Spin and pseudospin symmetry along with orbital dependency of the Dirac–Hulthén problem

Ikhdair, Sameer M.; Berkdemir, Cüneyt; Sever, R.

doi:10.1016/j.amc.2011.03.109

Cited by 42 publications

(52 citation statements)

References 52 publications

(85 reference statements)

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“…For the spherical case, extensive investigations have been made for the spherical harmonic oscillator [88][89][90]92,95,96], anharmonic oscillator [97], Coulomb [76,[99][100][101], Deng-Fan [102], diatomic molecular [103,104], Eckart [105,106], Hellmann [107], Hulthén [108][109][110][111], Manning-Rosen [112][113][114], Mie-type [115][116][117], Morse [118][119][120][121][122][123], Pöschl-Teller [124][125][126][127][128][129][130][131][132][133], Rosen-Morse [134][135][136][137], Tietz-Hua [138], Woods-Saxon …”

Section: Analytical Solutions At Pss Limitmentioning

confidence: 99%

“…Although the doubt on the connection between the pseudospin symmetry and the condition Σ(r) = 0 or dΣ(r)/dr = 0 exists [83][84][85], following the pseudospin symmetry limit, a lot of discussions about the pseudospin symmetry in singleparticle spectra have been made by exactly or approximately solving the Dirac equation with various potentials, for examples, the one-dimensional Woods-Saxon potential [86], the two-dimensional Smorodinsky-Winternitz potential [87], the spherical harmonic oscillator [88][89][90][91][92][93][94][95][96], anharmonic oscillator [97], Coulomb [76,[98][99][100][101], Deng-Fan [102], diatomic molecular [103,104], Eckart [105,106], Hellmann [107], Hulthén [108][109][110][111], Manning-Rosen [112][113][114], Mie-type [115][116][117], Morse [118][119][120][121][122][123], Pöschl-Teller [124][125]…”

Section: Introductionmentioning

confidence: 99%

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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: Analytical Solutions At Pss Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

2015

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“…Quite recently, we have also proposed a new approximation scheme for the centrifugal term [13,14]. The Nikiforov-Uvarov (NU) method [60] and other methods have also been used to solve the D-dimensional Schrödinger equation [61] and relativistic D-dimensional KG equation [62], Dirac equation [6,15,39,40,63] and spinless Salpeter equation [64].…”

Section: Introductionmentioning

confidence: 99%

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Ikhdair¹

2011

JQIS

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The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials

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“…Following the procedure stated in (Greiner, 2000;Wei & Dong 2009;Ikhdair, 2010;Ikhdair et al, 2011), the spinor wave functions can be written using the Pauli-Dirac representation as: to the total angular momentum j and its projection m on the z−axis. The orbital and pseudo-orbital angular momentum quantum numbers for SS (ℓ) and PSS (ℓ) refer to the upper (F nκ (r)) and lower (G nκ (r)) spinor components, respectively, for which ℓ(ℓ + 1)=κ(κ + 1) and ℓ(ℓ + 1)=κ(κ − 1).…”

Section: Basic Equations For the Upper-and Lower-components Of The DImentioning

confidence: 99%

Approximate Solutions of the Dirac Equation for the Rosen-Morse Potential in the Presence of the Spin-Orbit and Pseudo-Orbit Centrifugal Terms

Oyewumi¹

2012

Theoretical Concepts of Quantum Mechanics

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1 2 ) and (n − 1, ℓ + 2, j = ℓ + 3 2 ), where n, ℓ and j are the single-nucleon radial, orbital and total angular momentum quantum numbers for a single particle, respectively (Arima et al., 1969;Hecht & Adler, 1969;Ginocchio, 2004 ). The total angular momentum is given as j = ℓ + s, where ℓ = ℓ + 1 is a pseudo-angular momentum and s = 1 2 is a pseudo-spin angular momentum. Meng et al., (1998) deduced that in real nuclei, the PSS is only an approximation and the quality of approximation depends on the pseudo-centrifugal potential and pseudo-spin orbital potential. The orbital and pseudo-orbital angular momentum quantum numbers for SS ℓ and PSS ℓ refer to the upper-and lower-spinor components (for instance, F n,κ (r) and G n,κ (r), respectively. Ginocchio (1997); (1999); (2004); (2005a); (2005b) and Meng et al., (1998) showed that SS occurs when the difference between the vector potential V(r) and scalar potential S(r) in the Dirac Hamiltonian is a constant (that is, ∆(r)=V(r) − S(r)) and PSS occurs when the sum of two potential is a constant (that is, Σ(r)=V(r)+S(r)). A large number of investigations have been carried out on the SS and PSS by solving the Dirac equation with various methods (Alberto et al

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Spin and pseudospin symmetry along with orbital dependency of the Dirac–Hulthén problem

Cited by 42 publications

References 52 publications

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Approximate Solutions of the Dirac Equation for the Rosen-Morse Potential in the Presence of the Spin-Orbit and Pseudo-Orbit Centrifugal Terms

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