Ground-state Properties Of Finite Nuclei Research Articles

GW190814: Impact of a 2.6 solar mass neutron star on the nucleonic equations of state

Is the secondary component of GW190814 the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system [R. Abbott et al., ApJ Lett., 896, L44 (2020)]? This is the central question animating this letter. Covariant density functional theory provides a unique framework to investigate both the properties of finite nuclei and neutron stars, while enforcing causality at all densities. By tuning existing energy density functionals we were able to: (a) account for a 2.6 Msun neutron star, (b) satisfy the original constraint on the tidal deformability of a 1.4 Msun neutron star, and (c) reproduce ground-state properties of finite nuclei. Yet, for the class of models explored in this work, we find that the stiffening of the equation of state required to support super-massive neutron stars is inconsistent with either constraints obtained from energetic heavy-ion collisions or from the low deformability of medium-mass stars. Thus, we speculate that the maximum neutron star mass can not be significantly higher than the existing observational limit and that the 2.6 Msun compact object is likely to be the lightest black hole ever discovered.

“Sloppy” nuclear energy density functionals. II. Finite nuclei

A study of parameter sensitivity of nuclear energy density functionals, initiated in the first part of this work \cite{NV.16}, is extended by the inclusion of data on ground-state properties of finite nuclei in the application of the manifold boundary approximation method (MBAM). Density functionals used in self-consistent mean-field calculations, and nuclear structure models based on them, are generally "sloppy" and exhibit an exponential range of sensitivity to parameter variations. Concepts of information geometry are used to identify the presence of effective functionals of lower dimension in parameter space associated with parameter combinations that can be tightly constrained by data. The MBAM is used in an iterative procedure that systematically reduces the complexity and the dimension of parameter space of a sloppy functional, with properties of nuclear matter and data on finite nuclei determining not only the values of model parameters, but also the optimal functional form of the density dependence.

Relativistic Brueckner—Hartree—Fock Theory for Finite Nuclei**Supported by the National Basic Research Program of China No 2013CB834400, the National Natural Science Foundation of China under Grants Nos 11175002, 11335002, 11405090, 11375015 and 11621131001, the Research Fund for the Doctoral Program of Higher Education under Grant No 20110001110087, the DFG cluster of excellence “Origin and Structure of the Universe” (www.universe-cluster.de), the CPSC

Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner—Hartree—Fock equations are solved for finite nuclei in a Dirac—Woods—Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus 16O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner—Hartree—Fock results and much closer to the experimental data. This opens the door for ab initio covariant investigations of heavy nuclei.

Information and statistics: a new paradigm in theoretical nuclear physics

Theoretical predictions of physical observables often involve extrapolations to regions that are poorly constrained by laboratory experiments and astrophysical observations. Without properly quantified theoretical errors, such model predictions are of very limited utility. In this contribution we use maximum-likelihood estimation to compute theoretical errors and assess correlations between physical observables. We illustrate the power and elegance of these methods using examples of both pedagogical and realistic interest. In particular, we implement a Gaussian approximation to the likelihood function to develop a new relativistic effective interaction constrained by ground-state properties of finite nuclei, their monopole response, and masses of neutron stars.

Building relativistic mean field models for finite nuclei and neutron stars

Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed chi-square objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, FSUGold2, is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter--suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme--properly supplemented by a covariance analysis--provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.

New effective interactions in improved quark mass density-dependent model with ω tensor and non-linear ω–ρ couplings

A new parametrization for improved quark mass density-dependent (IQMDD) model by including ω tensor and non-linear ω – ρ couplings has been proposed. By employing this model, the ground-state properties of finite nuclei, the saturation properties of the nuclear matter and the equation of state (EOS) of neutron star matter are studied. It has been shown that this model is able to provide a good description not only for the ground-state properties of finite nuclei but also for the saturation properties of the nuclear matter. The results obtained by using the new IQMDD model are compared with the relativistic mean field model and experimental findings.

Finite- to zero-range relativistic mean-field interactions

We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the σ-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.

Validating relativistic models of nuclear structure against theoretical, experimental, and observational constraints

Relativistic mean-field models of nuclear structure have been enormously successful at reproducing ground-state properties of finite nuclei throughout the periodic table using a handful of accurately calibrated parameters. In this contribution, we use powerful theoretical, experimental, and observational constraints on the equation of state of asymmetric nuclear matter--not employed in the calibration procedure--to validate two such models: NL3 and FSUGold. It is observed that FSUGold is consistent with all these constraints, except perhaps for a high-density equation of state that appears mildly softer than required by astronomical observations. It is argued that incorporating such constraints goes a long way in removing much of the ambiguity left over from the standard calibrating procedure.

The symmetry energy in nuclei and in nuclear matter

We discuss to what extent information on ground-state properties of finite nuclei (energies and radii) can be used to obtain constraints on the symmetry energy in nuclear matter and its dependence on the density. The starting point is a generalized Weizsacker formula for ground-state energies. In particular, effects from the Wigner energy and shell structure on the symmetry energy are investigated. Strong correlations in the parameter space prevent a clear isolation of the surface contribution. Use of neutron skin information improves the situation. The result of the analysis appears consistent with a rather soft density dependence of the symmetry energy in nuclear matter.

THE SYMMETRY ENERGY IN NUCLEI AND IN NUCLEAR MATTER

We discuss to what extent information on ground-state properties of finite nuclei (energies and radii) can be used to obtain constraints on the symmetry energy in nuclear matter and its dependence on the density. The starting point is a generalized Weizsäcker formula for ground-state energies. In particular effects from the Wigner energy and shell structure on the symmetry energy are investigated. Strong correlations in the parameter space prevent a clear isolation of the surface contribution. Use of neutron skin-information improves the situation. We find that inclusion of the Wigner effect leads to a larger value of the symmetry energy of nuclear matter at the saturation point.

Relativistic Hartree-Bogoliubov Description of Ground-State Properties of Finite Nuclei

A fully Relativistic Hartree-Bogoliubov (RHB) theory is applied in the description of ground state properties of finite nuclei. The NL3 parameter set is used for the effective meanfield Lagrangian, and pairing correlations are described by a phenomenological relativistic one-meson interaction. Fully self-consistent RHB solutions are calculated for Sn and Ni isotopes. Binding energies, two-neutron separation energies are compared with experimental data and other relativistic calculations performed by using the Gogny force DSA1 in the pp-channel. Relativistic effects induced by the relativistic pairing interaction are discussed.

GIANT RESONANCE PROPERTIES IN β STABLEAND UNSTABLE NUCLEI

We study the giant resonances of stable and unstable nuclei in the framework of the consistent relativistic random phase approximation built on the nonlinear relativistic mean field (RMF) ground states. The isoscalar and isovector modes of giant resonances for stable nuclei, such as 208Pb,144Sm,116Sn,90Zr,40Ca,16O and Ca isotope chains are investigated. The contribution to the giant resonances from the Dirac sea states and the currents of vector mesons are examined. The results show that the effects of the Dirac sea states on the isoscalar giant modes are pronounced, but become weaker for light nuclei, while the contributions of the isovector modes are negligible. The few sets of parameterizations of nonlinear RMF model, which are commonly used to give a good description of ground-state properties of finite nuclei, could also well describe the nuclear dynamic properties-giant resonances. For nuclei with the extreme value of N/Z, low-lying collective excitations are found in isovector dipole modes, which are mainly due to the ph excitation of the weakly bound states near Fermi surface and the isospin mixture effect.

Towards a universal nuclear density functional

A new form of the nuclear energy-density functional for describing the ground-state properties of finite nuclei up to the drip lines and beyond is proposed. The volume part in this functional is fit to the Friedman-Pandharipande and Wiringa-Fiks-Fabrocini equation of state for the UV14 plus TNI model up to densities ρ≈1 fm−3 by a fractional expression in ρ which can be extended to higher densities while preserving causality. For inhomogeneous systems, a surface energy-density term is added, with two free parameters, which also has a fractional form like the Pade approximant containing (∇ρ)2 in both the numerator and denominator. In addition to the Coulomb direct and exchange interaction energy, an effective ρ-dependent Coulomb-nuclear correlation term is included with one more free parameter. A three-parameter fit to the masses and radii of real nuclei shows that the latter term gives a contribution to the Coulomb displacement energy of the same order of magnitude as the Nolen-Schiffer anomaly. The first self-consistent run with the proposed functional, performed for about 100 spherical nuclei, gives rms deviations from experiment of ≈1.2 MeV in the masses and ≈0.01 fm in the radii, which are about a factor of two better than those obtained with the Skyrme functionals or with the Gogny force. The extrapolation to the drip lines lies in between the ETFSI and the macroscopic-microscopic model predictions.

Effective interaction for relativistic theory of nuclear structure

An effective interaction for relativistic Hartree-Fock (HF) calculations of nuclear structure is constructed. It includes a nonlinear functional of the most simple general form taking into account interactions and self-interactions of isoscalar meson fields. The parameters are determined to reproduce Dirac-Brueckner HF nuclear matter results obtained from different types of one-boson-exchange potential (OBEP) fitting NN scattering data. The effective interaction is used then to calculate ground-state properties of finite nuclei. Results for some specific OBEP{close_quote}s (BM-B version) are in reasonable agreement with experiment. The symmetry energy coefficient, in particular, is well reproduced. It is found that the {sigma}{sup 2}{omega}{sup 2} and {omega}{sup 4} components of the effective interaction play an important role. {copyright} {ital 1997} {ital The American Physical Society}

Relativistic extended Thomas-Fermi calculations with exchange term contributions

In this investigation we present self-consistent relativistic extended Thomas-Fermi (ETF) and extended Thomas-Fermi-Fock (ETFF) approaches, derived from the semiclassical treatment of the relativistic nuclear Hartree-Fock problem. The approximations are used to describe the ground-state properties of finite nuclei. The resulting equations are solved numerically for several one-boson-exchange (OBE) lagrangians. The results are discussed and compared with the outcome of full quantal Hartree and Hartree-Fock calculations, other semiclassical treatments and experimental data.

Finite nuclei: Just a droplet of nuclear matter?

Differences in the evalution of the saturation properties of infinite nuclear matter and finite nuclei are discussed. It is demonstrated that ground-state properties of finite nuclei are much more affected by the finite range of realistic nucleon-nucleon interactions than the saturation point of nuclear matter. Therefore very simple local-density approximations in calculating properties of finite nuclei are not reliable. The finite range effects yield a larger incompressibility for finite nuclei as compared to nuclear matter.

Effective local interactions and the equation of state for nuclear matter and finite nuclei

Differences in the evaluation of the saturation properties of infinite nuclear matter and finite nuclei are discussed. It is demonstrated that ground-state properties of finite nuclei are much more affected by the finite range of realistic nucleon-nucleon interactions than the saturation point of nuclear matter. Due to surface effects, a larger incompressibility for finite nuclei is obtained as compared to nuclear matter. Local nucleon-nucleon interactions are determined, which simulate the main features of the Brueckner G-matrix and allow for a simple calculation and analysis of the ground-state properties. These effective local interactions of finite range could be very useful in dynamical calculations of heavy-ion scattering.

Coulomb displacement energies in relativistic and non-relativistic self-consistent models

Coulomb displacement energies in mirror nuclei are comparatively analyzed in Dirac-Hartree and Skyrme-Hartree-Fock models. Using a non-linear effective lagrangian fitted on ground-state properties of finite nuclei, it is found that the predictions of relativistic models are lower than those of Hartree-Fock calculations with a Skyrme force. The main sources of reduction are the kinetic energy and the Coulomb-nuclear interference potential. The discrepancy with the data is larger than in the Skyrme-Hartree-Fock case.

Meson exchange potentials and the problem of saturation in finite nuclei

The status of the microscopic explanation of the ground-state properties of finite nuclei (in a non-relativistic framework) is updated, and compared to the corresponding situation in nuclear matter. In addition, modifications of the meson exchange parameters in the nuclear medium are explored. It is demonstrated that a change of the effective meson mass for the scalar and vector mesons yields quite different effects on the saturation properties of nuclear matter and finite nuclei than a change of e.g. the effective mass of the pion. The origin of such differences are explored.

Constrained variational calculations for finite nuclei

The technique of lowest-order constrained variational calculations used by the authors to study the bulk properties of homogeneous, quantal fluids (1978) is extended for use in discussing the ground-state properties of finite nuclei. The significance of various constraints in finite systems is discussed. It is shown that the saturating effects of explicit allowance for N*(1234) excitations is essential if the calculations are to yield sensible binding energies and RMS radii. Specific application is made to the light closed-shell nuclei 4He, 12C and 16O.