Pseudospin and nuclear deformation

Blokhin, A. L.; Beuschel, T.; Draayer, J. P.; Bahri, C.

doi:10.1016/s0375-9474(97)80004-8

Cited by 18 publications

(27 citation statements)

References 18 publications

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“…It is also proven that there exist no bound states in the Fermi sea at the pseudospin symmetry limit (17) within the nonconfining potentials.…”

Section: From Non-confining Potentials To Confining Potentialsmentioning

confidence: 97%

“…(17), the potential Σ(r) is simply a constant Σ 0 , and then Eq. (14) for the lower component of the Dirac spinor can be reduced to…”

Section: Analytical Solutions At Pss Limitmentioning

confidence: 99%

“…(17), the Schrödinger-like equation for the lower component F (r) of the Dirac spinor is expressed as as seen in Eq. (19).…”

Section: Pss In Single-particle Wave Functionsmentioning

confidence: 99%

“…(76), one finds that this requirement can be fulfilled either by M + (r) > 0 and M − (r) < 0 or by M + (r) < 0 and M − (r) > 0 at large r. The bound states in the non-confining potentials belong to the former case. On the other hand, the exact PSS limit (17) indicates M − is simply a constant, in particular, it should be positive for all possible solutions belonging to the Fermi sea. These solutions become the bound states as long as M + (r) < 0 at large r, which corresponds to the condition given in Eq.…”

Section: Nodal Structure For Confining Potentialsmentioning

confidence: 99%

“…The pseudospin symmetry remains an important physical concept in axially deformed [13][14][15][16] and even triaxially deformed [17,18] nuclei. Based on this concept, a simple but useful pseudo-SU(3) model was proposed, and this model was generalized to be the (pseudo-)symplectic model [15,16,[19][20][21][22], (also see Ref.…”

Section: Introductionmentioning

confidence: 99%

See 4 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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“…It is also proven that there exist no bound states in the Fermi sea at the pseudospin symmetry limit (17) within the nonconfining potentials.…”

Section: From Non-confining Potentials To Confining Potentialsmentioning

confidence: 97%

“…(17), the potential Σ(r) is simply a constant Σ 0 , and then Eq. (14) for the lower component of the Dirac spinor can be reduced to…”

Section: Analytical Solutions At Pss Limitmentioning

confidence: 99%

“…(17), the Schrödinger-like equation for the lower component F (r) of the Dirac spinor is expressed as as seen in Eq. (19).…”

Section: Pss In Single-particle Wave Functionsmentioning

confidence: 99%

Section: Nodal Structure For Confining Potentialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hidden pseudospin and spin symmetries and their origins in atomic nuclei

2015

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Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential-type potentials

Arda

Sever²,

Tezcan

2009

Ann. Phys.

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The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method.The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and qdeformed Rosen-Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number κ = 0, or κ = 0.

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Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential‐type potentials

2009

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The solvability of The Dirac equation is studied for the exponential‐type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov–Uvarov method. The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and q‐deformed Rosen–Morse potentials are obtained within the framework of an approximation to the spin‐orbit coupling term, so the solutions are given for any value of the spin‐orbit quantum number κ = 0, or κ ≠ 0.

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Pseudospin and nuclear deformation

Cited by 18 publications

References 18 publications

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential-type potentials

Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential‐type potentials

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