Isospin Asymmetry in the Pseudospin Dynamical Symmetry

Alberto, P.; Fiolhais, M.; Malheiro, M.; Delfino, A.; Chiapparini, M.

doi:10.1103/physrevlett.86.5015

Cited by 110 publications

(112 citation statements)

References 26 publications

(54 reference statements)

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“…In Refs. [21,22], it was shown that the observed pseudospin splitting arises from a cancellation of the several energy components, and the PSS in nuclei has a dynamical character. A similar conclusion was reached in Refs.…”

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confidence: 99%

“…(4), it can be seen that the system possesses exact PSS when Σ ′ = 0. Unfortunately, the condition cannot be realized in real nuclei, many efforts are devoted to analyze the contributions of various terms to the PSS [21][22][23][24]. However, as there exist deficiencies mentioned before, we decouple Eq.…”

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confidence: 99%

“…As seen in the following Eq. (4), it seems that only κ r Σ ′ 4M 2 − destroys the PSS, but the pseudospin splittings are related to every component [21][22][23][24]. In order to cure these defects, in the paper we transform the Dirac operator into a diagonal form by similarity renormalization group (SRG), in which the upper(lower) diagonal part becomes an operator describing Dirac (anti)particle with the singularity and the coupling disappearing.…”

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confidence: 99%

“…Although the contributions of O 4 , O 7 and O 8 to ∆ǫ are minor, their influences on PSS can not be ignored, which supports partly with the claim in Refs. [21][22][23], i.e., the observed pseudospin splitting arises from a cancellation of the several energy components, and the PSS in nuclei has a dynamical character.…”

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Exploration of relativistic symmetry by the similarity renormalization group

Guo

2012

Phys. Rev. C

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The similarity renormalization group is used to transform Dirac Hamiltonian into a diagonal form, which the upper(lower) diagonal element becomes an operator describing Dirac (anti)particle. The eigenvalues of the operator are checked in good agreement with that of the original Hamiltonian. Furthermore, the pseudospin symmetry is investigated. It is shown that the pseudospin splittings appearing in the non-relativistic limit are reduced by the contributions from these terms relating the spin-orbit interactions, added by those relating the dynamical terms, and the quality of pseudospin symmetry origins mainly from the competition of the dynamical effects and the spin-orbit interactions. The spin symmetry of antiparticle spectrum is well reproduced in the present calculations.PACS numbers: 21.10. Hw,21.10.Pc,03.65.Pm,05.10.Cc Many years ago a quasidegeneracy was observed in heavy nuclei between single-nucleon doublets with quantum numbers (n, l, j = l + 1/2) and (n − 1, l + 2, j = l + 3/2) where n, l, and j are the radial, the orbital, and the total angular momentum quantum numbers, respectively [1,2]. The quasidegenerate states were suggested to be pseudospin doublets j =l ±s with the pseudo orbital angular momentuml = l + 1, and the pseudospin angular momentums = 1/2, and have explained a number of phenomena in nuclear structure. Because of these successes, there have been comprehensive efforts to understand the origin of this symmetry. Until 1997, it was identified as a relativistic symmetry [3]. Nevertheless, there is still a large amount of attention on this symmetry. The pseudospin symmetry (PSS) of nuclear wave functions was tested in Refs. [4,5] with conclusion supporting the claim in Ref. [3]. The existence of broken PSS was checked in Refs. [6,7], where the quasidegenerate pseudospin doublets were confirmed to exist near the Fermi surface for spherical and deformed nuclei. The isospin dependence of PSS was investigated in Ref. [8], where it is found that PSS is better for exotic nuclei with a highly diffuse potential. PSS was shown to be approximately conserved in medium-energy nucleon scattering from even-even nuclei [9][10][11]. In combination with the analytic continuation method, the resonant states were exposed to hold the PSS in Refs. [12,13]. In Ref.[14], the conditions which originate the spin and pseudospin symmetries in the Dirac equation were shown to be the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. Furthermore, the symmetries and super-symmetries of the Dirac Hamiltonian were checked for particle moving in the spherical or axially-deformed scalar and vector potentials [15]. More reviews on the PSS can be found in the literature [16] and the references therein. Recently, a perturbation method was adopted to investigate the spin and pseudospin symmetries by dividing the Dirac Hamiltonian into the part of possessing the exact (pseudo)spin symmetry and that of breaking the symmetry [17].Despite the...

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Exploration of relativistic symmetry by the similarity renormalization group

Guo

2012

Phys. Rev. C

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“…Since those terms arise from the coupling of those spinor components in their first-order Dirac equations, they have a non-trivial, i.e., different from identity, matrix structure. Therefore, their suppression amounts to have the upper (spin symmetry) or lower (pseudospin symmetry) spinors satisfying second-order equations of Shrödinger type, i.e, with no matrix structure (see [6][7][8][9][10], and [11] for a brief review). This is possible because we have both scalar and vector potentials S and V .…”

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General spin and pseudospin symmetries of the Dirac equation

et al. 2015

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In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of second-order equation equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also 2-and 1-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.

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Relativistic Pseudospin Symmetry in Nuclei

Ginocchio

Leviatan

2002

The Nuclear Many-Body Problem 2001

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Isospin Asymmetry in the Pseudospin Dynamical Symmetry

Cited by 110 publications

References 26 publications

Exploration of relativistic symmetry by the similarity renormalization group

Exploration of relativistic symmetry by the similarity renormalization group

General spin and pseudospin symmetries of the Dirac equation

Relativistic Pseudospin Symmetry in Nuclei

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