Nilsson mean-field plus the extended pairing model description of rare earth nuclei

The Nilsson mean-field plus the extended pairing model for well-deformed nuclei is applied to some representative rare earth examples. The binding energies, some low-lying pair-excited states and even-odd mass differences of Er, Yb and Hf isotopes are calculated systematically within the proton frozen-pair excitation limit. A comparison with experimental data for these nuclei shows that the results of the extended pairing model are better than those for the standard pairing model with the BCS approximation and the nearest-orbit pairing model.     

超重核的基态性质

用Skyrme Hartree Fock+BCS方法计算了超重核的基态性质,讨论了结合能、α衰变、形变、壳结构和自发裂变等问题.计算得到的结合能较好地反映了实验测量值,α衰变能与实验值符合很好.发现基本上有两种类型的超重核形变:在270108核附近的β2≈0.2的长椭球形变和在298114核附近的近球形形变.单粒子能级分布计算表明:在质子Z=108和中子N=162存在变形壳,在质子Z=114和中子N=184存在球形壳.用得到的α衰变能和Viola Seaborg公式估算了α衰变半寿命,能合理地符合实验测量值. The ground state properties of superheavy nuclei are investigated using the Skyrme Hartree Fock model. The pairing correlation is treated by the BCS method with the pairing δ force. Binding energies, α decays, spontaneous fissions, shell structures and deformations are discussed. Our calculations reproduce experimential binding energies and α decay energies.It is found that superheavy nuclei can be grouped with two kinds of deformations: i) well deformed prolate shapes (β2≈0.2) around 270108...     

平均场加邻近轨道相互作用对力模型在大形变核中的应用

利用严格可解的平均场加邻近轨道相互作用对力模型来描述大形变核.将该模型应用于稀土区和超铀区的核素.计算了^158—171Er,^160—178Yb,^170—183Hf,^226—234Th, ^230—240U,及^236—243Pu同位素的结合能和对激发能,并与实验结果进行了比较     

基于壳模型对力加四极力研究sd和pf壳偶偶原子核

本文在原子核壳模型框架下基于唯象相互作用(对力加四极力)研究sd壳和pf壳的偶偶核低激发集体态。在提取了USDB和GXPF1相互作用的单粒子能量和单极相互作用的基础上,我们用一套统一参数计算重现了球形核和形变核的低激发谱;将对相互作用中的单极成分扣除后可以得到较好的结合能计算结果。同位旋标量的对相互作用对计算结果影响不大。单极相互作用在经验质子—中子相互作用、原子核对称能和Wigner能中产生重要贡献。     

Exact treatment of pairing correlations in Yb isotopes with covariant density functional theory

The effects of pairing correlation in Yb isotopes are investigated by covariant density functional theory with pairing correlations and blocking effects treated exactly by a shell model like approach(SLAP). Experimental one- and two-neutron separation energies are reproduced quite well. The traditional BCS calculations always give larger pairing energies than those given by SLAP calculations, particularly for the nuclei near the proton and neutron drip lines. This may be caused because many of the single particle orbits above the Fermi surface are involved in the BCS calculations, but many of them are excluded in the SLAP calculations.     

Pairing and quarteting correlations in nuclei

The Gorkov approach to the pairing problem has been generalized in order to take into account pairing and quarteting correlations with a model Hamiltonian including a charge independent pairing interaction and a n-p isopairing term. The single quasi-particle and quasi-hole energies calculated for all the doubly even nuclei of the $\text{7}\text{2}$^? shell show the importance of quarteting correlations in nuclei.     

Er，Yb和Hf同位素的基态占有率（英文）

应用严格求解的Nilsson 平均场加推广对力模型,在同时考虑质子-质子和中子-中子间对力相互作用的情况下,对稀土区的152-164Er,154-166Yb 和156-168Hf 核素的结合能、奇偶能差、低激发态转动惯量等基态性质进行系统的统一描述。通过计算结果与实验数值比较分析显示,对力相互作用在阐明以上核素能谱的基态性质中起到了关键的作用。应用拟合上述物理量所确定的模型参数,对156-162Yb 核素基态中价核子配成角动量J = 0,1,… ,12的价核子对占有率的计算结果显示,配成角动量为偶数价核子对的占有率远远高于配成角动量为奇数价核子对的占有率,其数值结果揭示了配成角动量为S,D和G的价核子对在所考虑的核素基态性质中占主导地位。The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, moments of inertia for the ground-state band of 152-164Er, 154-166Yb, and 156-168Hf are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. In comparison with the corresponding experimental data, it is shown that for these rare-earth nuclei, pairing interaction is crucial in elucidating the properties of the ground state. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum J =0,1, …,12 for even-even 156-162Yb are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that S, D, and G valence nucleon pairs dominate in the ground state of these nuclei.     

Skyrme-hartree-fock approach to spherical nuclei with density-dependent pairing correlations

The ground-state properties of spherical nuclei over the entire periodic table are investigated by the Skyrme-Hartree-Fock approach with new force parameters SKI4 [P. G. Reinhard and H. Flocard, Nucl. Phys. A584 467 (1995)] plus a density-dependent pairing correlation. By introducing the density-dependent pairing correlation in the Skyrme-Hartree-Fock model with SKI4, both the isospin degree of freedom and the nucleon-nucleon correlation have been suitably included in the theory. The theoretical results agree very well with experimental data of binding energies, single particle energies and radii of spherical nuclei. The isotope shifts of charge radii in Ca, Ni, Sn, and Pb are also well reproduced.     

Symmetry energies,pairing energies,and mass equations

Symmetry and pairing energies of atomic nuclei are related to the differences between the excitation energies of isobaric analog states in the same nucleus. Numerous such excitation energies are known experimentally. In addition, a comprehensive global set can be deduced from the available experimental masses by applying Coulomb energy corrections. Replacing the experimental mass data by available theoretical mass predictions as basis for this procedure to extract symmetry and pairing energies makes it possible to directly compare theoretical and experimental quantities. These comparisons reflect upon the goodness or possible shortcomings of the respective mass equation since symmetry energies are related to the curvature of the nuclear mass surface. A discussion of eleven selected mass equations or procedures for reproducing experimental masses and extrapolating into regions of unknown nuclei is presented.     

Skyrme-Hartree-Fock approach to spherical nuclei with density-dependent pairing correlations

The ground-state properties of spherical nuclei over the entire periodic table are investigated by the Skyrme-Hartree-Fock approach with new force parameters SKI4 [P. G. Reinhard and H. Flocard, Nucl. Phys. A584 467 (1995)] plus a density-dependent pairing correlation. By introducing the density-dependent pairing correlation in the Skyrme-Hartree-Fock model with SKI4, both the isospin degree of freedom and the nucleon-nucleon correlation have been suitably included in the theory. The theoretical results agree very well with experimental data of binding energies, single particle energies and radii of spherical nuclei. The isotope shifts of charge radii in Ca, Ni, Sn, and Pb are also well reproduced.     

Isovector pairing and particle-number fluctuation effects on the spectroscopic factors of one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei

Expressions of the spectroscopic factors(SFs) corresponding to one-particle transfer reactions have been established using a schematic definition.These expressions have been derived by taking into account the isovector neutron-proton(np) pairing correlations and a particle-number projection in the framework of the generalized SharpBCS(SBCS) method.Recently proposed expressions of the projected wave-functions of odd-mass nuclei have been used for this purpose.The formalism has first been tested using the single-particle energies of the schematic picketfence model.It is shown that the np pairing and particle-number fluctuation effects are far from negligible and they depend on the pairing gap parameter values.Their behavior is not the same when the parent nuclei are even-even or odd.Predictions dealing with the SFs corresponding to one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei have then been established within the framework of the realistic Woods-Saxon model.It is shown that the np pairing effect as well as the particle-number projection effect are important and thus have to be included in future calculations of the SF corresponding to these kinds of reactions.     

平均场加区分质子和中子的邻近轨道对力模型及对超铀区核的统一描述

利用严格可解的平均场加区分质子和中子的邻近轨道相互作用对力模型,对超铀区部分大形变核进行了统一的描述.计算了^227—233Th,^232—239U,^236—243Pu同位素和同中异质素²²⁸Ra-²²⁹Ac-²³⁰Th-²³¹Pa-²³²U,²³²Th-²³³Pa-²³⁴U-²³⁵Np-²³⁶Pu,²³⁶U-²³⁷Np-²³⁸Puv-²³⁹Am的结合能,对激发能和奇偶能差并与相应核的实验值进行了比较     

描述大形变核中对力的硬核Bose-Hubbard模型

讨论了一种描述大形变偶偶核邻近轨道对力相互作用近似的硬核Ｂｏｓｅ－Ｈｕｂｂａｒｄ模型．利用代数方法得到了该模型对激发谱和相应波函数的严格解．该结果可推广到具有任意自旋和有限格点的硬核Ｂｏｓｅ－Ｈｕｂｂａｒｄ和Ｆｅｒｍｉ－Ｈｕｂ－ｂａｒｄ模型中去．     

Effect of resonant continuum on pairing correlations in the relativistic approach

A proper treatment of the resonant continuum is to take account of not only the energy of the resonant state, but also its width. The effect of resonant states on pairing correlations is presented in the framework of the relativistic mean-field theory plus Bardeen-Cooper-Schrieffer (BCS) approximation with a constant pairing strength. The study is performed in an effective Lagrangian with the parameter set NL3 for neutron-rich even-even Ni isotopes. Results show that the contribution of the proper treatment of the resonant continuum to pairing correlations for those nuclei close to the neutron drip line is important. The pairing gaps, Fermi energies, pairing correlation energies, and binding energies are considerably affected by a proper consideration of the width of resonant states. The problem of unphysical particle gas, which may appear in the calculation of the traditional mean field plus BCS method for nuclei in the vicinity of the drip line could be well overcome when the pairing correlation is performed by using the resonant states instead of the discretized states in the continuum.PACS: 21.60.-n Nuclear-structure models and methods - 24.10.Jv Relativistic modelsZhong-Yu Ma: Also at Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, PRC and Institute of Theoretical Physics, Beijing 100080, PRC.     

α decay energies and half-lives from a macroscopic-microscopic model

α decay energies of 323 heavy nuclei with Z≥82 are evaluated with a macroscopic-microscopic model.In this model,the macroscopic part is treated by the continuous medium model and the microscopic part consists of shell and pairing corrections based on the Nilsson potential.α decay half-lives are calculated by Viola-Seaborg formula.The results of α decay energies and half-lives are compared with experimental values and satisfactory agreement is found.The recoiling effect of the daughter nucleus on α decay half-life is also discussed.     

平均场加邻近轨道对力模型描述N=94同中异质素性质

利用严格可解的Nilsson平均场加邻近轨道对力模型,在区分质子和中子情况下,研究了大形变核的性质,主要计算了中子数为N=94的同中异质素的结合能、奇偶能差和转动惯量,并与相应的实验值进行了系统比较,结果表明此模型可以合理描述这些性质,正确反映原子核奇偶性质的变化规律。然后以偶偶核160Dy为例,研究了基态中各角动量J=0,1,...,12价核子对的占有率。结果表明,偶角动量占有率远高于奇角动量占有率,其中S,D,G价核子对各组份在基态波函数中是主要的。The Nilsson mean-field plus the nearest orbit pairing model for deformed nuclei is applied to investigate systematically the properties of the N=94 nuclei,employing both proton-proton and neutron-neutron pairing interactions.The binding energies,even-odd mass differences,moments of inertia are calculated and compared with the corresponding experimental data.The results show that this model can reasonably describe these properties.Further,the ground-state occupation probabilities of valence nucleon pairs with angular momentum J=0,1,...,12 for even-even 160Dy are calculated,and the results show that it is much higher for the even angular momenta than the odd angular momenta,and the S,D,G components in the ground-state wave function are dominant.     

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

Isovector neutron-proton(np) pairing and particle-number fluctuation effects on the spectroscopic factors(SF) corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS(SBCS) discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in N =Z nuclei, and must then be taken into account.     

An isospin invariant form of the interacting boson model for odd nuclei (IBFM-3)

The interacting boson-fermion model IBFM for odd nuclei is extended to incorporate isospin symmetry in nuclei where valence neutrons and protons occupy the same orbits. A mapping is established with shell-model states. A boson-fermion hamiltonian is derived for the special case of charge-independent pairing forces and is found to reproduce the shell-model energies exactly. A comparison of the extension (IBFM-3) with the earlier version IBFM-2 shows that the latter omits some low-lying shell-model states.