RMF理论中Zr同位素链壳结构的形变依赖性

基于球形与轴对称形变的相对论平均场（Relativistic Mean Field, 简称RMF）理论模型, 分别计算了Zr同位素链的基态总能量, 并根据其差值提取了形变修正能后发现, Zr同位素链丰中子区的核具有大的长椭形变, 对应的形变修正能可达到10 MeV。 利用RMF理论计算的基态能量, 在扣除液滴模型计算的结合能后, 得到了Zr同位素链的壳修正能。 通过对壳修正能的分析后发现, 形变使N=50壳效应显著减弱。 特别是在丰中子区, 大形变导致了N=50壳结构的消失。 The total binding energy of nuclei for Zr isotopic chain is calculated by the spherical and axial deformed relativistic mean field(RMF) theory respectively, and the energy contribution due to the deformation(i.e., deformation correction energy) is extracted. It is found that the neutron rich nuclei in the isotopic chain have large prolate deformation, and corresponding deformation correction energy can be up to 10 MeV. The shell correction energy is obtained by the difference between the binding energies calculated by the liquid model and those by the RMF calculations. Detailed analysis indicates that the deformation weakens the shell effect of N=50 remarkably. Especially for the neutron rich nuclei, large deformation leads to disappearance of the N=50 shell structure.     

相对论平均场理论对Pt同位素形状演化的研究

利用形变约束的相对论平均场理论研究了Pt同位素偶-偶核的形状演化,比较了基态结合能和四极形变的理论计算值和实验值, 分析了这些核的位能曲线、单粒子能级及其随四极形变β₂ 的变化规律,发现从N=88到N=126, Pt同位素的基态变形从球形对称核经X(5)对称性核、演化为具有稳定形变的核,再演化为球形核的变化过程.其中, ^166-172Pt是近球形核, ¹⁷⁴Pt和^192-196Pt位于球形和稳定形变之间,可能具有X(5)对称性, ^176-190Pt具有稳定的变形, ^198-202Pt是近球形核, ²⁰⁴Pt是球形核,这些结果与实验一致.     

Skyrme-hartree-fock approach to spherical nuclei with density-dependent pairing correlations

The ground-state properties of spherical nuclei over the entire periodic table are investigated by the Skyrme-Hartree-Fock approach with new force parameters SKI4 [P. G. Reinhard and H. Flocard, Nucl. Phys. A584 467 (1995)] plus a density-dependent pairing correlation. By introducing the density-dependent pairing correlation in the Skyrme-Hartree-Fock model with SKI4, both the isospin degree of freedom and the nucleon-nucleon correlation have been suitably included in the theory. The theoretical results agree very well with experimental data of binding energies, single particle energies and radii of spherical nuclei. The isotope shifts of charge radii in Ca, Ni, Sn, and Pb are also well reproduced.     

Skyrme-Hartree-Fock approach to spherical nuclei with density-dependent pairing correlations

The ground-state properties of spherical nuclei over the entire periodic table are investigated by the Skyrme-Hartree-Fock approach with new force parameters SKI4 [P. G. Reinhard and H. Flocard, Nucl. Phys. A584 467 (1995)] plus a density-dependent pairing correlation. By introducing the density-dependent pairing correlation in the Skyrme-Hartree-Fock model with SKI4, both the isospin degree of freedom and the nucleon-nucleon correlation have been suitably included in the theory. The theoretical results agree very well with experimental data of binding energies, single particle energies and radii of spherical nuclei. The isotope shifts of charge radii in Ca, Ni, Sn, and Pb are also well reproduced.     

超重核的四面体对称性(英文)

基于反射不对称壳模型的投影位能面计算预言原子核310126 是继208Pb 之后的双幻核,其基态呈现出四面体形状。四面体对称性驱动的量子效应可以使基态的结合能,相较球形而言增加达13 MeV,这反映了在最重核的计算中,考虑四面体自由度的重要性。计算结果还表明,四面体对称性驱动的量子效应能够明显地增加裂变位垒,从而导致超重核合成几率的增加。     

Multifragmentation of hot and compressed nuclei within a time dependent thomas fermi and percolation model

We have used a spherical time dependent Thomas Fermi model to study the expansion of hot and/or compressed nuclei. This approach was coupled to a site-bond percolation model to study the disassembly of the nucleus into many pieces (multifragmentation). We find that a non compressed nucleus undergoes multifragmentation if the thermal excitation energy is larger than 70% of its binding energy. If the nucleus is compressed this value is notably decreased.     

Binding energies of nuclei and their density distributions in a nonlocal extended Thomas-Fermi approximation

Basic properties of the ground states of spherical nuclei are investigated in a nonlocal extended Thomas-Fermi approximation under the assumption of Skyrme forces. It is shown that, for nuclei occurring near the β-stability line, the binding energies, the root-mean-square radii, and the density distributions found on this basis agree well with experimental data. Binding energies, root-mean-square radii, and density distributions are also calculated for the ground states of nuclei lying far off the β-stability line and for superheavy elements. For the proton, the neutron, and the total particle density, the thickness of the diffuse layer is investigated as a function of the number of neutrons in tin isotopes.     

基于壳模型对力加四极力研究sd和pf壳偶偶原子核

本文在原子核壳模型框架下基于唯象相互作用(对力加四极力)研究sd壳和pf壳的偶偶核低激发集体态。在提取了USDB和GXPF1相互作用的单粒子能量和单极相互作用的基础上,我们用一套统一参数计算重现了球形核和形变核的低激发谱;将对相互作用中的单极成分扣除后可以得到较好的结合能计算结果。同位旋标量的对相互作用对计算结果影响不大。单极相互作用在经验质子—中子相互作用、原子核对称能和Wigner能中产生重要贡献。     

Self-consistent calculation of the ground state properties of some rare-earth nuclei

Ground state intrinsic deformation properties of some rare earth nuclei are calculated within the Hartree-Fock approximation using a Skyrme effective interaction. After a careful optimization of basis parameters, calculations have been performed with a basis corresponding to 13 spherical oscillator shells. In order to obtain the multipole moments, good numerical convergence is necessary. Calculated quadrupole and hexadecapole moments are in agreement with available experimental data. Ground state binding energies are also well reproduced.     

Generalized shells in nuclei: Hartree-Fock calculations for bubble nuclei

Hartree-Fock calculations in the bubble degree of freedom have been performed on a variety of spherical nuclei. Of particular importance are incipient bubble configurations in ³⁶Ar, ⁶⁸Se, ⁸⁴Se, ¹⁰⁰Sn, ¹¹⁶Ce, ¹³⁸Ce and ²⁰⁰Hg, each of which possesses a binding energy which is comparable to that of the normal spherical closed-shell configuration. The densities of the above nuclei display strong deviations from a uniform shape, and give rise to depletions in the nuclear interior. These nonuniformities are due both to the absence of low angular momentum states in otherwise normally occupied spherical shells, and also to strong self-consistency effects. The nonuniformities in the mass density are further enhanced for nuclei whose neutron and proton densities have depressions or peaks at approximately the same distance from the center of the nucleus. A depression of the central density is most pronounced in the nuclei ³⁶Ar, ¹³⁸Ce and ²⁰⁰Hg. Interior depletions of the density are associated with the relatively higher energies of low angular momentum single-particle levels as compared to high angular momentum single-particle levels. This effect can give rise to moderately large gaps at the Fermi surface. Finally, it is shown that in a bubble configuration, the spin-orbit splitting of low lying doublets is sometimes reversed, and that this effect is especially pronounced for levels with low angular momentum.     

Statistical spectroscopy for nuclei in the fp shell

Nuclei in the fp shell have been studied using the spectral averaging method. This was attempted with a view to provide a rather simple alternative to detailed microscopic calculations. We have considered a decomposition of the overall spectroscopic space (m particles in the fp shell) in terms of a spherical j-orbit, isospin, configuration-isospin and SU(4) isospin subspaces. Centroid energies and widths of these subspaces are evaluated and used to determine binding energies, low-energy spectra and fractional occupancy of j-orbits. We have also examined the extent of Wigner SU(4) symmetry mixing for nuclei in this shell. The ratio of binding energies of isobars suggested by Franzini and Radicati to test the validity of SU(4) symmetry is also evaluated from the calculated binding energies. Comparisons are made with microscopic calculations like the shell model and Hartree-Fock where available. We find that the distribution method is able to determine ground-state energies and spectra of nuclei very well despite the fact that the vector spaces are quite large. The SU(4) symmetry in the ground-state region of these nuclei is strongly mixed largely due to the single particle spin-orbit coupling.     

Short-range correlations with pseudopotentials. IV

Using a unitary model operator, the short-range correlations between nucleons in nuclei have been considered. To achieve healing in the wave functions, short-range pseudopotentials are required to be added to the nucleon-nucleon potential. With the introduction of the pseudopotentials, the matrix element for the effective interaction in nuclei is developed with correlated basis wave functions. The tensor forces and the short-range pseudopotentials are renormalized in second-order perturbation theory. Hartree-Fock calculations are carried out for the two finite closed-shell spherical nuclei¹⁶O and⁴⁰Ca. The calculations of the resulting effective Hamiltonian are carried out with an effective interaction derived from the Tabakin potential. The present calculations of the binding energies per particle for the¹⁶O and⁴⁰Ca nuclei are in agreement with the experimental measurements.     

Electrostatic binding in the first-row AH and A2 diatomic molecules

The charge migration that converts two overlapping spherical atoms into a bound molecule produces attractive Hellmann-Feynman fields at the two nuclear positions, offsetting the repulsive field that each nucleus encounters on penetrating inside the charge cloud of its neighbour. The magnitudes of these fields correlate positively with the molecular dissociation energies. The contribution of the σ valence orbitals to the field at a first-row nucleus varies regularly from binding in lithium to anti-binding in fluorine. The electrostatic effect of these orbitals is weakened by reversed polarization inside the 2s nodal sphere and is further opposed by a tiny but effective exchange polarization of the core. The major binding role in the first row thus falls to the π orbitals, which, like the σ orbital in hydrogen, have no radial node to inhibit a uniformly binding forward polarization.

The net electrostatic interaction of two spherical atoms, derived with neglect of antisymmetry, is always binding. Especially in the heavier first-row A₂ molecules, this classical Coulomb attraction provides more of the binding energy than either charge accrual on the bond axis, which is opposed by the exclusion principle, or contraction towards the nuclei, which is characteristic of hydrogen but hardly occurs in first-row atoms.     

Adjustment of Non-linear Interaction Parameters for Relativistic Mean Field Approach by Using Artificial Neural Networks

The relativistic mean field (RMF) model with a small number of adjusted parameters has been used successfully in the last thirty years for predictions of various ground-state nuclear properties of nuclei. In this model, Dirac and Klein–Gordon like equations obtained from application of variation principle on phenomenological Lagrangian density are solved iteratively for calculations of nuclear properties of nuclei. For this purpose, parameters such as masses of considered mesons, nucleon–meson coupling constants, and self-couplings of mesons are needed and they are fitted from experimental data. Some parameter sets for RMF model introduced to correct predictions of nuclear properties of nuclei cover nuclidic chart. Besides Artificial Neural Network (ANN) method is used successfully in many field of science as in nuclear physics. ANN is known as a very powerful tool that are used when standard techniques fail to estimate the correlation between the variables. In the present study, ANN method has been employed to check its understanding capability of relations between RMF model parameters and their predictions on the ground-state binding energies of some spherical nuclei. Understanding capability of ANN method for these relations of considered nuclei has been found well. Based on this success, new non-linear parameter set for RMF model called DEFNE by us have been produced by using ANN method. Furthermore, predictions of RMF model with DEFNE parameter set for ground-state binding energies and charge radii of nuclei cover nuclidic chart have been found as in agreement with the available experimental data.     

Critical analysis of quark-meson coupling models for nuclear matter and finite nuclei

Three versions of the quark-meson coupling (QMC) model are applied to describe properties of nuclear matter and finite nuclei. The models differ in the treatment of the bag constant and in terms of non-linear scalar self-interactions. In two versions of the model the bag constant is held fixed at its free-space value whereas in the third model it depends on the density of the nuclear environment. As a consequence opposite predictions for the medium modifications of the internal nucleon structure arise. After calibrating the model parameters at equilibrium nuclear matter density, binding energies, charge radii, single-particle spectra and density distributions of spherical nuclei are analyzed and compared with QHD calculations. For the models which predict a decreasing size of the nucleon in the nuclear environment, unrealistic features of the nuclear shapes arise.     

Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.