Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations

Liang, Haozhao; Shen, Shihang; Zhao, Pei; Meng, J.

doi:10.1103/physrevc.87.014334

Cited by 72 publications

(141 citation statements)

References 164 publications

(185 reference statements)

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“…[31] for a review and Refs. [32,33,34,35,36,37,38,39,40,41,42] for recent progresses. In particular, a very extensive overview was given in Ref.…”

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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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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“…[31] for a review and Refs. [32,33,34,35,36,37,38,39,40,41,42] for recent progresses. In particular, a very extensive overview was given in Ref.…”

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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“…Another possible but also yet incomplete solution for the supersymmetric representation of pseudospin symmetry based on the U(3)-symmetry limit is that with the similarity renormalization group [136,137]. In this Subsection, we will first introduce the basic idea of similarity renormalization group for the Dirac Hamiltonian [130,131,132], then present the perturbative nature of pseudospin symmetry by combining the supersymmetric quantum mechanics, the similarity renormalization group, and the perturbation calculations [136,137].…”

Section: Supersymmetric Representation Of Pss With Srgmentioning

confidence: 99%

“…In other words, the SUSY is exact for all the cases of κ < 0, whereas SUSY is broken for all the cases of κ > 0. This is crucial to understand the intruder states in the PSS [128,136].…”

Section: Susy For Schrödinger-like Equationsmentioning

confidence: 99%

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Pseudospin symmetry in nuclear structure and its supersymmetric representation

Liang¹

2016

Phys. Scr.

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The quasi-degeneracy between the single-particle states (n, l, j = l + 1/2) and (n − 1, l + 2, j = l + 3/2) indicates a special and hidden symmetry in atomic nuclei-the so-called pseudospin symmetry (PSS)-which is an important concept in both spherical and deformed nuclei. A number of phenomena in nuclear structure have been successfully interpreted directly or implicitly by this symmetry, including nuclear superdeformed configurations, identical bands, quantized alignment, pseudospin partner bands, and so on. Since the PSS was recognized as a relativistic symmetry in 1990s, there have been comprehensive efforts to understand its properties in various systems and potentials. In this Review, we mainly focus on the latest progress on the supersymmetric (SUSY) representation of PSS, and one of the key targets is to understand its symmetry-breaking mechanism in realistic nuclei in a quantitative and perturbative way. The SUSY quantum mechanics and its applications to the SU(2) and U(3) symmetries of the Dirac Hamiltonian are discussed in detail. It is shown that the origin of PSS and its symmetry-breaking mechanism, which are deeply hidden in the origin Hamiltonian, can be traced by its SUSY partner Hamiltonian. Essential open questions, such as the SUSY representation of PSS in the deformed system, are pointed out.

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“…Further, the supersymmetric description of PSS was presented for the spherical nuclei and axially deformed nuclei [29][30][31]. 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.…”

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 supersymmetric quantum mechanics: Schrödinger equations

Cited by 72 publications

References 164 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

Pseudospin symmetry in nuclear structure and its supersymmetric representation

Further investigation of relativistic symmetry with the similarity renormalization group

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