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。     

Structure of Light Nuclei on Neutron Drip Line

In order to extend the conventional shell model (SM) calculation with harmonic oscillator bases to light nuclei on neutron drip line, a self-similar-structure shell model (SSM) is proposed. We do this by a rescaling of both the kinetic and potential energy terms of the harmonic oscillator so that the single-particle orbit in SSM has its own state(orbit)-dependent frequency. Meanwhile, a new method to imitate the Woods-Saxon potential with harmonic oscillator potential is introduced. By the rescaling method and imitation procedure, all light exotic nuclei together with the light stable nuclei are studied in a unified way. The results are in good agreement with experimental data. Furthermore, the puzzle of the unexistence of ⁵He, ^{10Li and 13B is naturaUy explained in SSM.}     

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.     

Extended Glauber Theory and Its Application in Halo Nucleus Scattering

We introduced an extended Glauber theory for a halo nucleus scattering, where the halo nucleons and the nuclear core were treated separately. Expressions of reaction and interaction cross sections of the halo nucleus scattering were derived. We took the halo structure of the projectile nucleus into account and adopted an improved optical limit approximation. In the framework of the extended Glauber theory, we studied the reaction cross section for the halo nucleus ¹⁴Be scattering on a target ¹²C. For comparison, the reaction cross sections of ¹²Be+¹²C were calculated as well. The density distribution of target ¹²C is taken from experiments, and those of the projectiles ¹²Be and ¹⁴Be were obtained by two methods. One is that the harmonic oscillator wave functions for ¹²Be and ¹⁴Be are used. The length of harmonic oscillator is adjusted to reproduce the reaction cross section of ¹²Be+¹²C at the high energy E=790MeV/u . The density distribution of ¹⁴Be was also calculated self-consistently in the relativistic mean field (RMF) theory, with a long tail wave functions for the two neutrons in ¹⁴Be. It was found that the calculated reaction cross sections for ¹²Be+¹²C at E=790MeV/u and E=56.5MeV/u were in good agreement with the experimental data no matter harmonic oscillator or RMF wave functions were used. In contrast, the experiments of the reaction cross sections for ¹⁴Be+ ¹²C could only be reproduced when the wave functions of two 2s_1/2 neutrons spreaded over with a long tail. It comes to a conclusion that two outside neutrons in ¹⁴Be form a halo structure.     

Single Particle Schr dinger Fluid and Moments of Inertia of Deformed Nuclei

We have applied the theory of the single-particle Schrodinger fluid to the nuclear collective motion of axially deformed nuclei. A counter example of an arbitrary number of independent nucleons in the anisotropic harmonic oscillator potential at the equilibrium deformation has been also given. Moreover, the ground states of the doubly even nuclei in the s-d shell ²⁰Ne,²⁴Mg,²⁸Si,³²S and ³⁶Ar are constructed by filling the single particle states corresponding to the possible values of the number of quanta of excitations n_x,n_y, and n_z. Accordingly, the cranking-model, the rigid-body model and the equilibrium-model moments of inertia of these nuclei are calculated as functions of the oscillator parameters ω_x,ω_yand ω_z which are given in terms of the non deformed value ω00 , depending on the mass number A, the number of neutrons N, the number of protons Z, and the deformation parameter β. The calculated values of the cranking-model moments of inertia of these nuclei are in good agreement with the corresponding experimental values and show that the considered axially deformed nuclei may have oblate as well as prolate shapes and that the nucleus ²⁴Mg is the only one which is highly deformed. The rigid body model and the equilibrium model moments of inertia of the two nuclei ²⁰Ne and ²⁴Mg are also in good agreement with the corresponding experimental values.     

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.     

Neutron Halo Structure of 11Li

The neutron rich nucleus ¹¹Li is considered as a three-body system composed of ⁹Li core and two outside neutrons.The coreneutron and neutron-neutron interactions are chosen to be of the attractive exponential potentials.The Shrdinger equation is solved by diagonalizing the Hamiltonian with the aid of the harmonic oscillator formalism. The structure of this system and the interparticle correlation are investigated by inspecting the shape-density and the neutron halo structure is obtained.     

Relativistic corrections to Coulomb energy calculations

Coulomb energies of nuclei have been calculated using a recently introduced relativistic nuclear shell model¹). The results are very close to those of the usual non-relativistic, isotropic harmonic oscillator shell model, showing the most deviation for heavy elements such as lead.     

Theoretical investigation of the Gamow-Teller transition across N=40 shell

The Gamow-Teller transitions for pf shell nuclei with proton number less than 40 and neutron number larger than 40 were believed to be blocked, due to the full filling of the neutron orbit. However, recent experimental research shows that the Gamow-Teller transitions for these kinds of nuclei are not blocked. In this paper, we systematically calculate the GT transition of pf shell nuclei ⁷⁶Se in different truncations, and the results are compared with experimental results. It is shown that, due to correlations, the believed blocked GT transition occurs, and the shell model calculations reproduce the experimental GT strength. In addition, the electron capture rates in a stellar environment are calculated and discussed.     

The effect of Fermi momentum cutoff on the binding energy of closed shell nuclei in the LOCV framework

The ground state binding energies of the light symmetric closed-shell nuclei, i.e., ⁴He, ¹²C, ¹⁶O and ⁴⁰Ca and the heavy asymmetric ones, i.e., ⁴⁸Ca, ⁹⁰Zr and ¹²⁰Sn are calculated in the harmonic oscillator (HOS) basis, by imposing the relative Fermi momentum cutoff of two point-like interacting nucleons on the density dependent average effective interactions (DDAEI). The DDAEI are generated through the lowest order constrained variational (LOCV) method calculations for the asymmetric nuclear matter with the operator and the channel dependent type bare nucleon-nucleon potentials, such as the Argonne $Av_{18}^{j_{\max } = 2}$ and the Reid soft core, Reid68, interactions. In the framework of harmonic oscillator shell model, the cutoff is imposed by defining the maximum value of the relative quantum numbers (RQN_max) in two ways: (1) The RQN_max of the last shell and (2) the RQN_max of each shell, in the ground state of the nucleus. It is shown that present results on the binding energies and the root means square radius are closer to the corresponding experimental data than, our previous works with the same DDAEI potentials, but without the cutoff constraint. However, for the light symmetric nuclei, the second scheme gives less binding energy and larger root mean square radius compare to the first one. While the situation is reversed for the heavier nuclei.     

Further Studies on Halo Nuclei 11Li,14Be and 17B

Based on the three-body model with Yukawa interactions,the halo nuclei ¹¹Li,¹⁴Be and ¹⁷B are further studied by the variation calculation.An analytical expression for the density distribution of the halo neutron is given.The theoretical resultsagree with the recent experimental data.     

Oblique-basis shell-model calculations

A one-dimensional harmonic oscillator in a box is used to introduce the oblique-basis concept. The method is extended to the nuclear shell model by combining traditional spherical shell model states, which yield a diagonal representation of the usual single-particle interaction, with SU(3) shell model collective configurations that track deformation. An application to ²⁴Mg, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this mixed-mode shell-model scheme. The theory is also applied to lower pf-shell nuclei, ^44–48Ti and ⁴⁸Cr, using the Kuo-Brown-3 interaction. These nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2) values are insensitive to fragmentation of SU(3) symmetry. Specifically, the quadrupole collectivity as measured by B(E2) strengths remains high even though the SU(3) symmetry is rather badly broken. The results suggest that an oblique-basis mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics.     

Exotic Behavior of Elastic Scattering Differential Cross-Sections of Weakly Bound Nucleus 17F at Small Angles

The differential cross-sections for elastic scattering of ¹⁷F and ¹⁷O on ²⁰⁸Pb have been measured at Radioactive Ion Beam Line at Lanzhou (RIBLL). The variation of the logarithms of differential cross-sections with the square of scattering angles shows clearly that there exists a turning point in the range of small scattering angles (6°—20°) for ¹⁷F having exotic structure, while no turning point was observed in the ¹⁷O elastic scattering. The experimental results have been compared with previous data. Systematical analysis on the available data seems to conclude that there is an exotic behavior of elastic scattering differential cross-sections of weakly bound nuclei with halo or skin structure as compared with that of the ordinary nuclei near stable line. Therefore the fact that the turning point of the logarithms of differential cross-sections appears at small angle for weakly bound nuclei could be used as a new probe to investigate the halo and skin phenomenon.     

Overlaps of deformed and non-deformed harmonic oscillator basis states

A systematic approach for expanding non-deformed harmonic oscillator basis states in terms of deformed ones, and vice versa, is presented. The objective is to provide analytical results for calculating these overlaps (transformation brackets) between deformed and non-deformed basis states in spherical, cylindrical, and Cartesian coordinates. These overlaps can be used for reducing the complexity of different research problems that employ three-dimensional harmonic oscillator basis states, for example as used in coherent state theory and the nuclear shell-model, especially within the context of ab initio symmetry-adapted no-core shell model.     

Two-dimensional friction oscillator: group-preserving scheme and handy formulae

With vibration isolation of buildings and turbomachinery blades in mind, we study the dynamic behaviour of a single-mass two-degree-of-freedom oscillator with dry friction damper, viscous damper and elastic spring connected in parallel. The mass is mounted on an elastic supporting plate allowing movement in two directions on a plane. We formulate a multi-dimensional friction model, from which the sliding conditions and the sticking conditions of the mass are derived. For calculations we develop a group-preserving scheme, which preserves the projective proper orthochronous Lorentz group PSO_o(2,1) symmetry of the model in the sliding phase so as to satisfy automatically the sliding conditions at each time step without iteration at all. The oscillator is then subjected to simple harmonic excitations, and the responses are displayed. According to the simple harmonic balance method together with a circular orbit assumption on displacements, we derive closed-form formulae for handily estimating the steady state responses, which are then compared with the results calculated by the group-preserving scheme to confirm the applicability of the formulae. We also derive formulae specifically for a two-dimensional friction oscillator with rigid base support, which include an exact formula of the magnification factor and a simple formula for estimating the minimum driving force amplitude (or the maximum friction force bound) to avoid sticking.     

Angular Momentum Projected Deformed HF Spectra of 46Ti and 48Cr With MSDI

Taking the modified surface delta interaction (MSDI) and using a spherical shell model basis set, we carry out the deformed Hartree-Fock (HF) calculation for the even-even nuclei ⁴⁶Ti and ⁴⁸Cr in the fp shell, and construct the deformed HF intrinsic states which are the Slater determinants from the HF single-particle states.The angular momentum projection program is then carried out and the reasonable results are obtained.     

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.