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Attractive fixed-point solution study of shell model for homogeneous isotropic turbulence

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Applied Mathematics and Mechanics(English Edition) 2013年第3期34卷 259-268页

作者：郭昊李超屈秋林刘沛清 Institute of Fluid Mechanics Beihang University Key Laboratory of Fluid Mechanics Under the Ministry of Education Beihang University

The attractive fixed-point solution of a nonlinear cascade model is stud- ied for the homogeneous isotropic turbulence containing a parameter C, introduced by Desnyansky and Novikov. With a traditional constant positive external force added on the first shell equation, it can be found that the attractive fixed-point solution of the model depends on both the parameter C and the external force. Thus, an explicit force is introduced to remove the effects of the external force on the attractive fixed-point solu- tion. F^arthermore, two groups of attractive fixed-point solutions are derived theoretically and studied numerically. One of the groups has the same scaling behavior of the velocity in the whole inertial range and agrees well with those observed by Bell and Nelkin for the nonnegative parameters. The other is found to have different scaling behaviors of the velocity at the odd and even number shells for the negative parameters. This special characteristic may be used to study the anomalous scaling behavior of the turbulence.

关键词： turbulence shell model attractive fixed-point scaling

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

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Communications in Theoretical Physics 2022年第9期74卷 284-298页

作者： Nicolas Michel Jianguo Li Furong Xu CAS Key Laboratory of High Precision Nuclear Spectroscopy Institute of Modern PhysicsChinese Academy of SciencesLanzhou 730000China School of Nuclear Science and Technology University of Chinese Academy of SciencesBeijingChina School of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijing 100871China

Ab initio approaches are among the most advanced models to solve the nuclear many-body *** 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,*** Berggren *** continuum coupling is included at basis level and as configuration mixing takes care of internucleon correlations,halo and resonance nuclei can be properly described with the Gamow shell *** development of the no-core Gamow shell model and the introduction of the■-box method in the Gamow shell model,as well as their first ab initio applications,will be reviewed in this *** compared to models using harmonic oscillator bases will be shortly *** current power and limitations of ab initio Gamow shell model will also be discussed,as well as its potential for future applications.

关键词： binding energy lifetimes nucleon-nucleon interactions shell model continuum coupling

SD-pair structure in the pair approximation of the nuclear shell model

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Science China(Physics,Mechanics & Astronomy) 2010年第8期53卷 1460-1465页

作者： LEI Yang XU ZhengYu ZHAO YuMin LU DaHai Department of Physics Shanghai Jiao Tong UniversityShanghai 200240China Center of Theoretical Nuclear Physics National Laboratory of Heavy Ion AcceleratorLanzhou 730000China CCAST World LaboratoryBeijing 100080China School of Physics Peking UniversityBeijing 100871China

In this paper we study the structure coeficients of collective pairs with spin zero and spin two (SD) in a number of configurations by a few realistic nuclei. We investigate the robustness of these structure coeffcients with respect to different configurations and the evolution of SD-pair structure coeffcients with valence nucleon number.

关键词： nuclear structure collective levels nuclear structure models and methods shell model

Many-body correlations in shell model effective interactions derived by ab initio methods and the V_(low-k) approach

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Chinese Physics C 2018年第11期42卷 78-84页

作者：王小保董国香王华磊袁岑溪陈永静图雅 School of Science Huzhou University School of Physics and Engineering Zhengzhou University Sino-French Institute of Nuclear Engineering and Technology Sun Yat-Sen University Key Laboratory of Science and Technology on Nuclear Data China Institute of Atomic Energy School of Physics Science and Technology Shenyang Normal University

We investigate many-body correlations caused by two- and three-body （2-, 3bd） forces. shell-model effective interactions derived from ab initio methods （coupled-cluster method, no-core shell model） are adopted. Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence. We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.

关键词： shell model effective interactions tensor force three-body force

The nuclear shell model： Simplicity from complexity

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Frontiers of physics 2018年第6期13卷 11-27页

作者： Igal Talmi Department of Particle Physics and Astrophysics The Weizmann Institute of Science Rehovot 76100 Israel

The shell model of atomic nuclei has been in intensive use since the middle of the previous century. This simple model of very complex nuclei, offers a quantitative description of its many features. Other features follow from small deviations from the extreme picture. Our friend and colleague Akito Arima made seminal contributions to this field starting with his famous paper with Horie on the magnetic moments of nuclei [Prog. Theor. Phys. 11, 509 （1954）]. In the following, a detailed description of a simple example is considered. It is the 1f7/2 shell of the neutrons in the nuclei between 40Ca and 4sca and of the protons in the nuclei between 4SCa and 56Ni. The results demonstrate the power and elegance of the shell model. They show how simplicity arises out of complexity. It is also shown how small deviations from the simple shell model lead to effects, in which valence neutrons act as if they carry electric charge.

关键词： shell model effective interactions seniority binding energies effective charges nuclear radii

Prediction of Radioactive Half-Lives and Atomic Nucleus Dimensions in a Concentric shell model or Flocon model

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Journal of Modern Physics 2022年第8期13卷 1216-1251页

作者： Marc Mignonat Société d’Astronomie des Pyrénées Occidentales Pau France

Considering only the wave aspect, we determine the energy of a bond between 2 nucleons;this quantified energy is associated with a standing wave. Then, starting from the mass loss corresponding to this energy, we determine the number of bonds in this nucleus. The mass defect value for a link is used to determine a specific length at that link. Fixing a precise distance between nucleons makes it possible to determine a geometry of the nucleus and its dimensions. It makes it possible to understand when this bond is stronger than the electrostatic force and allows deducing a shell model built in a precise order. The calculation on the mass defect will also make it possible to determine that one or more nucleons concerned by the radioactivity will be bound by a single bond to the rest of the nucleus or, on the contrary, bound by several bonds which induce short 1/2 lives or, on the contrary, very long. The analysis of the bonds on H, He and C make it possible to write formulae which are then applied to the nuclei to find the radioactive 1/2 lives. To find by equations the radioactive 1/2 lives does not call into question the standard model since it concerns only the defect of mass of the nuclei with energies that are not used to find the main particles of the standard model. This model, which favours a geometric approach to the detriment of a mathematical approach based on differential equations, can lead to theoretical questions about the possibility of interpreting the structure of the nucleus in a more undulatory way. It is possible to explain radioactivity in a more deterministic way.

关键词： ½ Radioactive Lives Atomic Nucleus Dimensions shell model

shell-model study on properties of proton dripline nuclides with Z,N=30-50 including uncertainty analysis

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Chinese Physics C 2022年第8期46卷 196-210页

作者：蔡博帅陈广尚袁岑溪何建军 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-Sen UniversityZhuhai 519082China Key Laboratory of Beam Technology and Materials Modification of Ministry of Education College of Nuclear Science and TechnologyBeijing Normal UniversityBeijing 100875China Beijing Radiation Center Beijing 100875China

The binding and proton separation energies of nuclides with Z,N=30-50 are investigated based on the shell model,with an uncertainty analysis via statistical *** formulas are used to obtain the binding and proton separation energies according to shell-model *** non-parametric bootstrap method is applied to establish an uncertainty decomposition and recomposition ***,this is used to estimate the stability of proton(s) emission for each *** formulas for calculating the binding energies with a systematic uncertainty of~0.3 Me V are proposed,and a reliable extrapolation ability is *** binding energy formulas deduce similar forms for their respective S_(p) and S_(2 p) energies,which predict the extension of the nuclear boundary of this region.A good description of the binding and proton separation energies is *** one-and twoproton separation energies and partial half-lives of proton emission are predicted,thus revealing a new ***,there are 30 unstable nuclides predicted to be bound against proton(s)-*** nuclear properties will be useful in nuclear astrophysics.

关键词： shell model proton dripline uncertainty analysis

Anomalous scaling in a non-Gaussian random shell model for passive scalars

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Chinese Physics B 2007年第10期16卷 2848-2854页

作者：赵英奎陈式刚王光瑞 Graduate School of China Academy of Engineering Physics Beijing 100088 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

In this paper, we have introduced a shell-model of Kraichnan＇s passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and σ correlated in time, and its introduction is inspired by She and Levveque （Phys. Rev. Lett. 72, 336 （1994））. For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H（p） of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H（p） advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.

关键词： scaling shell model She and Leveque (SL) model non-Gaussian passive scalar

SD-PAIR shell model FOR EVEN-EVEN SYSTEMS

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SD-PAIR SHELL MODEL FOR EVEN-EVEN SYSTEMS