Relativistic wave functions for single-proton resonant states

With the relativistic boundary condition, single-proton resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean-field (RMF) theory. In this scheme, we investigate the wave functions for l≠ 0 proton resonant states close to the continuum threshold in the stable nuclide ¹²⁰Sn for the first time. Some hints for pseudospin symmetry in the resonant states of nuclei are mentioned as well.     

Solutions of Dirac equations with the Pöschl-Teller potential

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic P?schl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.     

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.     

∧超核中单粒子谱的自旋及赝自旋对称性研究(英文)

原子核中单粒子谱的自旋和赝自旋对称性对核结构的研究具有重要意义。本文基于相对论平均场理论,以132Sn,_∧133Sn,及_2∧134Sn为例,研究了∧超核中单∧谱和单中子谱的自旋和赝自旋对称性。研究发现,单∧谱的自旋对称性保持得相当好,与实验观测一致;而其赝自旋对称性只是近似保持,与核子谱的情况类似。此外,还研究了∧超子对中子谱的杂质效应,发现∧超子使中子谱的自旋对称性变差,赝自旋对称性变好。Spin and pseudospin symmetries in the single-particle spectra of atomic nuclei are of great significance for the study of nuclear structure. In this work, taking 132Sn, _∧133Sn, and _2∧134Sn as examples, the spin and pseudospin symmetries in ∧ hypernuclei are studied by using the relativistic mean-field model. For the single-∧ spectra, results show that the spin symmetry maintains well while the pseudospin symmetry is approximately conserved. Besides, as impurities, the ∧ hyperons worsen the spin symmetry of single-neutron spectra while improve the pseudospin symmetry.     

伪自旋对称情形下Rosen-Morse类型势场中相对论粒子的束缚态

在伪自旋对称情形下研究了Rosen-Morse类型势场中相对论粒子的束缚态,利用Nikiforov-Uvarov方法求解了伪自旋对称情形下的Klein-Gordon和Dirac方程,得到了相对论粒子被束缚在Rosen-Morse类型势场的精确束缚态解.     

New insights on pseudospin doublets in nuclei

The relevance of pseudospin symmetry in nuclei is considered. New insights are obtained from looking at the continuous transition from a non-relativistic model satisfying spin symmetry to another one satisfying pseudospin symmetry. This study suggests that there are models allowing no missing single-particle states in this transition, contrary to what is usually advocated. It rather points to an association of pseudospin partners that is quite different from the one generally assumed, together with a strong violation of the corresponding symmetry. This assignment is supported by an examination of the wave functions and related quantities for the pseudospin partners.     

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.     

Solution of the Dirac equation in the tridiagonal representation with pseudospin symmetry for an anharmonic oscillator and electric dipole ring-shaped potential

An anharmonic oscillatory potential is proposed in which a noncentral electric dipole is included. The pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relation for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by the diagonalization of the radial recursion relation. The algebraic properties of the energy equation are also discussed, showing the exact pseudospin symmetry.     

Pseudospin symmetry as an accidental symmetry in the relativistic framework

We analyse the arguments used in the relativistic context to base the quasi-degeneracy of pseudospin doublets (PSDs) observed in atomic nuclei on the smallness of the single-particle central potential (Σ _S + Σ₀), discussing, especially, the implications of the results obtained in the limit (Σ _S + Σ₀ = 0. We study also the transition from a relativistic model, where Σ _S + Σ₀ is a harmonic-oscillator potential and exhibits degenerate PSDs, to a more realistic one with broken pseudospin symmetry. We examine, in particular, the effect of the corresponding pseudospin symmetry-breaking term on the Dirac spinors of the PSDs. An extension of the Nilsson model to the relativistic case is also considered. Communicated by V. Vento     

Ground-State Properties of Ca Isotopes and the Density Dependence of the Symmetry Energy

A relativistic mean field model is used to study the ground-state properties of neutron-rich nuclei in Ca isotopes. An additional isoscalar and isovector nonlinear coupling has been introduced in the relativistic mean field model, which could soften the symmetry energy, while keep the agreement with the experimental data. The sensitivity of proton and neutron density distributions and single particle states in Ca isotopes to the additional isoscalarisovector nonlinear coupling term is investigated. We found that the binding energies, the density distributions of single particle levels are strongly correlated with the density dependence of the symmetric energy in nuclear matter.     

Cross-like terahertz metamaterial absorber for sensing applications

Relativistic effects are employed to describe the weakly bound nuclei of \({}^{17}\)F and \({}^{11}\)Be. In order to calculate the energy levels of the ground state and the excited states of these nuclei, we solved the Dirac equation with pseudospin symmetry in the shell model by using the basic concept of supersymmetric shape invariance method. The results obtained from this approach are compared with a non-relativistic approach and experiment. It was then seen that the relativistic approach matches more with the experimental results.     

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.     

包含非中心电耦极矩的环状非谐振子势场赝自旋对称性的三对角化表示

提出了一个包含非中心电耦极矩分量的环状非谐振子势模型,在能够负载Dirac波动算子三对角化表示的完全平方可积L~2空间讨论了这一势场的赝自旋对称性.利用三对角化矩阵方案,使得求解Dirac方程转换为寻求波函数展开系数满足的三项递推关系式.角向波函数和径向波函数分别以Jacobi多项式和Laguerre多项式表示.由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱,显示出这一势模型具有严格的赝自旋对称性     

Reliability of the pseudospin symmetry in atomic nuclei

The reliability of the pseudospin symmetry (PSS) in atomic nuclei is analyzed in the framework of the relativistic Hartree approach. We find that the nuclear surface strongly increases the effect of the pseudospin-orbit potential (PSOP), spoiling the possibility of the exact realization of the PSS even in the limit of a vanishing PSOP. It is also shown that the PSS cannot be explained by the fact that Σ_S ≃ - Σ. New arguments to explain the PSS in finite nuclei are given. The important role the spin-orbit interaction plays in the achievement of the PSS is also discussed. Received: 22 July 2002 / Accepted: 18 February 2003 / Published online: 20 May 2003     

Origin of the pseudospin symmetry in the relativistic formalism

The grounds on which the nuclear pseudospin symmetry (PSS) is supposed to be based are analysed within the relativistic mean-field framework. A connection between the mechanisms responsible for the spin-orbit and pseudospin-orbit splittings is shown. The nature of the PSS is investigated through an extended Dirac equation which allows a generalization of the PSS breaking term. It is shown that the PSS breaking in real nuclei can be explained as a result of a non-perturbative transformation from non-physical solutions of the Dirac equation, which satisfy exactly the PSS, to the physical ones. The PSS breaking term produces important, though qualitatively similar, effects on both states of a pseudospin-orbit doublet. The similarity of these effects increases with the number of nodes of the small component of the Dirac spinor of these states.Received: 28 April 2003, Revised: 30 October 2003, Published online: 18 June 2004PACS: 24.10.Jv Relativistic models - 21.60.Cs Shell model - 21.10.Pc Single-particle levels and strength functions - 24.80. + y Nuclear tests of fundamental interactions and symmetries     

Some Aspects of Nuclear Structure in Relativistic Approach

The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.     

Some Aspects of Nuclear Structure in Relativistic Approach

The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.     

Pseudospin symmetry in finite nuclei

The pseudospin symmetry (PSS) is an important feature of the nuclear structure. Most of the authors working in this field at present consider the PSS as an approximate symmetry, although there exist certain essential differences in opinions about the particularities of its realization. We have shown that the PSS in the nucleus is strongly related to the spin-orbit interaction and, consequently, to the spin symmetry (SS). We conclude that the PSS, as well as the SS, can be studied appropriately in the framework of the relativistic formalism. The text was submitted by the authors in English.