Solutions for a generalized Woods–Saxon potential

Gönül, B.; Köksal, Koray

doi:10.1088/0031-8949/76/5/026

Cited by 26 publications

(45 citation statements)

References 31 publications

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“…(23) [44][45][46] provides the flexibility to construct the surface structure of the related nucleus [72]. Thus, the non-relativistic solutions obtained in [44][45][46] are only reasonable for the hyperbolic [73,74] exponential (RM) potential 1 , not WS potential.…”

Section: Discussionmentioning

confidence: 99%

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Ikhdair

Sever

2010

Open Physics

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Abstract:We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin-and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper-and lower-spinor components of two Dirac particles. The special cases κ = ±1 ( = = 0 -wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.

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Section: Discussionmentioning

confidence: 99%

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Ikhdair

Sever

2010

Open Physics

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“…In contrast to these reports, however, the work in Ref. [3] clearly proved that neither the spherically symmetric usual W-S potential nor its generalized form in there have a closed analytical solution even in one dimension for 0  , which is also in agreement with the results of [12,13].…”

Section: Introductionmentioning

confidence: 72%

“…From the standpoint of a refined W-S functional form, the work in Ref. [3] has investigated the mathematical structure of a physically plausible single-particle potential which seems more accurate and applicable to a wider nuclidic region than attained before considering the related exhaustive study in Ref. [4].…”

Section: Introductionmentioning

confidence: 99%

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Remarks on the Woods–Saxon potential

Capak

Gönül

2016

Mod. Phys. Lett. A

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More recently, comprehensive application results of approximate analytical solutions of the Woods-Saxon potential in closed form for the 5-dimensional Bohr Hamiltonian have been appeared [14] and its comparison to the data for many different nuclei has clearly revealed the domains for the sucsess and failure in case of using such potential forms to analyse the data concerning with the nuclear structure of deformed nuclei within the frame of the collective model. Gaining confidence from this work, exact solvability of the Woods-Saxon type potentials in lower dimensions for the bound states having zero angular momentum is carefully reviewed to finalize an ongoing discussion in the related literature and clearly shown that such kind of potentials have no analytical solutions even for 0  case.

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“…Furthermore, the exactly or quasi-exactly solutions of the Woods-Saxon type potential for the wave equations (Schrödinger, Dirac, Klein-Gordon) are of high scientific importance in the conceptual understanding of the interactions between the nucleon and the nucleus for both the bound and resonant states. The modified version of the Woods-Saxon potential consists of the volume (standard) Woods-Saxon and its derivative called the Woods-Saxon surface potential and is given by [11][12][13][14][15]:…”

Section: Introductionmentioning

confidence: 99%

Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019

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In this paper, the approximate analitical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well V 0 and W , the radial n r and l orbital quantum numbers and parameters D, a, R 0 are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a 56 F e nucleus are calculated in D = 2 and D = 3, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of D = 2 and D = 3.

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Solutions for a generalized Woods–Saxon potential

Cited by 26 publications

References 31 publications

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

Remarks on the Woods–Saxon potential

Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

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