相对论谐振子下的自旋和赝自旋轨道伙伴态劈裂

通过求解具有谐振子势的径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着谐振子的振动频率参数ω和描述谐振子势阱底偏离中心参数r₀的变化关系. 研究发现, 这些参数对于赝自旋和自旋双重态的能级劈裂和波函数劈裂都有着显著的影响. 此外, 也研究了能级劈裂和波函数劈裂随着量子数的变化关系. 由于参数ω与核子数有关, 而参数r₀与形变核有关, 所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的, 研究的结果至少可以定性地应用到大部分原子核中.     

方阱势下的赝自旋劈裂和自旋劈裂

通过求解具有方阱势的径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着方阱势的势阱深度参数和势阱半径参数的变化关系, 此外, 能级劈裂和波函数劈裂随着量子数的变化关系也被进行了研究. 由于在特定的同位素链中, 势阱深度参数和势阱半径参数与核子数有关系, 所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的, 研究的结果至少可以定性的应用到大部分原子核中.     

原子核的赝自旋对称性近似

基于相对论平均场理论,讨论了Dirac方程中严格的赝自旋对称性,以及实际原子核中的近似赝自旋对称性.在严格的赝自旋对称性下,除赝自旋单态外,所有的态都有简并的赝自旋伙伴态,而且赝自旋双重态的径向量子数相同.以正常核²⁰⁸Pb和奇特核²⁶⁴Pb为例,分析了赝离心势和赝自旋–轨道耦合势的贡献,发现对于赝自旋单态,赝离心势恒为零;对赝自旋双重态,赝自旋–轨道耦合势的贡献很小,赝自旋对称性近似满足;但对于闯入态,相对于赝离心势,赝自旋–轨道耦合势的贡献很大,赝自旋对称性被完全破坏,也即闯入态不具有赝自旋伙伴态的可能原因.     

从Sn质子滴线核到Sn中子滴线核的自旋对称性和赝自旋对称性

在球形相对论平均场模型下, 采用NLSH相互作用全面研究了从Sn质子滴线核到Sn中子滴线核的自旋对称性和赝自旋对称性. 发现: 1) 随着核子数的增大, 中子和质子的赝自旋波函数劈裂基本上都是减小的, 并且质子的变化趋势更加明显. 中子高能级的自旋波函数劈裂随着核子数的增大也是减小的. 2) 对于特定的同位素, 当n=1时, 赝自旋波函数劈裂随着l的增大而增大. 当n=2时, 中子的自旋波函数劈裂随着l的增大而增大. 当l=2或l=3时, 中子的自旋波函数劈裂随着n的增大而增大. 3) 中子和质子的赝自旋劈裂之间的差别总是比自旋劈裂的差别更大一些.     

相对论平均场理论中的张量项对自旋-轨道劈裂的影响

在相对论平均场理论中引入同位旋标量-矢量介子ω张量项, 以²⁰⁸Pb为例,研究了张量项对原子核平均势场、介子场、自旋-轨道耦合势、单粒子能级的自旋-轨道劈裂和原子核壳层结构等的影响.结果发现张量项对核子平均势的影响主要表现在原子核的表面.随着张量耦合强度的增加, 自旋-轨道耦合势增强,单粒子能级的自旋-轨道劈裂增大,从而导致原子核单粒子能级的壳层结构发生很大变化,传统幻数所对应的主壳消失, 新的主壳出现.     

赝自旋对称性在连续谱中是否存在？

在相对论边界条件下, 用基于相对论平均场的耦合常数解析延拓方法研究球形核单质子共振态. 此法计算的¹²⁰Sn质子共振态能量、宽度和波函数首次用于分析共振态中赝自旋对称性存在的可能性, 包括相应量子数的单粒子态的能级劈裂, 以及宽度和波函数的行为.     

用推广的矩分析方法确定过程J/ψ→V1,X→V2+V3中粒子X的自旋-宇称

本文用推广的矩分析方法对J/ψ的强衰变过程J/ψ→V₁,X→V₂+V₃,V₂、V₃→2P或3P(其中V_i代表有质量的矢量粒子,P代表赝标介子)进行了讨论.对于具有不同自旋和宇称的中间态X,给出了相应的矩的表达式.在非相对论情况下,计算了过程X→V₂+V₃的螺旋度振幅值.通过比较部分矩的理论值和实验值,可以确定中间态粒子X的自旋、宇称和所处的分波态.     

强子衰变过程J/ψ→V+X,X→V+V的角分布分析

本文讨论了J/ψ的强子衰变过程J/ψ→V₁+X,X→V₂+V₃,V₂,V₃→2P(或3P)(其中V_i代表矢量介子,P代表赝标介子).对于具有不同自旋-宇称J^P的中间态X,得到了相应的角分布的螺旋度形式.这些公式对于利用BEPC上得到的J/ψ事例,确定上述过程中间态X的自旋-宇称是有帮助的.     

层子模型里介子的波函数和能级

本文利用Bethe-Salpeter型的方程处理了层子模型中的介子内部波函数,指出如果层子和反层子之间的作用可以用一个赝标型位阱来代表,那么0^-和1^-介子将满足相同的近似迳向波动方程,从而导致SU₆对称性。我们以前曾经证明赝标型位阱是唯一可以导致这个对称性的单一型位阱。我们的位阱是V=V₀+V₁,V₀代表一个超强的深位阱,它的作用是降低层子的原始质量M,使它的有效值M′变得很小,使得层子在强子内部的运动是相对论的。V₁代表数量级为1/M的简谐振子位阱,另外还引入一个张量力来解释自旋和轨道角动量相同态的能级分裂。我们得出基态和角动量激发态0^-和1^-介子的解,基本上解释了所有观察到的介子。我们的理论可以同样处理重子态,只要唯象位阱V₀只有介子的值的一半。     

94Mo高自旋态能级纲图

通过重离子融合蒸发反应¹⁶O(⁸²Se+4n)⁹⁴Mo布局了⁹⁴Mo核的高自旋态.利用多探头探测器阵列GASP进行了在束γ测量,从而重新研究了⁹⁴Mo核的高自旋态能级结构.基于新发现的一些重要的连接跃迁,对⁹⁴Mo核的高自旋态能级纲图做了重要修改.将新的能级结构与壳模型计算进行了比较和讨论.结果表明要正确的描述94?Mo核的高自旋态(自旋值大于14)能级结构,应考虑价中子在d_5/2,g_7/2和h_11/2轨道上的激发.     

Pseudospin and spin symmetry in Dirac-Morse problem with a tensor potential

Under the conditions of the pseudospin and spin symmetry, approximate analytical solutions of the Dirac-Morse problem with Coulomb-like tensor potential are presented. The energy eigenvalue equations are found and corresponding radial wave functions are obtained in terms of confluent hypergeometric functions. The energy eigenvalues are calculated numerically in the absence and presence of the tensor potential. We also investigate the contribution of the potential parameters to the energy splitting of the pseudospin and spin doublets.     

Perturbative pseudospin symmetry limit with linear spin-orbit potential

The pseudospin symmetry (PSS) limits which conserve substantial spin-orbit splitting are investigated. It is found that while the strength of the spin-orbit potential as well as the spin-orbit splitting increase, the pseudospin doublets, e.g., 2p_3/2 and 1f_5/2 states, are always degenerate. Furthermore, by examining the perturbation corrections to the single-particle energies, the perturbative nature of the proposed PSS limits is also discussed.     

Exploration of Pseudospin Symmetry in the Resonant States

Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.     

Dirac Equation with a New Tensor Interaction under Spin and Pseudospin Symmetries

The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method. Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability, we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study. The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely. The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.     

Dirac Equation with a New Tensor Interaction under Spin and Pseudospin Symmetries

The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method. Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability, we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study.The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely. The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.     

Isospin asymmetry in the pseudospin dynamical symmetry

Pseudospin symmetry in nuclei is investigated considering the Dirac equation with a Lorentz structured Woods-Saxon potential. The isospin correlation of the energy splittings of pseudospin partners with the nuclear potential parameters is studied. We show that, in an isotopic chain, the pseudospin symmetry is better realized for neutrons than for protons. This behavior comes from balance effects among the central nuclear potential parameters. In general, we found an isospin asymmetry of the nuclear pseudospin interaction, opposed to the nuclear spin-orbit interaction which is quasi-isospin symmetric.     

Influences on the pseudospin symmetry from the different fields of mesons in deformed nuclei

Influences from different fields of mesons on the pseudospin symmetry are investigated for deformed nuclei. The energy splitting between pseudospin partners are extracted from the relativistic mean field calculations. The results show that the σ-field contribution to the pseudospin energy splitting has nearly the same magnitude as the one obtained by the ω-field, but with opposite signs. The pseudospin energy splittings either for neutron or for protons are almost the same if the σ-field (V _σ ) and the ω-field (V _ω ) change at the same scale. The pseudospin energy splitting depends in the same way as the nucleus binding energy of the cancellation of these two potentials, and is controlled by the same nuclear physics scale as the potential sum V _ω + V _σ In comparison with the σ- and ω-fields, it is seen that the ρ meson field produces a minor influence on the pseudospin symmetry.     

Pseudospin symmetry and structure of nuclei with <Emphasis Type="Italic">Z</Emphasis> ≥ 100

In the framework of the relativistic mean-field approach, a pseudospin dependence of the residual forces in nuclei is considered. It is shown that this dependence is relatively weak. As a consequence, a pseudospin dependence of the particle-core coupling is weak as well. This leads to a small splitting of the pseudospin doublets produced by a vector coupling of an odd particle pseudospin and a pseudoorbital momentum of the core. Some possibilities for experimental investigation of the manifestations of the pseudospin symmetry in the spectra of odd nuclei with Z ≥ 100 are indicated. The text was submitted by the authors in English.     

Effects of Parametrization of A Woods—Saxon Potential on Single Particle Orbits in 66Ca

A Woods—Saxon potential is introduced to serve as initial conditions for an iterative solution of the exotic nuclei in relativistic mean field approach. Effects of parametrization of the Woods—Saxon potential on single particle orbits around the Fermi surface are investigated in ⁶⁶Ca. A semi-parabolic curve of orbital radius appears when the width of the central potential changes. The pseduospin splitting is more sensitive to the potential width than to the depth and the diffuseness. The spin-orbit splitting is more sensitive to the potential depth than to the width and the diffuseness.     

The spin and pseudospin symmetries in the relativistic formalism: Similarities and differences

The effects of the symmetry breaking terms, spin-orbit potential (SOP) and pseudospin-orbit potential (PSOP), in the spin and pseudospin symmetries, respectively, are studied in a comparative way. The analytical properties of the small component F of the Dirac spinor for pseudospin doublets (PSDs) are investigated around the singularity point of the PSOP. We show that the PSOP and the pseudocentrifugal barrier must be appropriately related to each other to describe adequately the wave functions in the nuclear surface, whereas it is not the case for the centrifugal barrier and the SOP. We also determine a modified PSOP smaller than the PSOP when the parameter ˉ, appearing in it, is left to vary in the domain of real numbers. The inclusion of this modified PSOP allows us to define a continuous way that connects the two states of a PSD as ˉ varies continuously between the physical (integer) values of ˉ corresponding to these states. Our results indicate that whereas the SOP can be considered as a small spin symmetry breaking term that allows a simple explanation of the spin symmetry, the consideration of the PSOP as the pseudospin symmetry breaking term presents serious difficulties. Thus, we propose a new strategy to explain, in a simple way, the quasi-degeneracy of the PSDs.