Bound state solutions of the Dirac equation with the Deng—Fan potential including a Coulomb tensor interaction

Ortakaya, Sami; Hassanabadi, H.; Yazarloo, B. H.

doi:10.1088/1674-1056/23/3/030306

Cited by 15 publications

(11 citation statements)

References 32 publications

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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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“…Arda and Sever 3 studied bound state solutions of Dirac equation for Kratzer potential with pseudo-scalar Coulomb term. Ortakaya et al 61 investigated bound state solutions of Dirac equation with Deng–Fan potential including a Coulomb tensor interaction within the framework of asymptotic iteration method where they presented their numerical results for spin and pseudospin limits. A lot of research work have been carried out by Ikot and co-authors on Dirac equation as seen in Refs 62 , 63 .…”

Section: Introductionmentioning

confidence: 99%

Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

Okon

Omugbe

Antia

et al. 2021

Sci Rep

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In this research article, the modified approximation to the centrifugal barrier term is applied to solve an approximate bound state solutions of Dirac equation for spin and pseudospin symmetries with hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential using parametric Nikiforov–Uvarov method. The energy eigen equation and the unnormalised wave function were presented in closed and compact form. The nonrelativistic energy equation was obtain by applying nonrelativistic limit to the relativistic spin energy eigen equation. Numerical bound state energies were obtained for both the spin symmetry, pseudospin symmetry and the non relativistic energy. The screen parameter in the potential affects the solutions of the spin symmetry and non-relativistic energy in the same manner but in a revised form for the pseudospin symmetry energy equation. In order to ascertain the accuracy of the work, the numerical results obtained was compared to research work of existing literature and the results were found to be in excellent agreement to the existing literature. The partition function and other thermodynamic properties were obtained using the compact form of the nonrelativistic energy equation. The proposed potential model reduces to Hulthen and exponential inversely quadratic potential as special cases. All numerical computations were carried out using Maple 10.0 version and Matlab 9.0 version softwares respectively.

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“…Hassanabadi et al analyzed the relativistic spinless particles under Deng-Fan potential [28]. By using the asymptotic iteration method, Ortakaya et al [29] obtained the approximate analytical solutions of the Dirac equation with the Deng-Fan potential including a Coulomb tensor interaction in the presence of spin symmetry and pseudo-spin symmetry. In 2009, Zhang et al [30] obtained the approximate analytical solutions of the Dirac equation with the generalized Morse potential model in the presence of spin symmetry and pseudo-spin symmetry by using the supersymmetric shape invariance formalism.…”

Section: Introductionmentioning

confidence: 99%

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

Maireche

2022

Rev. Mex. Fís.

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In this paper, we investigate the new approximate bound state solution of deformed Klein--Gordon, Dirac and Schr\"{o}dinger equations in the symmetries of extended relativistic quantum mechanics ERQM and extended nonrelativistic quantum mechanics ENRQM have been obtained with a newly proposed potential called improved Hellmann-generalized Morse potential (IHGMP, for short). To the best of our knowledge, this problem is examined in literature in the usual RQM and NRQM with Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential, generalized Morse or Deng-Fan potential, and some other exponential terms. By employing the improved approximation to deal with the centrifugal term, Bopp's shift and standard perturbation theory method. The new approximate analytical energy shift and the corrections of bound state energyeigenvalues in ERQM and ENRQM are obtained for some selected diatomic molecules such as (HCl, LiH, H2, ScH, TiH, VH, CrH, CuLi, TiC, NiC, ScN and ScF). The new values that we get appeared sensitive to the quantum numbers $% \left( j,l,s,m\right) $, the potential depths of the improved Hellmann-generalized Morse potential ($a,b$), the range of the potential $%\alpha $, the dissociation energy $D_{e}$, the equilibrium bond length $%r_{e} $, and noncommutativity parameters$\left( \Theta ,\sigma ,\chi \right)$ . We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first physical phenomena are the perturbative spin-orbit coupling, the second the magnetic induction while the third corresponds to the rotational proper phenomena. In both relativistic and nonrelativistic problems, we show thatthe corrections on the spectrum energy are smaller than the main energy in the ordinary cases of quantum field theory and quantum mechanics. In the new symmetries of NCQM, it is not possible to get the exact analytical solutions for $l=0$ and $l\neq 0$, the approximate solutions are available. Four special cases, i.e., l wave are investigated in the context of deformed Klien-Gordon and Schr\"{o}dinger theories. The relativistic energy equations and the new nonrelativistic energy for some potentials such as improved Hellmann potential and improved generalized Morse potential have also been obtained by varying some potential parameters. We have clearly shown that the Schr\"{o}dinger and Klein Gordon equations in the new symmetries canphysically describe each of the two Dirac equations and the Duffin--Kemmer equation under the effect of IHGMP.

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Bound state solutions of the Dirac equation with the Deng—Fan potential including a Coulomb tensor interaction

Cited by 15 publications

References 32 publications

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

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