Nuclear Mass Table Research Articles

Nuclear mass table in density functional approach inspired by neutron-star observations

Nuclear mass table in density functional approach inspired by neutron-star observations

Nuclear Mass Model Based on Bayesian Estimate of Local Difference Experssions of Binding Energies

The Bayesian estimates of the value of the residual neutron–proton interaction energy Δnp using the Markov chain Monte Carlo method and Tikhonov regularization. These estimates are used for calculation of the nuclear mass table for A 20. The accuracy of the obtained predictions is evaluated by comparison with experimental data from AME2020 and other theoretical nuclear mass models.

Examination of machine learning for assessing physical effects: Learning the relativistic continuum mass table with kernel ridge regression* *Supported by the National Natural Science Foundation of China (11875075, 11935003, 11975031, 12141501, 12070131001), the China Postdoctoral Science Foundation under (2021M700256), the State Key Laboratory of Nuclear Physics and Technology, Peking University (NPT2023ZX01, NPT2023KFY02), and the President's Undergraduate Research Fellowship (PURF) of

The kernel ridge regression (KRR) method and its extension with odd-even effects (KRRoe) are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory. With respect to the binding energies of 9035 nuclei, the KRR method achieves a root-mean-square deviation of 0.96 MeV, and the KRRoe method remarkably reduces the deviation to 0.17 MeV. By investigating the shell effects, one-nucleon and two-nucleon separation energies, odd-even mass differences, and empirical proton-neutron interactions extracted from the learned binding energies, the ability of the machine learning tool to grasp the known physics is discussed. It is found that the shell effects, evolutions of nucleon separation energies, and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods, although the odd-even mass differences can only be reproduced by the KRRoe method.

Beyond-mean-field dynamical correlations for nuclear mass table in deformed relativistic Hartree-Bogoliubov theory in continuum * *Supported by the National Natural Science Foundation of China (11875225, 12005175, 11935003, 11875075, 11975031, 12070131001, 11790325), the Fundamental Research Funds for the Central Universities, the National Key R&D Program of China (2017YFE0116700, 2018YFA0404400), the State Key Laboratory of Nuclear Physics and Technology, Peking University (NPT2020ZZ01)

We extend the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) to go beyond-mean-field framework by performing a two-dimensional collective Hamiltonian. The influences of dynamical correlations on the ground-state properties are examined in different mass regions, picking Se, Nd, and Th isotopic chains as representatives. It is found that the dynamical correlation energies (DCEs) and the rotational correction energies in the cranking approximation have an almost equivalent effect on the description of binding energies for most deformed nuclei, and the DCEs can provide a significant improvement for the (near) spherical nuclei close to the neutron shells and thus reduce the rms deviations of by 17%. Furthermore, it is found that the DCEs are quite sensitive to the pairing correlations; taking Nd as an example, a 10% enhancement of pairing strength can raise the DCE by 37%.

Nuclear mass table in deformed relativistic Hartree–Bogoliubov theory in continuum, I: Even–even nuclei

Ground-state properties of even–even nuclei with 8≤Z≤120 from the proton drip line to the neutron drip line have been investigated using the deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1. With the effects of deformation and continuum included simultaneously, 2583 even–even nuclei are predicted to be bound. The calculated binding energies, two-nucleon separation energies, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, quadrupole deformations, and neutron and proton Fermi surfaces are tabulated and compared with available experimental data. The rms deviation from the 637 mass data is 1.518 MeV, providing one of the best microscopic descriptions for nuclear masses. The drip lines obtained from DRHBc calculations are compared with other calculations, including the spherical relativistic continuum Hartree–Bogoliubov (RCHB) and triaxial relativistic Hartree–Bogoliubov (TRHB) calculations with PC-PK1. The deformation and continuum effects on the limits of the nuclear landscape are discussed. Possible peninsulas consisting of bound nuclei beyond the two-neutron drip line are predicted. The systematics of the two-nucleon separation energies, two-nucleon gaps, rms radii, quadrupole deformations, potential energy curves, neutron densities, neutron mean-field potentials, and pairing energies in the DRHBc calculations are also discussed. In addition, the α decay energies extracted are in good agreement with available data.

A New Mass Model for Nuclear Astrophysics: Crossing 200 keV Accuracy

By using a machine learning algorithm, we present an improved nuclear mass table with a root mean square deviation of less than 200 keV. The model is equipped with statistical error bars in order to compare with available experimental data. We use the resulting model to predict the composition of the outer crust of a neutron star. By means of simple Monte Carlo methods, we propagate the statistical uncertainties of the mass model to the equation of state of the system.

Towards a high-precision nuclear mass table with deformed relativistic Hartree-Bogoliubov theory in continuum

<p indent=0mm>As one of the most fundamental quantities for the atomic nucleus, nuclear mass is very important for various fields such as nuclear physics, particle physics, astrophysics, and cosmology. It is the key to understand the interaction between nucleons, the evolution of shell structures, and the location of drip lines. It also provides the basic information for nuclear reactions and the necessary inputs to study the origin of elements. Although dramatic progress for the mass measurement of short-lived nuclei has been made, the masses of most exotic nuclei far away from the stability valley still rely on the predictions by nuclear models in the foreseeable future. The popular nuclear mass models are briefly reviewed, including the finite-range droplet model (FRDM), Weizsäcker-Skyrme 4 (WS4) model, and HFB-27* model, etc. The efforts in applying the machine learning to improve the nuclear mass predictions are introduced. The relativistic density functional theory has been proved to be a powerful theory in nuclear physics by its successful description of many nuclear phenomena. The relativistic density functional theory has many attractive advantages, such as the automatic inclusion of nucleonic spin degree of freedom, explaining naturally the pseudospin symmetry in the nucleon spectrum and the spin symmetry in antinucleon spectrum, and the natural inclusion of nuclear magnetism, which plays an important role in nuclear magnetic moments and nuclear rotations. The relativistic density functional PC-PK1 has turned out to be very successful in providing good descriptions of the isospin dependence of the binding energy along either the isotopic or the isotonic chain. The relativistic continuum Hartree-Bogoliubov (RCHB) theory, which takes into account self-consistently the pairing correlations and continuum effects, is very suitable to describe the exotic nuclei. The first nuclear mass table including the continuum effects based on the RCHB theory with PC-PK1 has been constructed, predicting 9035 bound nuclei with 8≤<italic>Z</italic>≤120, which remarkably extends the existing nuclear landscape. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) was developed for exotic nuclei including deformation and continuum effects, with the deformed relativistic Hartree-Bogoliubov equations solved in a Dirac Woods-Saxon basis. The success of the DRHBc theory has been demonstrated in predicting an interesting shape decoupling between the core and the halo in ⁴⁴Mg and ⁴²Mg, resolving the puzzles concerning the radius and configuration of valence neutrons in ²²C, and studying particles in the classically forbidden regions for magnesium isotopes. A DRHBc Mass Table Collaboration, presently consisting of sixteen institutions from China and South Korea, which aims to construct the first relativistic nuclear mass table including simultaneously the deformation and continuum effects based on the DRHBc theory and density functional PC-PK1, has been founded. The recent progress in the construction of the DRHBc mass table for even-even nuclei is introduced. By taking even-even Nd isotopes as examples, the improvement for the description of the nuclear masses by deformation effects is shown in comparison with the RCHB calculations. The investigation of the possible exotic structure on the neutron-rich side and the possible proton radioactivity beyond the proton drip line for Nd isotopes is discussed. Possible topics to be investigated based on the DRHBc mass table are proposed.

Improvements to a quantum mechanical abrasion-ablation model of nuclear fragmentation: Revised nuclear level densities and improved ablation code

Transport codes used for space radiation protection require accurate nuclear fragmentation cross sections as input. The fragmentation process is modeled in two stages: a fast step, called abrasion or knockout, and a slower step, called evaporation or ablation. In this work, the ablation step is calculated via Monte Carlo (MC) methods using the recently modified legacy EVAporation (EVA) code. The code is based on the Weisskopf-Ewing particle emission formalism and has been extensively overhauled and modernized. Updates include a new nuclear mass table and modifications to the nuclear level density expression. The new formulation enables calculated results to exhibit the odd-even effect observed in experimental measurements. The revised ablation code, EVAporation-University of Tennessee, Knoxville (EVA-UTK), has been coupled with the quantum multiple scattering abrasion formalism incorporated in the nuclear fragmentation code, Optical PoTential FRAGmentation (OPTFRAG), and resulted in substantial improvements in agreement between fragmentation cross section estimates and experimental measurements.

Relativistic mean-field approach in nuclear systems

A new scheme to study the properties of finite nuclei is proposed based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach starting from a bare nucleon-nucleon interaction. The relativistic structure of the nucleon self-energies in nuclear matter depending on density, momentum and isospin asymmetry are determined through a subtracted T-matrix technique and parameterized, which makes them easily accessible for general use. The scalar and vector potentials of a single particle in nuclei are generated via a local density approximation (LDA). The surface effect of finite nuclei can be taken into account by an improved LDA (ILDA), which has successfully been applied in microscopic derivations of the optical model potential for nucleon-nucleus scattering. The bulk properties of nuclei can be determined in a self-consistent scheme for nuclei all over the nuclear mass table. Calculated binding energies agree very well with the empirical data, while the predicted values for radii and spin-orbit splitting of single-particle energies are about 10 \% smaller than the experimental data. Basic features of more sophisticated DBHF calculations for finite nuclei are reproduced.

The isospin and neutron-to-proton excess dependence of short-range correlations

We provide a systematic study of the isospin composition and neutron-to-proton (NZ) ratio dependence of nuclear short-range correlations (SRC) across the nuclear mass table. We use the low-order correlation operator approximation (LCA) to compute the SRC contribution to the single-nucleon momentum distributions for 14 different nuclei from A=4 to A=208. Ten asymmetric nuclei are included for which the neutrons outnumber the protons by a factor of up to 1.54. The computed momentum distributions are used to extract the pair composition of the SRC. We find that there is a comprehensive picture for the isospin composition of SRC and their evolution with nucleon momentum. We also compute the non-relativistic kinetic energy of neutrons and protons and its evolution with nuclear mass A and NZ. Confirming the conclusions from alternate studies it is shown that the minority species (protons) become increasingly more short-range correlated as the neutron-to-proton ratio increases. We forge connections between measured nucleon-knockout quantities sensitive to SRC and single-nucleon momentum distributions. It is shown that the LCA can account for the observed trends in the data, like the fact that in neutron-rich nuclei the protons are responsible for an unexpectedly large fraction of the high-momentum components.

Nuclear Statistical Equilibrium equation of state for core collapse

Extensive calculations of properties of supernova matter are presented, using the extended Nuclear Statistical Equilibrium model of Ref. [1] based on a statistical distribution of Wigner–Seitz cells modeled using realistic nuclear mass and level density tables, complemented with a non-relativistic Skyrme functional for unbound particles and beyond drip-line nuclei. Both thermodynamic quantities and matter composition are examined as a function of baryonic density, temperature, and proton fraction, within a large domain adapted for applications in supernova simulations. The results are also provided in the form of a table, with grid mesh and format compatible with the CompOSE platform [2] for direct use in supernova simulations. Detailed comparisons are also presented with other existing databases, all based on relativistic mean-field functionals, and the differences between the different models are outlined. We show that the strongest impact on the predictions is due to the different hypotheses used to define the cluster functional and its modifications due to the presence of a nuclear medium.

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

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. The first component of this functional 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. A 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. 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 $\Delta$ 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 noticeable better than the more phenomenological Skyrme functionals. The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies. 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 have not been taken into account yet.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Binary and ternary ionic compounds in the outer crust of a cold nonaccreting neutron star

The outer crust of a cold nonaccreting neutron star has been generally assumed to be stratified into different layers, each of which consists of a pure body-centered cubic ionic crystal in a charge compensating background of highly degenerate electrons. The validity of this assumption is examined by analyzing the stability of multinary ionic compounds in dense stellar matter. It is thus shown that their stability against phase separation is uniquely determined by their structure and their composition irrespective of the stellar conditions. However, equilibrium with respect to weak and strong nuclear processes imposes very stringent constraints on the composition of multinary compounds, and thereby on their formation. By examining different cubic and noncubic lattices, it is found that substitutional compounds having the same structure as cesium chloride are the most likely to exist in the outer crust of a nonaccreting neutron star. The presence of ternary compounds is also investigated. Very accurate analytical expressions are obtained for the threshold pressure, as well as for the densities of the different phases irrespective of the degree of relativity of the electron gas. Finally, numerical calculations of the ground-state structure and of the equation of state of the outer crust of a cold nonaccreting neutron star are carried out using recent experimental and microscopic nuclear mass tables.

Nuclear mass table in relativistic continuum Hartree-Bogoliubov theory

We present nuclear mass table in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory which properly treats pairing correlations in the presence of the continuum. We study the nuclear mass table mainly with spherical symmetry using the density functional PC-PK1. We then briefly discuss on-going calculations for deformed nuclei with axial symmetry in the framework of deformed RCHB theory.

Stylized features of single-nucleon momentum distributions

Nuclear short-range correlations (SRC) typically manifest themselves in the tail parts of the single-nucleon momentum distributions. We propose an approximate practical method for computing those SRC contributions to the high-momentum parts. The framework adopted in this work is applicable throughout the nuclear mass table and corrects mean-field models for central, spin–isospin and tensor correlations by shifting the complexity induced by the SRC from the wave functions to the operators. It is argued that the expansion of these modified operators can be truncated to a low order. The proposed model can generate the SRC-related high-momentum tail of the single-nucleon momentum distribution. These are dominated by correlation operators acting on mean-field pairs with vanishing relative radial and angular-momentum quantum numbers. The proposed method explains the dominant role of proton–neutron pairs in generating the SRC and accounts for the magnitude and mass dependence of SRC as probed in inclusive electron scattering. It also provides predictions for the ratio of the amount of correlated proton–proton to proton–neutron pairs which are in line with the observations. In asymmetric nuclei, the correlations make the average kinetic energy for the minority nucleons larger than for the majority nucleons.

Half-lives of double β +-decay with two neutrinos

Nuclear double $\beta ^-$-decays with two neutrinos were observed for many years and a systematic law describing the relation between their half-lives and decay energies was also proposed recently [Phys. Rev. C89, 064603 (2014)]. However, double $\beta ^+$-decay ($\beta ^+\beta^+)$ with emission of both two positrons and two neutrinos has not been observed up to date. In this article, we perform a systematic analysis on the candidates of double $\beta ^+$-decay, based on the 2012 nuclear mass table. Eight nuclei are found to be the good candidates for double $\beta ^+$-decay and their half-lives are predicted according to the generalization of the systematic law to double $\beta ^+$-decay. As far as we know, there is no theoretical result on double $\beta ^+$-decay of nucleus $^{154}Dy$ and our result is the first prediction on this nucleus. This is also the first complete research on eight double $\beta ^+$-decay candidates based on the available data of nuclear masses. It is expected that the calculated half-lives of double $\beta ^+$-decay in this article will be useful for future experimental search of double $\beta ^+$-decay.

Microscopic nuclear mass table with high-performance computing

We overview the methodology behind the large-scale mass table calculations based on the nuclear density functional theory (DFT) with Skyrme energy density functionals (EDFs). The calculations employing massively parallel computers are done in a large configuration space of an axially deformed harmonic oscillator. Nuclear mass tables tabulating global nuclear properties such as binding energies, radii, shape deformations, and pairing gaps are obtained for several Skyrme EDFs augmented by a mixed-type pairing functional, using an approximate particle number projection before variation. Specialty visualization tools have been developed to analyze the results. As an illustrative example of our current capabilities, we show some results for a wide range of even-even nuclei with Z ≤ 120 and N ≤ 300.

Neutron Star Crust in Strong Magnetic Fields

We discuss the effects of strong magnetic fields through Landau quantization of electrons on the structure and stability of nuclei in neutron star crust. In strong magnetic fields, this leads to the enhancement of the electron number density with respect to the zero field case. We obtain the sequence of equilibrium nuclei of the outer crust in the presence of strong magnetic fields adopting most recent versions of the experimental and theoretical nuclear mass tables. For B ∼ 1016G, it is found that some new nuclei appear in the sequence and some nuclei disappear from the sequence compared with the zero field case.Further we investigate the stability of nuclei in the inner crust in the presence of strong magnetic fields using the Thomas-Fermi model. The coexistence of two phases of nuclear matter - liquid and gas, is considered in this case. The proton number density is significantly enhanced in strong magnetic fields B ∼ 1017G through the charge neutrality. We find nuclei with larger mass number in the presence of strong magnetic fields than those of the zero field. These results might have important implications for the transport properties of the crust in magnetars.

Best Linear Unbiased Estimation of the nuclear masses

This paper presents methods to provide an optimal evaluation of the nuclear masses. The techniques used for this purpose come from data assimilation that allows combining, in an optimal and consistent way, information coming from experiment and from numerical model. Using all the available information, it leads to improve not only masses evaluations, but also to decrease uncertainties. Each newly evaluated mass value is associated with some accuracy that is sensibly reduced with respect to the values given in tables, especially in the case of the less well-known masses. In this paper, we first introduce a useful tool of data assimilation, the Best Linear Unbiased Estimation (BLUE). This BLUE method is applied to nuclear mass tables and some results of improvement are shown.