Pseudospin symmetry in the resonant states of nuclei

Guo, Jian-You; Wang, Ruo-Dong; Fang, Xiang-Zheng

doi:10.1103/physrevc.72.054319

Cited by 77 publications

(128 citation statements)

References 53 publications

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“…We also studied resonances in Woods-Saxon-like potentials, W (r) = W 0 /(1 + exp[(r − R)/a]) (W = V or S) with parameters connected with 208 Pb given in Ref. [55]: the depths V 0 − S 0 = 650 MeV and V 0 + S 0 = −66 MeV, the diffusivity parameter a = 0.6 fm, and R = 7 fm. Resonance parameters are obtained with the real stabilization method [49,50].…”

Section: Numerical Test Of Pseudospin Symmetry In Resonant Statesmentioning

confidence: 99%

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Exact conservation and breaking of pseudospin symmetry in single particle resonant states

Lü¹,

Zhao²,

Zhou³

2013

AIP Conference Proceedings

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Abstract. In this contribution we present some results on the study of pseudospin symmetry (PSS) in single particle resonant states. The PSS is a relativistic dynamical symmetry connected with the small component of the nucleon Dirac wave function. Many efforts have been made to study this symmetry in bound states. We recently gave a rigorous justification of the PSS in single particle resonant states by examining the zeros of Jost functions corresponding to the small components of the radial Dirac wave functions and phase shifts of continuum states [1]. We have shown that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Examples of exact conservation and breaking of this symmetry in single particle resonances are given for spherical square-well and Woods-Saxon potentials.

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Section: Numerical Test Of Pseudospin Symmetry In Resonant Statesmentioning

confidence: 99%

“…There have been some numerical studies on the PSS [55,56,57,58] and SS [59] in single particle resonant states. In a recent work, we have shown that the PSS in single particle resonant states is also exactly conserved under the same condition for the PSS in bound states, i.e., Σ(r) = 0 or dΣ(r)/dr = 0 [1].…”

Section: Introductionmentioning

confidence: 99%

Exact conservation and breaking of pseudospin symmetry in single particle resonant states

Lü¹,

Zhao²,

Zhou³

2013

AIP Conference Proceedings

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“…In combination with the analytic continuation method, the resonant states were exposed to hold the PSS in Refs. [12,13]. In Ref.…”

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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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“…In a very recent paper [32], supersymmetric quantum mechanics and similarity renormalization group (SRG) are used as the critical tools for understanding the origin of PSS and its breaking mechanism, and the cause why the PSS becomes better for the levels closer to the continuum is discussed in a quantitative way at the nonrelativistic limit. This symmetry is also checked in the resonant states [33,34] with similar features to bound states indicated in Ref. [35].…”

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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Pseudospin symmetry in the resonant states of nuclei

Cited by 77 publications

References 53 publications

Exact conservation and breaking of pseudospin symmetry in single particle resonant states

Exact conservation and breaking of pseudospin symmetry in single particle resonant states

Exploration of relativistic symmetry by the similarity renormalization group

Further investigation of relativistic symmetry with the similarity renormalization group

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