自相似结构壳模型

为了扩展以简谐振子为基矢的常规壳模型（ＳＭ）计算到晕核，提出了自相似结构壳模型（ＳＳＭ）．通过对简谐振子动能项和势能项的重度规以及单粒子平均场模拟，可以得到ＳＳＭ中的单粒子轨道有态相关的圆频率，在ＳＳＭ中，晕核大的均方根半径、厚的中子皮以及Ｂｏｒｒｏｍｅａｎ晕核和的束缚态性质能够再现出来。     

Self-Similar Strcture Shell Model

In Order to extend the conventional shell model(SM) calculation with harmonic oscillator bases to halo nuclei, a self-similar, structure shell model(SSM) is proposed. The SSM is achieved by a rescaling of both the Kinetic and potential energy term of the harmonic oscillator and a mean field imitation, so that the single particle orbit in SSM has state (orbit) -dependent frequency. The large r. m. s. radius and the thick neutron skin for halo nuclei as well as the bound state properties of Borromean nuclei such as ⁶He, ¹¹Li and ¹⁴Be can be reproduced.     

Ground state properties of halo nuclei

By a rescaling both the kinetic and potential energy terms of the harmonic oscillator in conventional shell model(SM) and a mean field imitating, a self-similar-structure shell model(SSM) in which the single-particle orbits have state- or orbit-dependent frequencies was proposed to extend the SM calculations to light nuclei near the neutron drip line.     

Ground state properties of halo nuclei

By a rescaling both the kinetic and potential energy terms of the harmonic oscillator in conventional shell model(SM) and a mean field imitating, a self-similar-structure shell model(SSM) in which the single-particle orbits have state- or orbit-dependent frequencies was proposed to extend the SM calculations to light nuclei near the neutron drip line.     

Ground state properties of halo nuclei

By a rescaling both the kinetic and potential energy terms of the harmonic oscillator in conventional shell model(SM) and a mean field imitating, a self-similar-structure shell model(SSM) in which the single-particle orbits have state- or orbit-dependent frequencies was proposed to extend the SM calculations to light nuclei near the neutron drip line.     

Velocity-dependent potentials in the shell model of O and F

The low-lying energy levels of ¹⁸O and ¹⁸F are calculated in the harmonic oscillator shell model taking Green's velocity-dependent N-N potential as the residual interaction. It is found that the shell-model matrix elements agree substantially with those calculated by Kuo and Brown from the unrenormalized Hamada-Johnston hard-core N-N potential. It is found furthermore that Green's parameters give rather unsatisfactory agreement with the experimental spectra. It is shown that somewhat improved agreements with experiment are possible by making appropriate parameter adjustments.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of a-decay is extended to the regions around doubly magic spherical nucleus ^208Pb and around deformed shell closure ^270Hs, respectively. The effects of spherical shell closures (N=126 and Z=82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical a-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus ^208Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of α-decays from the ground state of a parent nucleus to the ground state (0^ ) of its deformed daughter nucleus and to the first excited state (2^ ) are calculated in the framework of the cluster model. The results indicate that a measurement of α spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus ^270Hs.     

The Gamow shell model with realistic interactions: a theoretical framework for ab initio nuclear structure at drip-lines

Ab initio approaches are among the most advanced models to solve the nuclear many-body problem. In particular, the no-core–shell model and many-body perturbation theory have been recently extended to the Gamow shell model framework, where the harmonic oscillator basis is replaced by a basis bearing bound, resonance and scattering states, i.e. the Berggren basis. As continuum coupling is included at basis level and as configuration mixing takes care of inter-nucleon correlations, halo and resonance nuclei can be properly described with the Gamow shell model. The development of the no-core Gamow shell model and the introduction of the $\hat{\bar{Q}}$-box method in the Gamow shell model, as well as their first ab initio applications, will be reviewed in this paper. Peculiarities compared to models using harmonic oscillator bases will be shortly described. The current power and limitations of ab initio Gamow shell model will also be discussed, as well as its potential for future applications.     

手征胶子修正夸克平均场模型

这项工作利用考虑π介子与胶子效应的夸克平均场模型研究原子核结构的基本性质。在夸克平均场中,核子由三个束缚在谐振子势场中的组分夸克构成。描述强相互作用的量子色动力学必须满足手征对称性,此外夸克之间也需要通过交换胶子相互作用。因此,在夸克平均场模型中,对利用夸克势获得的核子质量考虑π介子修正与胶子修正。通过少数稳定有限核的结合能与半径实验值确定模型中的未知参数,获得了一组夸克平均场相互作用参数,QMF-NK。利用该组参数计算40Ca和208Pb的电荷密度分布,发现与实验值符合很好。随后获得了与经验值一致的对称核物质的饱和性质。包含π介子修正和胶子修正的夸克平均场模型能够更好地描述有限核和核物质的性质。The basic properties of nuclear structure are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account. In QMF, the nucleon is made up of three constituent quarks confined by a harmonic oscillator potential. The quantum chromodynamics describing the strong interaction must satisfy the chiral symmetry and quarks interact with each other through exchange of gluons. Therefore pion correction and gluon correction are included in the nucleon mass obtained by using quark confinement potential in quark mean field model. We determine the unknown parameters in the model by fitting the experimental data of the binding energies and radii of several stable finite nuclei and obtain a set of parameters of quark mean field interaction, named QMF-NK. The charge density distributions of 40Ca and 208Pb are calculated, which are in good agreement with the experimental data. Later the saturation properties of symmetric nuclear matter which are consistent with the empirical data are obtained. With the pion and gluon corrections, the QMF model could treat finite nuclei and nuclear matter better.     

A three-center shell model for ternary fission

We propose a generalization of the phenomenological shell model based on the harmonic oscillator potential with spin-orbit term andl ²-corrections to systems made up of three clusters. The centers of these may be in arbitrary geometrical configurations and the clusters may be of different masses. The method of determining the eigenstates of the single-particle Hamiltonian is sketched and results for the cluster structure of light nuclei and the ternary fission of a superheavy system are presented.     

Shell structure in nuclei

A review of shell structure for spherical and a variety of deformed nuclei is presented. The microscopic-macroscopic method of Strutinsky is used to calculate potential energy surfaces with the pure harmonic oscillator and the modified harmonic oscillator. New sets of “magic numbers” for a variety of different prolate, oblate and axially asymmetric shapes are generated. Experimental evidence for the special stability caused by these shell effects is presented with special emphasis on the lightest and heaviest nuclei where the effects are most pronounced. The radial diffuseness parameter is treated as a Strutinsky variable and its significance in extrapolating into the superheavy region considered. The calculation of shell effects for high spin states is also reviewed.     

Fusion Barrier of Super-heavy Elements in a Generalized Liquid Drop Model

The macroscopic deformed potential energies for super-heavy elements Z = 110,112,114,116,118 arc determined within a generalized liquid drop model (GLDM). A quasi-molecular mechanism is introduced to describe the deformation of a nucleus in the GLDM and the shell model simultaneously. The macroscopic energy of a twocenter nuclear system in the GLDM includes the volume-, surface-, and Coulomb-energies, the proximity effect at each mass asymmetry, and accurate nuclear radius. The shell correction is calculated by the Strutinsky method and the microscopic single particle energies are derived from a shell model in an axially deformed Woods-Saxon potential with the quasi-molecular shape. The total potential energy of a nucleus can be calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is applied to predict the fusion barriers of the cold reactions ^64Ni ^208 spb → ^272 110*, ^70Zn ^208pb → ^278 112*, ^76Ge ^208seb → ^284 114*,^82Se ^208pb → ^29 116*, ^86Kr ^208pb → ^294 118*. It is found that the neck in the quasi-molecular shape is responsible for the deep valley of the fusion barrier. In the cold fusion path, double-hump fusion barriers could be predicted by the shell corrections and complete fusion events may occur.     

Shell structure and orbit bifurcations in finite fermion systems

We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the “periodic orbit theory”. We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called “superdeformed” energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).     

Isobar doorway approach to pion scattering on open shell nuclei

Delta-hole approach developed for the pion scattering on closed shell nuclei is extended to be applied to the case of open shell nuclei. The doorway space is spanned by the states of the form |Ψ^(A−1)ψ^(Δ) which correspond to |Δ h states in the usual delta-hole approach for closed shell nuclei. In this approach, the effects of the couplings between elastic and inelastic channels are incorporated in a natural way. As a first application of this approach, some numerical calculations have been done for the elastic and inelastic pion scattering on ¹²C and the elastic scattering on ¹⁴N and ¹⁴C. The effects of the nuclear structure and the coupling between elastic and inelastic channels are discussed.     

Spectra of Halo Nuclei

Based on the self-similar-structure shell model a size resonance model, which includes the size resonance of halo neutron orbit and the correlation size resonance of core surface, is proposed. In terms of the size resonance model the excited spectra and the soft dipole resonances for ¹¹Be and ¹¹li are reproduced.     

A rotational model description of F

Rotational-particle coupling (RPC) model calculations have been performed for the positive parity states of ¹⁹F using a deformed oscillator potential (Nilsson) and a deformed Woods-Saxon potential. The energy spectra and spectroscopic factors (for the ¹⁸O(³He, d)¹⁹F reaction) are very similar for both calculations and in good agreement with experimental values and with recent full intermediate coupling shell-model calculations.