Shell structure for deformed nuclear shapes

Eigenvalues for the harmonic oscillator without l·s or l² terms suggest a deformed shell structure for nuclei with axes ratios 2 : 1 and deformation ? = 0.6 with corresponding nucleon “magic numbers” 2, 4, 10, 16, 28, 40, 60, 80 110 and 140, subject to small modifications due to spin-orbit and other correction terms. Experimental evidence of reasonably stable highly deformed structures corresponding to nucleon numbers 16, 20, 28, 40 and 60 (64) is presented. Attempts to calculate the corresponding potential energy surfaces using the Strutinsky shell correction method are described.     

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).     

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.}     

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。     

Application of the Strutinsky method to the rotational motion of 20Ne

The cranking model rotational behavior of ²⁰Ne obtained from the Strutinsky method is compared with that obtained from the analytical solution for the cranked deformed harmonic oscillator potential. It is found that the agreement is excellent except in the vicinity of the gs-band cut-off where the Strutinsky results are somewhat sensitive to the behavior of the liquid drop under rotation. The selfconsistency condition on the shapes of the equipotentials and the nuclear matter distribution is also found to have little influence except in the cut-off region.     

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.     

Shell energy in the heaviest nuclei using the Green’s function oscillator expansion method

The Greens function oscillator expansion method and the generalized Strutinsky smoothing procedure are applied to shell corrections in the heaviest elements. A macroscopic-microscopic method with a finite deformed Woods-Saxon potential is used. The stability condition for the shell correction is discussed in detail and the parameters defining the smoothing procedure are carefully determined. It is demonstrated that the spurious contribution to the total binding energy due to the unphysical particle gas that appears in the standard method can be as large as 1.5 MeV for weakly bound neutron-rich superheavy nuclei, but the effect on energy differences (e.g., alpha-decay values) is fairly small.     

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.     

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.     

Inclusion of temperature dependent shell corrections in Landau theory for hot rotating nuclei

Landau theory used for studying hot rotating nuclei usually uses zero temperature Strutinsky smoothed total energy for the temperature dependent shell corrections. This is replaced in this work by the temperature dependent Strutinsky smoothed free energy. Our results show that this replacement has only marginal effect for temperatures greater than 1 MeV but plays significant role at lower temperatures.     

High-performance algorithm for calculating non-spurious spin- and parity-dependent nuclear level densities

A new high-performance algorithm for calculating the spin- and parity-dependent shell model nuclear level densities using methods of statistical spectroscopy in the proton-neutron formalism was recently proposed. When used in valence spaces that cover more than one major harmonic oscillator shell, this algorithm mixes the genuine intrinsic states with spurious center-of-mass excitations. In this Letter we present an advanced algorithm, based on the recently proposed statistical moments method, that eliminates the spurious states. Results for unnatural parity states of several sd-shell nuclei are presented and compared with those of exact shell model calculations and experimental data.     

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.     

Fission Barrier for ^240Pu in the Quadrupole Constrained Relativistic Mean Field Approach

The fission barrier for ^240pu is investigated beyond the second saddle point in the potentiM energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essentiM to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.     

THE TWO-BODY SPIN-ORBIT COUPLING INTERACTION AND THE ENERGY SPECTRA OF f7/2 SHELL NUCLEI

In this paper we use the central and two-body spin-orbit coupling forces as theresidual interaction to calculate the energy spectra of f_7/2 shell nuclei,with the valuesof the exchanged parameters suitably regulated.The harmonic oscillator wave functionis employed as the radial wave function.The consistency between the calculated energylevels of the nuclei and the experimental data is rather satisfactory.The results showthat the effects of two-body spin-orbit coupling term in the residual interaction cannot be neglected.     

Shell corrections to the deformation energies of very high spin nuclei (I ≲ 100)

Deformation energies at spins I ? 100 of 16 rare earth nuclei have been calculated including shell corrections obtained by a straightforward generalization of the Strutinsky method. Largely deformed shapes are predicted for some high rotational states.     

Interaction potential between two 16O nuclei derived from the Skyrme interaction

The energy functional for the Skyrme density-dependent force is used to calculate the interaction potential between two ¹⁶O nuclei. A two-centre harmonic oscillator potential is employed to construct the density and kinetic energy density of the ground state of the combined system and of the separated nuclei. The antisymmetrization effects are investigated. The relative motion of the nuclei is taken approximately into account and the energy dependence of the potential derived from the Skyrme force is presented.     

Investigations on finite ideal quantum gases

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose–Einstein condensation are discussed.     

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.