Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

Abstract

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

“…It is shown that in general the single-particle energies increase with ω 2 , as ω 2 2 appears in the right hand side of Eq. (104). More importantly, the pseudospin-up states with j > =l + 1/2 increase faster than the pseudospindown states j < =l − 1/2.…”

“…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 …”

“…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]…”

Solution of the κ-Deformed Dirac Equation with Vector and Scalar Interactions in the Context of Spin and Pseudospin Symmetries

“…The resulting algebra of this contraction is a standard real Hopf algebra and depends on a dimension-full parameter κ instead of q. Since then, the algebraic structure of the κ -deformed Poincaré algebra has been investigated intensively and have become a theoretical field of increasing interest [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] . Through the field equations from the κ-Poincaré algebra (κ-Dirac equation [22][23][24]), we can study the physical implications of the quantum deformation parameter κ in relativistic and nonrelativistic quantum systems.…”

“…[32,33]). Some studies have been developed taking into account the spin and pseudospin symmetry limits to study relativistic dynamics of physical systems interacting with a class of potentials [34][35][36][37][38][39][40][41]. The present work is proposed to investigate the κdeformed Dirac equation derived in Refs.…”