in coordinate-space representation

The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform. To remedy the problems with pairing collapse, we implemented the soft energy cutoff and pairing annealing. The convergence of HFB solutions was improved by a sub-iteration method. The Hermiticity violation of differential operators brought by Fourier-transform-based differentiation has also been solved. Furthermore, the accuracy and performance of HFBFFT were tested by benchmarking it against other HFB codes, both spherical and deformed, for a set of nuclei, both well-bound and weakly-bound.

3D coordinate-space representation↗
DOE OSTI2022

Hot and dense matter equation of state probability distributions for astrophysical simulations

We add an ensemble of nuclei to the equation of state for homogeneous nucleonic matter to generate a new set of models suitable for astrophysical simulations of core-collapse supernovae and neutron star mergers. We implement empirical constraints from (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. Our model is also guided by microscopic many-body theory calculations based on realistic nuclear forces, including the zero-temperature neutron matter equation of state from quantum Monte Carlo simulations and thermal contributions to the free energy from finite-temperature many-body perturbation theory. We ensure that the parameters of our model can be varied while preserving thermodynamic consistency and the connection to experimental or observational data, thus providing a probability distribution of the astrophysical hot and dense matter equation of state. Furthermore, we compare our results with those obtained from other available equations of state. While our probability distributions indeed represent a large number of possible equations of state, we cannot yet claim to have fully explored all of the uncertainties, especially with regard to the structure of nuclei in the hot and dense medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Interstitialcy-mediated transport in Hematite

Defect transport mechanisms drive the performance of materials in both energy storage and energy generating systems. Iron oxide systems are of particular interest with use cases in both realms. Previous studies of a-Fe2O3 (hematite) determined that the primary point defects at elevated temperature are O vacancies and Fe interstitials, and these defects determine transport rates at temperatures >850°C. However, in advanced nuclear reactor designs, operating temperatures will range between 400-800°C. In this study, we utilize isotopic tracers and the nanoscale resolution of atom probe tomography to determine diffusivities at lower temperatures relevant to nuclear energy generating systems. Supported by a density functional theory informed rate theory model, we find a change from vacancy to interstitialcy-mediated transport < 800°C in the anion lattice.

Yano, Kayla H.↗
DOE OSTI2022

Diabatic Hamiltonian matrix elements made simple

With a view to applying the generator coordinate method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements. Here, the method is illustrated with two analytically solvable Hamiltonians based on the harmonic oscillator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Nucleonic shells and nuclear masses

The binding energy of an isotope is a sensitive indicator of the underlying shell structure as it reflects the net energy content of a nucleus. Since magic nuclei are significantly lighter, or more bound, compared to their neighbors, the presence of nucleonic shell structure makes an imprint on nuclear masses. In this study, using a carefully designed binding-energy indicator, we catalog the appearance of spherical and deformed shell and subshell closures throughout the nuclear landscape. After presenting experimental evidence for shell and subshell closures as seen through the lens of nuclear masses, we study the ability of global nuclear mass models to predict local binding-energy variations related to shell effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Electric and magnetic dipole strength in 112,114,116,118,120,124 Sn

Background: There is renewed interest in electric dipole strength distributions for a variety of reasons including the extraction of the dipole polarizability related to properties of the symmetry energy and a measure for the neutron skin thickness, understanding the structure of low-energy $\textit{E}$1 strength in nuclei with neutron excess, and establishing the systematics of the isovector giant dipole resonance (IVGDR). Inelastic proton scattering at energies of a few hundred MeV and very forward angles including 0° has been established as a tool for the study of electric and magnetic dipole strength distributions in nuclei. Purpose: The present work aims at a systematic investigation of the electric and magnetic dipole strength distributions in the chain of stable even-mass tin isotopes. Methods: Inelastic proton scattering experiments were performed at the Research Center for Nuclear Physics, Osaka, with a 295-MeV beam covering laboratory angles 0°–6° and excitation energies 6–22 MeV. Cross sections due to $\textit{E}$1 and $\textit{M}$1 excitations were extracted with a multipole decomposition analysis (MDA) and then converted to reduced transition probabilities with the “virtual photon method” for $\textit{E}$1 and the “unit cross section method” for $\textit{M}$1 excitations, respectively. Including a theory-aided correction for the high-excitation-energy region not covered experimentally, the electric dipole polarizability was determined from the $\textit{E}$1 strength distributions. Results: In this work, total photoabsorption cross sections derived from the $\textit{E}$1 and $\textit{M}$1 strength distributions show significant differences compared to those from previous ($\textit{γ, xn}$) experiments in the energy region of the IVGDR. The widths of the IVGDR deduced from the present data with a Lorentz parametrization show an approximately constant value of about 4.5 MeV in contrast to the large variations between isotopes observed in previous work. The IVGDR centroid energies are in good correspondence to expectations from empirical systematics of their mass dependence. Furthermore, a study of the dependence of the IVGDR energies on bulk matter properties is presented. The $\textit{E}$1 strengths below neutron threshold show fair agreement in this work with results from ($\textit{γ, γ'}$) experiments on 112,116,120,124 Sn in the energy region between 6 and 7 MeV, where also isoscalar $\textit{E}$1 strength was found for 124 Sn. At higher excitation energies, large differences are observed, pointing to a different nature of the excited states with small ground-state branching ratios. The isovector spin-$\textit{M}$1 strengths exhibit a broad distribution between 6 and 12 MeV in all studied nuclei. Conclusions: The present results contribute to the solution of a variety of nuclear structure problems including the systematics of the energy and width of the IVGDR, the structure of low-energy $\textit{E}$1 strength in nuclei, new constraints to energy density functionals (EDFs) aiming at a systematic description of the dipole polarizability across the nuclear chart, from which properties of the symmetry energy can be derived, and the systematics of the isovector spin-$\textit{M}$1 strength in heavy nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter

The energy density is calculated in coordinate space for 12 C, 40 Ca, 48 Ca, and 208 Pb using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The energy density of 8 Be is also calculated using the Green’s function Monte-Carlo method employing the Argonne/Urbana two and three-body interactions. The nuclear interior minimally contributes to the total binding energy due to the 4πr 2 phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in good agreement with ab initio self-consistent Green’s function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this work indicate that saturated nuclear matter does not require the canonical value of 16 MeV binding per particle but only about 13-14 MeV when the interior of 208 Pb is considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Microscopic origin of reflection-asymmetric nuclear shapes

The presence of nuclear ground states with stable reflection-asymmetric shapes is supported by rich experimental evidence. Theoretical surveys of odd-multipolarity deformations predict the existence of pear-shaped isotopes in several fairly localized regions of the nuclear landscape in the vicinity of near-lying single-particle shells with Δℓ = Δj = 3. We analyze the role of isoscalar, isovector, neutron-proton, neutron-neutron, and proton-proton multipole interaction energies in inducing the onset of reflection-asymmetric ground-state deformations. The calculations are performed in the framework of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory using two Skyrme energy-density functionals and density-dependent pairing force. We show that reflection-asymmetric ground-state shapes of atomic nuclei are driven by the odd-multipolarity neutron-proton (or isoscalar) part of the nuclear interaction energy. This result is consistent with the particle-vibration picture, in which the main driver of octupole instability is the isoscalar octupole-octupole interaction giving rise to large E3 polarizability. The necessary condition for the appearance of localized regions of pear-shaped nuclei in the nuclear landscape is the presence of parity doublets involving Δℓ = Δj = 3 proton or neutron single-particle shells. This condition alone is, however, not sufficient to determine whether pear shapes actually appear, and, if so, what the corresponding reflection-asymmetric deformation energies are. The predicted small reflection-asymmetric deformation energies result from dramatic cancellations between even- and odd-multipolarity components of the nuclear binding energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Global study of separable pairing interaction in covariant density functional theory

A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on the separable pairing interaction. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in the neutron subsystem. However, the situation is less certain in the proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. For a given part of the nuclear chart the scaling factors for spherical nuclei are smaller than those for deformed ones; this feature exists also in nonrelativistic density functional theories. Furthermore, its origin is traced back to particle-vibration coupling in odd-A nuclei which is missing in all existing global studies of pairing. Although the present investigation is based on the NL5(E) covariant energy density functional (CEDF), its general conclusions are expected to be valid also for other CEDFs built at the Hartree level.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Reexamining the variational two-particle reduced density matrix for nuclear systems

We report that in most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Global properties of nuclei at finite-temperature within the covariant energy density functional theory

In stellar environments nuclei appear at finite temperatures, becoming extremely hot in core-collapse supernovae and neutron-star mergers. However, due to theoretical and computational complexity, most model calculations of nuclear properties are performed at zero temperature, while those existing at finite temperatures are limited only to selected regions of the nuclide chart. In this study we perform the global calculation of nuclear properties for even-even 8 ≤ Z ≤ 104 nuclei at temperatures in range 0 ≤ T ≤ 2 MeV. Calculations are based on the finite-temperature relativistic Hartree-Bogoliubov model supplemented by the Bonche-Levit-Vautherin vapor subtraction procedure. We find that near the neutron-drip line the continuum states have significant contribution already at moderate temperature T ≈ 1 MeV, thus emphasizing the necessity of the vapor subtraction procedure. Results include neutron emission lifetimes, quadrupole deformations, neutron-skin thickness, proton and neutron pairing gaps, entropy and excitation energy. Up to the temperature T ≈ 1 MeV, the nuclear landscape is influenced only moderately by the finite-temperature effects, mainly by reducing the pairing correlations. Here, as the temperature increases further, the effects on nuclear structures become pronounced, reducing both the deformations and the shell effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Artificial Neural Networks as Mappings between Proton Potentials, Wave Functions, Densities, and Energy Levels

We report artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗