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.     

Self-consistent calculations for highly excited compound nuclei

A method for self-consistently calculating average nuclear properties at high excitation energies is derived. Calculations using this formalism have been performed for a double-magic and a deformed nucleus employing the Skyrme force for the nucleon-nucleon interaction. The effects of excitation energy on the nuclear structure are discussed and a comparison of self-consistently calculated level densities with those obtained in the usual statistical method is made. The calculations for the deformed nucleus show the transition from the deformed to a spherical shape with increasing excitation.     

Hartree-Fock and shell model calculations for giant nuclei

The properties of giant nuclear systems like Uranium/Uranium etc. (A?476) have been studied in statical, spherical Hartree-Fock approximation. Various effective forces of Skyrme type were used to calculate binding energies, density distributions and single particle spectra. A shell model of Woods-Saxon type is shown to be more or less equivalent with respect to the shell structure derived from Skyrme models and easy generizable to slightly deformed giant nuclei. Strong magic shells could be found even in this region of the periodic table, but it seems that they cannot contribute significantly to a stabilization of these systems. The total binding energy is in good agreement with liquid drop model extrapolations. Only very briefly we discuss possibilities and problems for calculating deformation energies.     

Behavior of shell effects with the excitation energy in atomic nuclei

We study the behavior of shell effects, like pairing correlations and shape deformations, with the excitation energy in atomic nuclei. The analysis is carried out with the finite temperature Hartree-Fock-Bogoliubov method and a finite range density dependent force. For the first time, properties associated with the octupole and hexadecupole deformation and with the superdeformation as a function of the excitation energy are studied. Calculations for the well quadrupole deformed 164Er and 162Dy, superdeformed 152Dy, octupole deformed 224Ra, and spherical 118Sn nuclei are shown. We find, in particular, the level density of superdeformed states to be 4 orders of magnitude smaller than for normal deformed ones.     

Excited states of deformable even-even atomic nuclei

A method of calculating the collective excited states of even-even atomic nuclei is proposed. A formula depending on three parameters appropriate for calculating the energy ratios of the excited states of deformed and spherical nuclei as well as those in the intermediate region is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 19–24, November, 1972.     

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.     

Transition from spherical to deformed shapes of nuclei in the Monte Carlo shell model

The transition from spherical to deformed shapes is studied in terms of large-scale shell-model calculations for Ba isotopes as a function of valence nucleon number with fixed single-particle space and Hamiltonian. A new version of the Monte Carlo shell model is introduced so as to incorporate pairing correlations efficiently, by utilizing condensed pair bases. The energy levels and electromagnetic matrix elements are described in agreement with experiments throughout the transitional region. The orbital M1 sum rule is calculated as a measure of the deformation evolution, and the Q-phonon picture is shown to be reasonable from spherical to deformed nuclei.     

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.     

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.     

A modified shell model for atomic nuclei

The shell model of spherical nuclei is updated by an approximate count of nucleon-nucleon correlations. A coordinated scheme for calculating the binding energy and nuclear radius is proposed. Good agreement with the experimental data on the binding energies of spherical even-even nuclei is attained.     

Potential energy surfaces in the two-center shell model

The two-center shell model of two equal overlapping spheroids is combined with Lawrence's liquid-drop shapes. Within this framework, potential energy surfaces for nuclei from different mass regions are calculated. In particular, the transition of the ground state deformation from spherical to deformed is investigated for a sequence of ruthenium isotopes.     

Renormalization for collective motion within a truncated space of the spherical shell model. I. Intrinsic frame in a schematic model

Using schematic Hamiltonians in the ²⁰Ne example, the series of perturbation terms for effective interactions and operators in a truncated space of a spherical shell model is found that, when summed, yields the results for intrinsic moments and energy of the unrestricted deformed Hartree-Fock state. Black-box and random phase approximation diagrams are shown to be important as is another (little used and to be called IBG) diagram and the ladder diagrams. A black-dot vertex renormalization is introduced corresponding to consistent renormalization of every transformation within the model space. The black-dot corresponds exactly to the self consistency of deformed Hartree-Fock.     

A Note on the Pair Excitation Across Major Shell in Deformed Nuclei

Valence nucleons usually play a dominant role in low energy nuclear spectra. The original version of the Interacting Boson Model[1](IBM) with the assumption that all degrees of freedom arise from the valence shell reproduces well large amount of experimental data. However this assumption does not work well in some cases, for instance, in the even isotopes of Sn, Cd, and Hg, Pb rather well developed intruder bands121 lie outside the IBA model space. K. Heyde et al. attributed these low lying intruder states to the pair excitation (PE) across major shell131. In the well deformed nuclei one can hardly think of the closed shell core as being spherical and inert. The rapid change of Nilsson levels with deformation seems to indicate that there should be excitations of nucleons across major shells in the well deformed nuclei.     

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000     

Superheavy nuclei in self-consistent models

The shell structure of superheavy nuclei is investigated within various parametrizations of relativistic and nonrelativistic nuclear mean-field models. The heaviest known even-even nuclei are used as a benchmark to estimate the predictive value of the models. From that starting point, spherical and deformed shell closures in the superheavy region are searched.     

水中分层弹性球壳高频时域回波的声学编码研究

针对水下集群目标及敌我目标识别的难题,该文提出了一种基于水中分层弹性球壳高频时域回波的声学编码原理及方法。推导了水中4层弹性球壳目标散射声压的简正级数解,并与有限元结果进行了对比验证。通过构造高频主动声呐的探测脉冲信号,与4层弹性球壳声传递函数的简正级数解做卷积运算,获得了目标的时域回波脉冲序列。研究了分层弹性球壳的厚度、各层材料属性、排布顺序等对时域回波特征的影响规律,提出了基于时域回波特征的声学编码方法。研究表明：利用水中分层弹性球壳目标高频时域回波特征能够实现声学编码,回波结构稳定,且不受限于探测方向。通过携带或安装这种分层弹性球壳结构,有望识别水下航行体/悬浮体等目标。该文的研究对水下目标的主动探测身份识别及导航等具有一定的参考价值。     

快速C60离子团在固体中的库仑爆炸过程Ⅰ球壳层模型

研究了快速C60 离子团在固体中穿行时的库仑爆炸过程 .假定离子团中离子之间位置矢量的取向是随机的 ,并且采用球壳模型描述C60 离子团的结构 .借助于线性介电响应理论和等离子 极点近似介电函数 ,推导出C60 离子团自能的解析表达式 .通过数值求解描述离子团半径变化的运动方程 ,可以发现自能中的“尾效应”可以降低C60 离子团的库仑爆炸速度 ,甚至可以稳定C60 离子团的结构     

Quasiclassical description of electronic supershells in simple metal clusters

A quasiclassical method for calculating shell effects, which has been used previously in atomic and plasma physics, is used to describe electronic supershells in metal clusters. An analytical expression is obtained, in the spherical jellium model, for the oscillating part of the binding energy of electrons of a cluster as a sum of contributions from supershells with quantum numbers 2n _r +l, 3n _r +l, 4n _r +l,... This expression is written in terms of the classical characteristics of the motion of an electron with the Fermi energy in a self-consistent potential. The conditions under which a new supershell appears and the relative contribution of this shell are investigated as a function of the cluster size and form of the potential. Specific calculations are performed for a “square well” of finite depth. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 333–337 (10 September 1999)     

采用MSDI严格角动量投影46Ti、48Cr形变HF谱

采用修正的表面δ相互作用(MSDI),以球形壳模型单粒子态作基矢,对fp壳层区偶偶核⁴⁶Ti、⁴⁸Cr进行形变Hartree–Fock(HF)计算,并用形变HF单粒子态构造Slater行列式波函数,即形变HF内禀态,然后对其实施严格角动量投影程序,得到比较合理的结果.