Ground State Properties Of Nuclei Research Articles

Effects of a kaonic meson on the ground-state properties of nuclei * *Supported by the National Natural Science Foundation of China (12175071, 11775081)

The effects of an additional meson on the ground-state properties of nuclei are investigated within an axially-deformed Skyrme-Hartree-Fock approach combined with a Skyrme-type kaon-nucleon interaction. The meson increases the binding energies of all nuclei, whereas it affects deformations only for light nuclei without shell closure. The nucleon drip lines are modified due to the strongly attractive interaction. This is attributed to the behavior of the highest-occupied nucleon single-particle levels near the drip lines, which is analyzed in detail.

A search for neutron magicity in the isotopic series of Z = 122, 128 superheavy nuclei

The superheavy nuclei have been examined systematically in the region 158 ⩽ N ⩽ 218, 162 ⩽ N ⩽ 212 for Z = 122 and 128, respectively. The explicit density-dependent meson-exchange (DD-ME) and point-coupling (DD-PC) models within the framework of covariant density functional theory (CDFT) have been used to study the structural and decay properties of the isotopic series which includes the separable form of a finite range of pairing interaction. From the potential energy curves, the ground state properties of nuclei are predicted. Due to the importance of the shell effect in the superheavy region, the Strutinsky shell correction method has been employed for a better understanding of the extra stability of nuclei. The results from neutron pairing energy, two-neutron separation energy (S 2n ), single-particle energy levels, and total shell-correction energy strongly support N = 168, 174, and 178 as deformed neutron-magic numbers from both the force parameter, in both the isotopic series. N = 172 and 184 are predicted as spherical magic with DD-ME2 interaction in the Z = 122 isotopic series. Using three different semi-empirical approaches named UNIV2, SemFIS2, and ImSahu, the α-decay properties are studied and compared with available experimental data, FRDM2012 and the WS4 mass model. The stability of synthesized superheavy nuclei can be determined by comparing spontaneous fission half-lives with α-decay half-lives.

Covariant density functional theory for rare isotopes

Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). The covariant version of this theory is based on a density functional which takes into account Lorentz symmetry in a self-consistent way. Pairing correlations play an important role in all open-shell configurations. They are included in relativistic Hartree Bogoliubov (RHB) theory by an effective residual interaction of finite range. With a minimal number of phenomenological parameters this theory allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently this method has also been extended for the investigations of excited states, such as collective vibrations and rotations.

Essential elements for nuclear binding

How does nuclear binding emerge from first principles? Our current best understanding of nuclear forces is based on a systematic low-energy expansion called chiral effective field theory. However, recent ab initio calculations of nuclear structure have found that not all chiral effective field theory interactions give accurate predictions with increasing nuclear density. In this letter we address the reason for this problem and the first steps toward a solution. Using nuclear lattice simulations, we deduce the minimal nuclear interaction that can reproduce the ground state properties of light nuclei, medium-mass nuclei, and neutron matter simultaneously with no more than a few percent error in the energies and charge radii. We find that only four parameters are needed. With these four parameters one can accurately describe neutron matter up to saturation density and the ground state properties of nuclei up to calcium. Given the absence of sign oscillations in these lattice Monte Carlo simulations and the mild scaling of computational effort scaling with nucleon number, this work provides a pathway to high-quality simulations in the future with as many as one or two hundred nucleons.

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory

The ground-state properties of nuclei with 8⩽Z⩽120 from the proton drip line to the neutron drip line have been investigated using the spherical relativistic continuum Hartree–Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. It is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the α-decay energies and proton emitters based on the RCHB calculations are investigated.

The highest limiting Z in the extended periodic table

The problem of finding the highest limiting Z in the extended periodic table is discussed. The upper limit suggested by the atomic many body theory at Z = 172 may be reached much earlier due to nuclear instabilities. Therefore, an extensive set of calculations based on the relativistic mean field formulation are carried out for the ground state properties of nuclei with Z = 100 to 180 and N/Z ratio ranging from 1.19 to 2.70. This choice of Z and N extends far beyond the corresponding values of all the known heavy to superheavy elements. To facilitate the analysis of the huge quantity of calculated results, various filters depending upon the pairing energies, one and two nucleon separation energies, binding energy per particle (BE/A) and α-decay plus fission half lives, are introduced. The limiting value of Z is found to be 146. For the specific filter with 5.5 MeV a few nuclei with Z = 180 also appear. No evidence for the limiting Z value 172 is found. We stress the need to bridge the atomic and nuclear findings and to arrive at an acceptable limiting value of highest Z (or rather combination of Z and N) of the extended periodic table.

A new covariant density functional with point-coupling and its application

The covariant density functional theory with a few number of parameters allows a very successful phenomenological description of ground state properties of nuclei all over the nuclear chart. The newly proposed point-coupling parametrization PC-PK1 [1] and its application is reported. In particular, the description of the nuclear ground state properties and the neutron single-particle spectrum in 132Sn is discussed in details.

Selected issues at the interface between nuclear physics and astrophysics as well as the standard model

The density functional theory (DFT) with a minimal number of parameters allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. The recent developments on the application of the covariant density functional theory as well as its extensions by the group in Beijing for a series of interests and hot topics in nuclear astrophysics and nuclear structure are reviewed, including the rapid neutron-capture process, Th/U chronometer, and isospin corrections for superallowed β transitions.

Covariant Density Functional Theory for Nuclear Structure and Application in Astrophysics

The density functional theory with a minimal number of parameters allows a very successful phenomenological description of ground state properties of nuclei all over the nuclear chart. The recent progress on the application of the covariant density functional theory for nuclear structure and astrophysics as well as its extensions by the group in Beijing is summarized. Particularly, its application to the low-lying excited states in exotic and/or transitional nuclei is discussed in details.

Higher-dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed Nilsson oscillator

Based on the Riemann and Caputo definitions of the fractional derivative we use the fractional extensions of the standard rotation group S O ( 3 ) to construct a higher-dimensional representation of a fractional rotation group with mixed derivative types. An extended symmetric rotor model is derived, which predicts the sequence of magic proton and neutron numbers accurately. The ground state properties of nuclei are correctly reproduced within the framework of this model.

Systematic studies on the exotic properties of isotopes from oxygen to calcium

Systematic calculations of the ground state properties of nuclei with proton number Z = 8 – 20 have been made by the macroscopic–microscopic (MM) model with isospin-dependent spin–orbit potential. Special emphases are placed on the exotic properties of neutron-rich nuclei, the evolution of deformations and the shell structures. The calculated binding energies agree well with the experimental data. The calculations well reproduce the deformations for both nuclei near stability-line and drip-line. The calculations extend the boundaries of the island of inversion and show that 28–32Ne, 29–33Na and 30–34Mg belong to the island. The large deformations and exotic properties of nuclei around N = 20 are discussed and their origin are explained. We stress that both protons and neutrons play important roles in the formation of the large deformations and the appearance of the island of inversion. The properties of nuclei around N = 28 are also discussed. The calculations show that the N = 28 shell seems to disappear in Mg, Al and Si isotopes. We show that most exotic properties of sd and pf shell nuclei can be understood in MM model.

Covariant density functional theory for extremely heavy nuclei

Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). The covariant version of this theory is based on a density functional which takes into account Lorentz symmetry in a self-consistent way. Pairing correlations play an important role in all open-shell configurations. They are included in relativistic Hartree Bogoliubov (RHB) theory by an effective residual interaction of finite range. With a minimal number of parameters this theory allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently this method has also been applied for the description of very heavy and super-heavy elements.

COVARIANT DENSITY FUNCTIONAL THEORY FOR COLLECTIVE EXCITATIONS IN NUCLEI FAR FROM STABILITY

Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). Relativistic Hartree Bogoliubov (RHB) theory is a covariant version of this method, which takes into account Lorentz symmetry and pairing correlations in a fully self-consistent way. This theory has been used in the past for a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently is also has been extended for the investigation of excited states. We discuss the calculation of rotational bands within cranked RHB-theory and recent investigations of vibrational excitations within the framework of relativistic Quasiparticle Random Phase Approximation (QRPA).

Nuclear structure based on correlated realistic nucleon–nucleon potentials

We present a novel scheme for nuclear structure calculations based on realistic nucleon–nucleon potentials. The essential ingredient is the explicit treatment of the dominant interaction-induced correlations by means of the unitary correlation operator method (UCOM). Short-range central and tensor correlations are imprinted into simple, uncorrelated many-body states through a state-independent unitary transformation. Applying the unitary transformation to the realistic Hamiltonian leads to a correlated, low-momentum interaction, which is well suited for all kinds of many-body models, e.g., Hartree–Fock or shell-model. We employ the correlated interaction, supplemented by a phenomenological correction, in the framework of variational calculations with antisymmetrised Gaussian trial states (fermionic molecular dynamics). Ground state properties of nuclei up to mass numbers A ≲ 60 are discussed. Binding energies, charge radii, and charge distributions are in good agreement with experimental data. We perform angular momentum projections of the intrinsically deformed variational states (projection after variation) to extract rotational spectra. Finally, we discuss perspectives for variation after projection and multi-configuration calculations.

Systematic calculations of the ground state properties of superheavy nuclei

We investigate the ground state properties of the nuclei with proton number $Z=94--110$ within the framework of deformed relativistic mean-field (RMF) theory. A systematic comparison between calculated binding energies and experimental data is made. The calculated binding energies are in good agreement with experimental ones. The reliability of the RMF model for superheavy nuclei has been tested by this comparison. The experimental data of alpha-decay energies and half-lives are reasonably reproduced by calculations. Calculated results further show that a prolate deformation is important for the ground state of these nuclei. The properties of some unknown nuclei are predicted and these are useful for future experimental researches of superheavy nuclei.

A Relativistic Point Coupling Model for Nuclear Structure Calculations

A relativistic point coupling model is discussed focussing on a variety of aspects. In addition to the coupling using various bilinear Dirac invariants, derivative terms are also included to simulate finite-range effects.The formalism is presented for nuclear structure calculations of ground state properties of nuclei in the Hartree approximation. Different fitting strategies for the determination of the parameters have been applied and the quality of the fit obtainable in this model is discussed. The model is then compared more generally to other mean-field approaches both formally and in the context of applications to ground-state properties of known and superheavy nuclei. Naturalness and perspectives for further extensions such as an exact treatment of the exchange terms using a higher-order Fierz transformation are discussed briefly.

Towards a Better Understanding of Nuclear Pairing and Its Interplay with Other Residual Interactions

Experimental evidence indicates that pairing interaction often plays a major role in determining physics of nuclear many-body systems. The goal of this work is to discuss properties of pairing in a mesoscopic nuclear environment, study the interplay of pairing and other residual interactions and develop new practical approaches. We use Sn isotopes as a testing arena. We utilize the exact solution of pairing problem based on quasispin formalism. 1), 2) This treatment of pairing (EP algorithm) is free of well-known BCS shortcomings and enables one to address fluctuating pair vibrations and chaotic effects of other residual interactions which significantly change the usual macroscopic BCS picture, 3) furthermore it provides a basis, with classification by seniority quantum numbers, that can be used for perturbatively accounting for other interactions. We demonstrate in a simple model that although in general twobody interactions do not preserve seniority, kinematics still often favors seniority conservation. The lowest seniority subspace can serve as a good starting truncation. Interactions of a non-pairing nature have only diagonal monopole contributions in this subspace. We show that this technique of exact pairing plus monopole 2) can be successful in the analysis of ground state properties of nuclei, furthermore being a well formulated variational method and part of a more general seniority truncation technique it is perfect for adjusting shell model parameters. Pairing and approximate treatment of other residual interactions can be combined through the Hartree-Fock (HF) and exact pairing (EP) technique. In Fig. 1 one-neutron separation energies are calculated for the Sn isotopes, including those beyond 132Sn. These energies were obtained from the fully self-consistent spherically symmetric solution of HF equations, using the SKX interaction, 4) with the EP solution based on renormalized G-matrix interactions from Ref. 5). The HF+EP approach can be considered as a variant of the density functional method. In this method we make an initial guess for the spherical HF potential from which the single particle energies are determined. In the valence subspace the pairing problem is solved using a fixed set of two-body matrix elements. This determines the particle distribution and pairing correlation energy. With new occupation numbers a new HF potential can be calculated. This procedure is repeated iteratively until convergence. The total energy is the sum of the Skyrme HF energy and the pairing correlation energy. Figure 1 shows an example of such calculations and exhibits an

QUARKS AND NEUTRON HALO NUCLEI, NUCLEAR CLUSTERS AND NUCLEAR MOLECULES

It is shown that the hole in the centre of 3 H , 3 He and 4 He , the neutron halos in nuclei, the α- and other clustering effects in nuclei and the nuclear molecules all basically arise due to the same underlying effect. We shall show that all these ground state properties of nuclei are manifestations of quark effects. The role of triton clustering in very neutron rich nuclei is emphasized. All these require the concept of hidden colour states which arise from confinement ideas of QCD for the multi-quark systems. This provides a comprehensive understanding of diverse nuclear effects and makes unique predictions.

Relativistic Effective Interaction11The project supported by National Natural Science Foundation of China

In analogy with the idea of the effective interaction commonly used in the nonrelativistic approach, the relativistic effective interactions are adopted to incorporate the relativistic Brueckner-Hartree-Fock (RBHF) results in the relativistic mean field approach (RMF) or relativistic Hartree-Fock approach (RHF). It is desired to remedy the deficiencies of RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The relativistic effective interactions are used to describe the ground state properties of nuclei and medium-energy nucleon-nucleus scattering in this paper.

Relativistic mean-field description of neutron-deficient platinum isotopes.

We have studied neutron-deficient even-mass platinum isotopes in the framework of the relativistic mean-field theory. The ground-state properties of nuclei have been calculated in the {sigma}{omega}{rho} model with the nonlinear scalar self-interaction of the {sigma} meson. The charge radii, binding energies, and deformation properties have been obtained in the relativistic Hartree approximation with deformed basis. Solutions have been obtained for both the prolate as well as oblate shapes. A comparison of the calculated properties has been made with data from recent measurements on these nuclei performed at the ISOLDE project at CERN. It has been shown that the isotopic shift measurements reveal an oblate shape for all even platinum isotopes, in contrast with some existing theoretical calculations which indicate prolate shape for highly neutron-deficient isotopes.