Symmetry of Dirac Equation and Corresponding Phenomenology

Ke, H. W.; Zuo, Liang; Chen, Jing-Ling; Ding, Yi-Bing; Li, Xue–Qian

doi:10.1142/s0217751x1004783x

Cited by 7 publications

(6 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that there have been some investigations of PSS connected with some specific forms of confining potentials [65]. Finally we mention that there have been some discussions on the physics behind Σ(r) ≈ 0 or dΣ(r)/dr ≈ 0 [66,67] and more investigations are expected.…”

Section: Introductionmentioning

confidence: 89%

Pseudospin symmetry in single-particle resonances in spherical square wells

2013

View full text Add to dashboard Cite

Background:The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently, we justified rigorously that the PSS in single-particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [Phys. Rev. Lett. 109, 072501 (2012)]. Purpose: To understand more deeply the PSS in single-particle resonant states, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single-particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. Methods: We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square-well potentials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. Results: By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single-particle potential varies from zero to a finite value. Conclusions: The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated.

show abstract

Section: Introductionmentioning

confidence: 89%

Pseudospin symmetry in single-particle resonances in spherical square wells

2013

View full text Add to dashboard Cite

show abstract

“…There are already some discussions on the physics behind the near equality of the vector and scalar potentials in the Dirac Hamiltonian [376][377][378] and more investigations are expected. In particular, it is highly necessary to search for the links with more fundamental models on strong interactions or realistic interactions between nucleons.…”

Section: Summary and Perspectivesmentioning

confidence: 99%

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

2015

View full text Add to dashboard Cite

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

show abstract

“…The SS and PSS have been investigated extensively within the relativistic framework including the PSS in deformed nuclei [12,13,14], the SS for Λ spectra in hyper-nuclei [15,16,17], and these symmetries in various potentials [18,19,20,21,22,23,24,25,26,27,28,29,30]. The readers are referred to Ref.…”

Section: Introductionmentioning

confidence: 99%

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

Lü¹,

Zhao²,

Zhou³

2013

AIP Conference Proceedings

View full text Add to dashboard Cite

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.

show abstract

Symmetry of Dirac Equation and Corresponding Phenomenology

Cited by 7 publications

References 26 publications

Pseudospin symmetry in single-particle resonances in spherical square wells

Pseudospin symmetry in single-particle resonances in spherical square wells

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

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

Contact Info

Product

Resources

About