Perturbative interpretation of relativistic symmetries in nuclei

Liang, Haozhao; Zhao, Pei; Zhang, Ying; Meng, J.; Giai, Nguyen Van

doi:10.1103/physrevc.83.041301

Cited by 75 publications

(122 citation statements)

References 31 publications

(42 reference statements)

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“…In this case, one cannot have exact spin symmetry (i.e., V = S) since now − = −(V − S) acts as binding potential. This behavior has been related by several authors to the perturbative nature of spin and pseudospin symmetry, namely that in the case of fermions (antifermions) the pseudospin (spin) symmetry is nonperturbative for nuclear mean-field potentials [6,[8][9][10]. Note, however, that for harmonic oscillator systems one can have exact pseudospin and spin symmetries for fermions and antifermions respectively [11].…”

Section: Introductionmentioning

confidence: 95%

“…In previous works in which the perturbative nature of pseudospin (or spin in the case of antifermions) was related to the onset of the respective symmetry, one would either examine the effect the pseudospin-orbit or spin-orbit term on the energy splittings of the respective doublets [6,8,9] or analyze the convergence of a perturbation expansion in the respective potential strength [10]. In Ref.…”

Section: Spin and Pseudospin Symmetries In The Dirac Hamiltonianmentioning

confidence: 99%

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Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

Castro

Alberto

2012

Phys. Rev. A

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We analyze in detail the analytical solutions of the Dirac equation with scalar S and vector V Coulomb radial potentials near the limit of spin and pseudospin symmetries (i.e., when those potentials have the same magnitude and either the same sign or opposite signs, respectively). By performing an expansion of the relevant coefficients we also assess the perturbative nature of both symmetries and their relations to the (pseudo)spin-orbit coupling. The former analysis is made for both positive and negative energy solutions and we reproduce the relations between spin and pseudospin symmetries found before for nuclear mean-field potentials. We discuss the node structure of the radial functions and the quantum numbers of the solutions when there is spin or pseudospin symmetry, which we find to be similar to the well-known solutions of hydrogenic atoms.

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Section: Introductionmentioning

confidence: 95%

Section: Spin and Pseudospin Symmetries In The Dirac Hamiltonianmentioning

confidence: 99%

Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

Castro

Alberto

2012

Phys. Rev. A

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“…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 large number of studies on PSS, it is still not fully understood the origin of PSS and its breaking mechanism since there is no bound states in the PSS limit. Hence, many efforts are devoted to compare the contributions of different terms in the Schrödinger-like equation for the lower component of Dirac spinor to the pseudospin energy splitting.…”

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confidence: 99%

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confidence: 99%

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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“…[25,26]. In addition, it was noted that, unlike the spin symmetry, the pseudospin breaking cannot be treated as a perturbation of the pseudospin-symmetric Hamiltonian [27]. The nonperturbation nature of PSS has also been mentioned in Ref.…”

Section: Introductionmentioning

confidence: 99%

Further investigation of relativistic symmetry with the similarity renormalization group

Chen

Guo

2013

Phys. Rev. C

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Following a recent rapid communications[Phys.Rev.C85,021302(R) (2012)], we present more details on the investigation of the relativistic symmetry by use of the similarity renormalization group. By comparing the contributions of the different components in the diagonal Dirac Hamiltonian to the pseudospin splitting, we have found that two components of the dynamical term make similar influence on the pseudospin symmetry. The same case also appears in the spin-orbit interactions. Further, we have checked the influences of every term on the pseudospin splitting and their correlations with the potential parameters for all the available pseudospin partners. The result shows that the spin-orbit interactions always play a role in favor of the pseudospin symmetry, and whether the pseudospin symmetry is improved or destroyed by the dynamical term relating the shape of the potential as well as the quantum numbers of the state. The cause why the pseudospin symmetry becomes better for the levels closer to the continuum is disclosed.

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Perturbative interpretation of relativistic symmetries in nuclei

Cited by 75 publications

References 31 publications

Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

Exploration of relativistic symmetry by the similarity renormalization group

Further investigation of relativistic symmetry with the similarity renormalization group

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