We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as well as intermediate and long-range dynamics, are encoded in the medium (nucleon density) dependence of the strength functionals of an effective interaction Lagrangian. Guided by the density dependence of microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz for the density-dependent coupling functionals is accurately determined in self-consistent mean-field calculations of binding energies of a large set of axially deformed nuclei. The relationship between the nuclear matter volume, surface and symmetry energies, and the corresponding predictions for nuclear masses is analyzed in detail. The resulting best-fit parametrization of the nuclear energy density functional is further tested in calculations of properties of spherical and deformed medium-heavy and heavy nuclei, including binding energies, charge radii, deformation parameters, neutron skin thickness, and excitation energies of giant multipole resonances.
The model of binding alpha-particles in nuclei is suggested. It is shown good (with the accuracy of 1-2%) description of the experimental binding energies in light and medium nuclear systems. Our preliminary calculations show enhancement of the binding energy for super heavy nuclei with Z~120.
Nuclear mass contains a wealth of nuclear structure information, and has been widely employed to extract the nuclear effective interactions. The known nuclear mass is usually extracted from the experimental atomic mass by subtracting the masses of electrons and adding the binding energy of electrons in the atom. However, the binding energies of electrons are sometimes neglected in extracting the known nuclear masses. The influence of binding energies of electrons on nuclear mass predictions are carefully investigated in this work. If the binding energies of electrons are directly subtracted fr…
There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.
The purpose of this note is to report predictions of the binding energy of the $Λ$ hyperon in nuclear matter using the latest version of the Juelich nucleon-nucleon meson-exchange potential. Results from a conventional Brueckner calculation are compared with previously reported values. A calculation including Dirac effects on the $Λ$ single-particle potential is also presented. Issues encountered in Dirac calculations with nucleon-hyperon potentials are discussed.
Influence of the nuclear binding in the deuteron deep inelastic structure function $F_2(x,Q^2)$ is investigated. The description is based on the Bethe-Salpeter formalism in the ladder approximation and the operator product expansion within an effective meson-nucleon theory. It is shown that the binding in a fully relativistic treatment can be simply parametrised and its origin can be understood in terms of conventional nuclear degrees of freedom. A numerical estimate of the EMC effect in the deuteron is given.
In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a parabolic approximation is often used in the literature. The variation in the binding energy value introduced by the parabolic approximation is quantitatively analyzed in detail. It is found that the approximation can introduce an uncertainty of 1-2 MeV near the saturation density.
$K^-$ optical potentials relevant to calculations of $K^-$ nuclear quasi-bound states were developed within several chiral meson-baryon coupled-channel interaction models. The applied models yield quite different $K^-$ binding energies and widths. Then, the $K^-$ multinucleon interactions were incorporated by a phenomenological optical potential fitted recently to kaonic atom data. Though the applied $K^-$ interaction models differ significantly in the $K^-N$ subthreshold region, our self-consistent calculations of kaonic nuclei across the periodic table lead to conclusions valid quite general…
The nuclear interaction is responsible for keeping neutrons and protons joined in an atomic nucleus. Phenomenological nuclear potentials, fitted to experimental data, allow one to know about the nuclear behaviour with more or less success where quantum mechanics is hard to be used. A nuclear potential is suggested and an expression for the potential energy of two nuclear entities, either nuclei or nucleons, is developed. In order to estimate parameters in this expression, some nucleon additions to nuclei are considered and a model is suggested as a guide of the addition process. Coulomb barrie…
Binding energies of ^{3}H, ^{4}He, and ^{16}O are calculated, using low-momentum nucleon-nucleon interactions (V_{low-k}) for a wide range of the cutoff momentum Λ. In addition, single-particle energies in nuclei around ^{16}O are computed. The dependence of the binding energies and the single-particle energies in these nuclei on the cutoff momentum Λof the V_{low-k} is examined. Furthermore, the availability of the V_{low-k} in nuclear structure calculations is discussed.
Brueckner-Hartree-Fock calculations are performed for nuclear matter with an exact treatment of the Pauli exclusion operator in the Bethe-Goldstone equation. The differences in the calculated binding energy, compared to the angle-average approximation, which is commonly used, are non-negligible. These difference exhibits a specific density dependence, which shifts the calculated saturation point towards smaller densities. This effect is observed for various versions of modern models for the NN interaction.
Isoscalar and isovector particle densities are derived analytically by using the approximation of a sharp edged nucleus within the local energy density approach with the proton-neutron asymmetry and spin-orbit effects. Equations for the effective nuclear-surface shapes as collective variables are derived up to the higher order corrections in the form of the macroscopic boundary conditions. The analytical expressions for the isoscalar and isovector tension coefficients of the nuclear surface binding energy and the finite-size corrections to the $β$ stability line are obtained.
A non-relativisitic nuclear density functional theory is constructed, not as usual, from an effective density dependent nucleon-nucleon force but directly introducing in the functional results from microscopic nuclear and neutron matter Bruckner G-matrix calculations at various densities. A purely phenomenological finite range part to account for surface properties is added. The striking result is that only four to five adjustable parameters, spin-orbit included, suffice to reproduce nuclear binding energies and radii with the same quality as obtained with the most performant effective forces,…
Extrapolations from nuclei to neutron stars hinge on the symmetry term in nuclear binding formulas. The term describes reduction in the binding associated with neutron-proton (np) imbalance. Regrettably, binding formulas in the literature commonly lack an intrinsic consistency with regard to the symmetry term. Our elementary considerations determine the universal macroscopic limit for the term and predict its weakening in light nuclei due to emergence of the nuclear asymmetry-skin. Experimental systematic of isobaric-analogue states allows for a determination of the volume and surface coeffici…
We report on our recent self-consistent calculations of $K^-$ nuclear quasi-bound states using $K^-$ optical potentials derived from chirally motivated meson-baryon coupled channels models [1,2]. The $K^-$ single-nucleon potentials were supplemented by a phenomenological $K^-$ multi-nucleon interaction term introduced to achieve good fits to $K^-$ atom data. We demonstrate a substantial impact of the $K^-$ multi-nucleon absorption on the widths of $K^-$ nuclear states. If such states ever exist in nuclear many-body systems, their widths are excessively large to allow observation.
The location of the proton dripline in a new phenomenological mass formula is calculated. Predictions of different mass formulas for the dripline are compared. The implications of the new mass formula for rapid proton nucleosynthesis beyond $^{56}$Ni are discussed. It is seen that the new formula indicates that masses up to A=80 are easily synthesized in a typical X-ray burst.
We extend the formulation of relativistic Coulomb sum rules to account for the average effects of nuclear binding on the initial and final states of ejected nucleons. Relativistic interactions are included by using a Dirac representation adapted from a vector-scalar field theory. The scalar field reduces the effective nucleon mass $M^*$ and increases the relativistic effects of recoil and Fermi motion. We consider two models for the off-shell behavior of the nuclear electromagnetic current, and demonstrate that the sum rule is accurate for applications to data over the interesting range of $M^…
We explore the abundance of light clusters in asymmetric nuclear matter at subsaturation density. With increasing density, binding energies and wave functions are modified due to medium effects. The method of Albergo, Costa, Costanzo and Rubbino (ACCR) for determining the temperature and free nucleon density of a disassembling hot nuclear source from fragment yields is modified to include, in addition to Coulomb effects and flow, also effects of medium modifications of cluster properties, which become of importance when the nuclear matter density is above 10$^{-3}$ fm$^{-3}$. We show how the a…
New formulas to calculate the nuclear charge radii and the nuclear binding energies have been derived in the framework of an alpha-cluster model. The particular features of the model are two assumptions that the proton-neutron pair interactions are responsible for adherence between alpha-clusters and that the proton and the neutron from a proton-neutron pair have equal nuclear potentials. These assumptions allow one to determine the charge and Coulomb radii in dependence on the amount of proton-neutron pairs in the nucleus. Unlike the Weizsacker's formula to calculate nuclear binding energies,…
Using separable potentials for $\bar{K}N-πΣ$ interaction, we investigated four-body kaonic nuclear systems such as $K^{-}ppn$ and $K^{-}K^{-}pp$, with the Faddeev AGS method in the momentum representation. The Faddeev calculations are based on the quasi-particle method and the method of the energy dependent pole expansion was used to obtain the separable representation for the integral kernels in the three- and four-body equations. Different types of $\bar{K}N-πΣ$ potentials based on phenomenological and chiral SU(3) approach are used and it was shown that the kaonic nuclear systems under cons…
The odd-even staggerings (OES) on nuclear binding energies are studied systematically within the covariant density functional (CDF) theories, specifically the relativistic Hartree-Fock-Bogoliubov (RHFB) and the relativistic Hartree-Bogoliubov (RHB) theories. Taking the finite-range Gogny force D1S as an effective pairing interaction, both CDF models can provide appropriate descriptions on the OESs of nuclear binding energies for C, O, Ca, Ni, Zr, Sn, Ce, Gd and Pb isotopes as well as for N=50 and 82 isotones. However, due to the inconsistence between the non-relativistic pairing interaction an…
Saturation of the nuclear binding energy is one of the most important properties of atomic nuclei. We derive the saturation in holographic QCD, by building a shell-model-like mean-field nuclear potential from the nuclear density profile obtained in a holographic multi-baryon effective theory. The numerically estimated binding energy is close to the experimental value.
Nuclear binding energies and two-neutron separation energies are analyzed starting from the liquid-drop model and the nuclear shell model in order to describe the global trends of the above observables. We subsequently concentrate on the Interacting Boson Model (IBM) and discuss a new method in order to provide a consistent description of both, ground-state and excited-state properties. We address the artefacts that appear when crossing mid-shell using the IBM formulation and perform detailed numerical calculations for nuclei situated in the 50-82 shell. We also concentrate on local deviations…
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 4$πr^2$ phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optica…
Sequences of experimental ground-state energies for both odd and even $A$ are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential $Ω(β,μ)$ for a mixture of nuclei at low or moderate temperatures $T=β^{-1}$ and at many chemical potentials $μ.$ The average nucleon number $<{\bf A} >(β,μ)$ then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to drip lines. We study the possible concavity of several thermodynamical …
In recent years, artificial neural networks and their applications for large data sets have became a crucial part of scientific research. In this work, we implement the Multilayer Perceptron (MLP), which is a class of feedforward artificial neural network (ANN), to predict ground-state binding energies of atomic nuclei. Two different MLP architectures with three and four hidden layers are used to study their effects on the predictions. To train the MLP architectures, two different inputs are used along with the latest atomic mass table and changes in binding energy predictions are also analyze…
Nuclear binding, correlations, and the $A$-dependence of the EMC effect
INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；Argonne National Laboratory（阿贡国家实验室）；INFN-TIFPA Trento Institute for Fundamental Physics and Applications（意大利国家核物理研究所-特伦托基础物理与应用研究所）；Instituto de Física Corpuscular (IFIC), Consejo Superior de Investigaciones Científicas (CSIC) and Universidad de Valencia（粒子物理研究所（IFIC），西班牙高等科学研究委员会（CSIC）和瓦伦西亚大学）
A nuclear model is extended to estimate binding energies and radii of neutron-rich nuclei. These calculations have been made for some representative examples of even-Z and odd-Z nuclei with nucleon numbers lower than sixty. A comparison of results with experimental data supports the value and development of the model in nuclear studies.
We explore the systematics of odd-even mass staggering with a view to identifying the physical mechanisms responsible. The BCS pairing and mean field contributions have A- and number parity dependencies which can help disentangle the different contributions. This motivates the two-term parametrization c_1 + c_2/A as a theoretically based alternative to the inverse power form traditionally used to fit odd-even mass differences. Assuming that the A-dependence of the BCS pairing is weak, we find that mean-field contributions are dominant below mass number A~40 while BCS pairing dominates in heavi…
The nuclear binding energy is studied using a finite temperature density functional theory. A Skyrme interaction is used in this work. Volume, surface, and symmetry energy contributions to the binding energy are investigated. The case of neutron skin is considered in detail. The neutron skin modifies the mass $A$ dependence of various terms and $I$ dependence of the skin thickness is proportional to $I$ for the case of same central density.
Despite great theoretical efforts the NN interaction can only be determined with a finite precision, implying an error upper bound for nuclear masses. We analyze for the first time the problem of estimating the systematic errors related to the form of the potential and their impact on nuclear binding. To this end we exploit the concept of coarse grained interactions to typical nuclear wavelengths. Our estimate gives an error of 0.1-0.4 MeV for the binding energy per particle and paves the way for ab initio calculations tailored to such a precision.
The binding energy (BE) or mass is one of the most fundamental properties of an atomic nucleus. Precise binding energies are vital inputs for many nuclear physics and nuclear astrophysics studies. However, due to the complexity of atomic nuclei and of the non-perturbative strong interaction, up to now, no conventional physical model can describe nuclear binding energies with a precision below 0.1 MeV, the accuracy needed by nuclear astrophysical studies. In this work, artificial neural networks (ANNs), the so called ``universal approximators", are used to calculate nuclear binding energies. We…
The existing nuclear masses formula and nuclear masses model has undoubtedly achieved very good results, but it is still not satisfactory for some nuclear masses. Although there are many studies in Odd-Even staggering (OES) of nuclear masses, but the research on nuclear masses by using the systematicness of OES is indeed very few. Our purpose in this paper is to describe an empirical formula for Odd-Even staggering of nuclear masses that can be useful in describing and predicting nuclear masses. We empirically obtained the formula of odd-Z (odd-N) nuclei and even-Z (even-N) nuclei based on stu…
The Faddeev-Yakubovsky equations for the alpha-particle are solved. Accurate results are obtained for several modern NN interaction models, which include charge-symmetry breaking effects in the NN force, nucleon mass dependences as well as the Coulomb interaction. These models are augmented by three-nucleon forces of different types and adjusted to the 3N binding energy. Our results are close to the experimental binding energy with a slight overbinding. Thus there is only little room left for the contribution of possible 4N interactions to the alpha-particle binding energy. We also discuss mod…
We report 3H binding energy calculations using inversion potentials generated from phase shifts corresponding to contemporary nucleon-nucleon potentials as well as modern phase shift analyses. We place limits upon local potential triton binding energy calculations due to the underlying uncertainties in their fit to the nucleon-nucleon phase shifts: 7.7 +/- 0.2 MeV. We explore the role of the nonlocality of momentum dependent potentials in the triton binding energy. In particular, we find the additional binding energy in the case of the Bonn-B potential is due to a long range nonlocality, which…
The well-known correlations of low-energy three and four-nucleon observables with a typical three-nucleon scale (e.g., the Tjon line) is extended to light nuclei and nuclear matter. Evidence for the scaling between light nuclei binding energies and the triton one are pointed out. We argue that the saturation energy and density of nuclear matter are correlated to the triton binding energy. The available systematic nuclear matter calculations indicate a possible band structure representing these correlations.
The Coulomb-nuclear interference is studied as a function of the projectile ground-state binding energy in the 8Li + 12C and 8Li + 208Pb breakup reactions, by considering an arbitrary range for the 8Li ground-state binding energies εb, varying from the experimental one 2.03 MeV down to 0.01 MeV. Regardless the target mass, we first show that the Coulomb breakup cross section is stronger dependent on εb than the nuclear breakup cross section, due to the long-range nature of the Coulomb forces and to the electromagnetic transition matrix elements. For example, in case of 8Li + 208Pb reaction at …
Symmetric nuclear matter is studied within the conserving, self-consistent T-matrix approximation. This approach involves off-shell propagation of nucleons in the ladder diagrams. The binding energy receives contributions from the background part of the spectral function, away form the quasiparticle peak. The Fermi energy at the saturation point fulfills the Hugenholz-Van Hove relation. In comparison to the Brueckner-Hartree-Fock approach, the binding energy is reduced and the equation of state is harder
The trends with mass number are examined for the odd-even-staggering (OES) in nuclear binding of neutrons and protons through the conventional measures $Δ^{(3)}$. The large differences previously observed between these trends for even and odd values of these measures is found to arise, in part, from the slow variation of binding energies with mass and charge which provides a background contribution. This background is estimated with the liquid-drop model, and accounts for the greater difference found in proton removal relative to neutron removal. The differences which persist after backgrounds…
Recent data for the slope of the EMC-ratio in the intermediate $x$-region for {\em light} nuclei, with $3 \leq A \leq 12$, have the potential to shed new light on the origin of the EMC effect. Here we study the role of nuclear binding using the scaling variable ${\tilde y}$, best suited to take into account this effect, and the understanding of the average nucleon removal energies, $\bar{E}$, provided by state-of-the-art calculations based on nuclear many body theory. We find an excellent correlation between the new EMC data at $x \sim 0.5$ and $\bar{E}$ for nuclei with $A$ from 3 to $\infty$,…
We present spectral calculations of nuclear matter properties including three-body forces. Within the in-medium T-matrix approach, implemented with the CD-Bonn and Nijmegen potentials plus the three-nucleon Urbana interaction, we compute the energy per particle in symmetric and neutron matter. The three-body forces are included via an effective density dependent two-body force in the in-medium T-matrix equations. After fine tuning the parameters of the three-body force to reproduce the phenomenological saturation point in symmetric nuclear matter, we calculate the incompressibility and the ene…
Theoretical investigation of two-proton halo-nucleus 17Ne has revealed that the valence protons are more likely to be positioned in the d-state than the s-state. In this study, this finding is clarified by calculation of the binding energy, it is found that the theoretical values for the d-state are closer to the experimental values, in contrast with those obtained for the s-state. The three-body model and MATLAB software are utilised to obtain theoretical values for the three-body-model 17Ne binding energy and matter radius. 17Ne has halo properties of a weakly bound valence proton, a binding…
It is shown that the nuclear binding correction in deep inelastic lepton scattering is essentially the same in light front and instant form representations. Some contradicting papers are discussed.
Within the nuclear density functional theory (DFT) we study the effect of reflection-asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver AxialHFB that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even-even isotopes of radium and thorium.
We use the classical BPS soliton solutions of the BPS Skyrme model together with corrections from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit breaking of the isospin symmetry - accounting for the proton-neutron mass difference - to calculate nuclear binding energies. We find that the resulting binding energies are already in excellent agreement with their physical values for heavier nuclei, demonstrating thereby that the BPS Skyrme model is a distinguished starting point for a detailed quantitative investigation of nuclea…
Isospin singlet (pn) pairing as well as quartetting in nuclei is expected to arise near the symmetry line $N=Z$. Empirical values can be deduced from the nuclear binding energies applying special filters. Within the local density approximation, theoretical estimates for finite nuclei are obtained from results for the condensation energy of asymmetric nuclear matter. It is shown that the isospin singlet condensation energy drops down abruptly for |N-Z|~4 for medium nuclei in the region A=40. Furthermore, alpha-like quartetting and the influence of excitations are discussed.
In this paper, we calculated the binding energy per baryon of the $Λ$ hypernuclei systemically, using the relativistic mean field theory (RMF) in a statistic frame. Some resemble properties are found among most of the hypernuclei found in experiments. The data show that a $Λ$ hypernucleus will be more stable, if it is composed of a $Λ$ hyperon adding to a stable normal nuclear core, or a $Λ$ hyperon replacing a neutron in a stable normal nuclear core. According to our calculations, existences of some new $Λ$ hypernuclei are predicted under the frame of RMF.
The two- and three-nucleon interaction derived in chiral effective field theory at next-to-next-to-leading order is used to obtain the binding energy of nuclear matter. Saturation is found at a binding energy per particle E/A = -16.2 \pm 0.3 MeV and a Fermi momentum k_F = 1.30 \pm 0.03 fm^{-1}, where the uncertainty is due to the cut-off dependence of the two-nucleon interaction. The sensitivity of these values to the three-nucleon force is also studied.
Non-relativistic Faddeev and Faddeev-Yakubovsky calculations were made for K^-pp, K^- ppn, K^-K^-p and K^- K^-pp kaonic nuclear clusters, where the quasi bound states were treated as bound states by employing real separable potential models for the K^ - - K^ - and the K^ - -nucleon interactions as well as for the nucleon-nucleon interaction. The binding energies and spatial shrinkages of these states, obtained for various values of the Kbar N interaction, were found to increase rapidly with the Kbar N interaction strength. Their behaviors are shown in a reference diagram, where possible change…
Using the model of hexagonal clusters we express the surface, curvature and Gauss curvature coefficients of the nuclear binding energy in terms of its bulk coefficient. Using the derived values of these coefficients and a single fitting parameter we are able to reasonably well describe the experimental binding energies of nuclei with more than 100 nucleons. To improve the description of lighter nuclei we introduce the same correction for all the coefficients. In this way we determine the apparent values of the surface, curvature and Gauss curvature coefficients which may be used for infinite n…
Nuclear masses are of great importance in nuclear physics and astrophysics. Descriptive experimental data on nuclear masses and the prediction of unknown masses based on residual proton-neutron interactions are a focus in nuclear physics. The accuracy of the residual interaction determines the accuracy of the nuclear mass values, so the study of residual interactions is essential. Before we carry out this study, there are many papers using artificial neural networks in nuclear physics. But no one uses BP neural network to study residual interactions. In this paper, we obtained a description an…
We investigate the binding energy per nucleon and hadron properties in infinite and homogeneous nuclear matter within the framework of the in-medium modified Skyrme model. We first consider the medium modifications of the single hadron properties by introducing the optical potential for pion fields into the original Lagrangian of the Skyrme model. The parameters of the optical potential are well fitted to the low-energy phenomenology of pion-nucleus scattering. Furthermore, the Skyrme term is also modified in such a way that the model reproduces bulk properties of nuclear matter, in particular…
We perform an analysis of a binding energy difference called delta V_{pn}(N,Z) =- 1/4(E(Z,N)-E(Z,N-2)-E(Z-2,N)+ E(Z-2,N-2) in the framework of a realistic nuclear model. Using the angular-momentum and particle-number projected generator coordinate method and the Skyrme interaction SLy4, we analyze the contribution brought to delta V_{pn} by static deformation and dynamic fluctuations around the mean-field ground state. Our method gives a good overall description of delta V_{pn} throughout the chart of nuclei with the exception of the anomaly related to the Wigner energy along the N=Z line. The…
With the goal of developing predictive ab-initio capability for light and medium-mass nuclei, two-nucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named NNLO$_{\rm sat}$, yield accurate binding energies and radii of nuclei up to $^{40}$Ca, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low…
