scholarly journals Exact Solution of the Dirac Equation for the Yukawa Potential with Scalar and Vector Potentials and Tensor Interaction

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mona Azizi ◽  
Nasrin Salehi ◽  
Ali Akbar Rajabi
Keyword(s):  
Dirac Equation ◽  
Yukawa Potential ◽  
Energy Eigenvalue ◽  
Tensor Interaction ◽  
Great Powers ◽  
Nuclear Potential ◽  
Relativistic Energy ◽  
Ansatz Method ◽  
Vector Potentials ◽  
Tensor Potential

We present exact solutions of the Dirac equation with Yukawa potential in the presence of a Coulomb-like tensor potential. For this goal we expand the Yukawa form of the nuclear potential in its mesonic clouds by using Taylor extension to the power of seventh and bring out its simple form. In order to obtain the energy eigenvalue and the corresponding wave functions in closed forms for this potential (with great powers and inverse exponent), we use ansatz method. We also regard the effects of spin-spin, spin-isospin, and isospin-isospin interactions on the relativistic energy spectra of nucleon. By using the obtained results, we have calculated the deuteron mass. The results of our model show that the deuteron spectrum is very close to the ones obtained in experiments.

scholarly journals Solutions to the Dirac Equation for Manning-Rosen Plus Shifted Deng-Fan Potential and Coulomb-Like Tensor Interaction Using Nikiforov-Uvarov Method

2018 ◽  
Vol 10 (3) ◽  
pp. 99 ◽  
Author(s):  
Hitler Louis ◽  
Ita B. Iserom ◽  
Magu T. Odey ◽  
Akakuru U. Ozioma ◽  
Nzeata-Ibe Nelson ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Energy Eigenvalue ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Special Cases ◽  
Tensor Potential ◽  
Eigen Values ◽  
Uvarov Method

We solve the Dirac equation for the Manning-Rosen plus shifted Deng-Fan potential including a Coulomb-like tensor potential with arbitrary spin–orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov–Uvarov method. Also Special cases of the potential as been considered and their energy eigen values as well as their corresponding eigen functions are obtained for both relativistic and non-relativistic scope.

scholarly journals Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

scholarly journals Eigen Spectra for q-Deformed Hyperbolic Scarf Potential Including a Coulomb-like Tensor Interaction

2011 ◽  
Vol 3 (2) ◽  
pp. 239-247 ◽  
Author(s):  
M. Eshghi ◽  
H. Mehraban
Keyword(s):  
Dirac Equation ◽  
Spin Symmetry ◽  
Tensor Interaction ◽  
Tensor Coupling ◽  
Energy Eigenvalues ◽  
Scarf Potential ◽  
Tensor Potential ◽  
Uvarov Method

We study the Dirac equation for the q-deformed hyperbolic Scarf potential including a coulomb-like tensor potential under the spin symmetry. The parametric generalization of the Nikiforov-Uvarov method is used to obtain the energy eigenvalues equation and the unnormalized wave functins.Keywords: Dirac equation; q-deformed hyperbolic Scarf; Spin symmetry; Tensor coupling.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.7295                 J. Sci. Res. 3 (2), 239-247 (2011)

Dirac equation in presence of the Hartmann and Higgs oscillator superintegrable potentials with the spin and pseudospin symmetries

2016 ◽  
Vol 31 (35) ◽  
pp. 1650190 ◽  
Author(s):  
V. Mohammadi ◽  
S. Aghaei ◽  
A. Chenaghlou
Keyword(s):  
Dirac Equation ◽  
Energy Spectra ◽  
Irreducible Representations ◽  
Relativistic Energy ◽  
Quadratic Algebras ◽  
Vector Potentials ◽  
Dirac Hamiltonian ◽  
Symmetry Algebras

The spin and pseudospin symmetries in the Dirac Hamiltonian are investigated in the presence of the Hartmann and the Higgs oscillator superintegrable potentials. The Pauli-Dirac representation is used in the Dirac equation with scalar and vector potentials of equal magnitude. Then, the Dirac equation is reduced to a Schrödinger-like equation. The symmetry algebras of the Schrödinger-like equation corresponding to the superintegrable potentials are represented. Also, the associated irreducible representations are shown by means of the quadratic algebras. Finally, the relativistic energy spectra of the Hartmann and the Higgs oscillator superintegrable potentials are calculated.

EXACTLY COMPLETE SOLUTIONS OF THE DIRAC EQUATION WITH PSEUDOHARMONIC POTENTIAL INCLUDING LINEAR PLUS COULOMB-LIKE TENSOR POTENTIAL

2011 ◽  
Vol 26 (07n08) ◽  
pp. 1363-1374 ◽  
Author(s):  
M. HAMZAVI ◽  
A. A. RAJABI ◽  
H. HASSANABADI
Keyword(s):  
Dirac Equation ◽  
Pseudospin Symmetry ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Spin Orbit Coupling ◽  
Energy Eigenvalues ◽  
Pseudoharmonic Potential ◽  
Tensor Potential ◽  
Uvarov Method ◽  
Coupling Number

In this paper, we present exact solutions of the Dirac equation with the pseudoharmonic potential including linear as well as Coulomb-like tensor potential with arbitrary spin–orbit coupling number κ under spin and pseudospin symmetry limits. The Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions in closed forms. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. Some numerical results are also given.

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