Resonant states and pseudospin symmetry in the Dirac-Morse potential

Liu, Q.; Niu, Zhong-Ming; Guo, Jian-You

doi:10.1103/physreva.87.052122

Cited by 21 publications

(20 citation statements)

References 80 publications

(89 reference statements)

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“…Many approaches developed for resonances [219], e.g., the analytical continuation in coupling constant method [220][221][222][223][224][225], the real stabilization method [226][227][228][229][230][231], the complex scaling method [232][233][234][235], the coupled-channel method [236][237][238], and some others [239,240], have been used to study nuclear single-particle resonant states. Based on some of these methods, the pseudospin symmetry [241][242][243][244][245] and the spin symmetry [246] in single-particle resonant states have been investigated. The pseudospin symmetry and/or spin symmetry in nucleon-nucleus and nucleon-nucleon scatterings have been also investigated [41][42][43][44].…”

Section: From Bound States To Resonant Statesmentioning

confidence: 99%

“…[243], the CSM was applied to study the PSS of resonant states of a Dirac particle in a Morse potential,…”

Section: Pss In Single-particle Resonant States With Csmmentioning

confidence: 99%

“…The study of symmetries in resonant states is certainly interesting, e.g., the pseudospin symmetry [241][242][243][244][245] and spin symmetry [246] in single-particle resonant states. Recently, Lu, Zhao, and Zhou [247] gave a rigorous verification of the pseudospin symmetry in single-particle resonant states.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

2015

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Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals $(n, l, j = l + 1/2)$ and $(n-1, l + 2, j = l + 3/2)$ indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS). Since the introduction of the concept of PSS in atomic nuclei, there have been comprehensive efforts to understand its origin. Both splittings of spin doublets and pseudospin doublets play critical roles in the evolution of magic numbers in exotic nuclei discovered by modern spectroscopic studies with radioactive ion beam facilities. Since the PSS was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry (SS) for anti-nucleon, and many new concepts have been introduced. In the present Review, we focus on the recent progress on the PSS and SS in various systems and potentials, including extensions of the PSS study from stable to exotic nuclei, from non-confining to confining potentials, from local to non-local potentials, from central to tensor potentials, from bound to resonant states, from nucleon to anti-nucleon spectra, from nucleon to hyperon spectra, and from spherical to deformed nuclei. Open issues in this field are also discussed in detail, including the perturbative nature, the supersymmetric representation with similarity renormalization group, and the puzzle of intruder states.Comment: Review Article, 242 pages, 58 figures, 10 table

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Section: From Bound States To Resonant Statesmentioning

confidence: 99%

“…[243], the CSM was applied to study the PSS of resonant states of a Dirac particle in a Morse potential,…”

Section: Pss In Single-particle Resonant States With Csmmentioning

confidence: 99%

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Hidden pseudospin and spin symmetries and their origins in atomic nuclei

2015

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“…For example, the Aharonov-Bohm effect [10,11], the Dirac particle in a Morse potential [12,13], the Dirac equation for an attractive Coulomb potential in supersymmetric quantum mechanics [14], the Dirac equation with scalar and vector potentials under the exact spin and pseudospin symmetries limits [15][16][17][18] and particles interacting with the Hulthén [19] and Rosen-Morse [20] potentials.…”

Section: Introductionmentioning

confidence: 99%

Scattering and bound states for the Hulthén potential in a cosmic string background

Hosseinpour¹,

Andrade²,

Silva³

et al. 2017

Eur. Phys. J. C

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In this work we study the Dirac equation with vector and scalar potentials in the spacetime generated by a cosmic string. Using an approximation for the centrifugal term, a solution for the radial differential equation is obtained. We consider the scattering states under the Hulthén potential and obtain the phase shifts. From the poles of the scattering S-matrix the states energies are determined as well.

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“…Many methods have been developed for the studies of resonances [109], for example, the analytical continuation in coupling constant method [110,111], the real stabilization method [112,113], the complex scaling method [114,115], the coupled channels method [116,117], and so on. Therefore, the exploration of symmetries in resonant states is certainly interesting [118,119,120].…”

Section: Introductionmentioning

confidence: 99%

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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Resonant states and pseudospin symmetry in the Dirac-Morse potential

Cited by 21 publications

References 80 publications

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Scattering and bound states for the Hulthén potential in a cosmic string background

Pseudospin symmetry in nuclear structure and its supersymmetric representation

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