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

Abstract

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.

A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

“…In relativistic quantum mechanics, one of the interesting problems is to obtain exact solutions of the Klein-Gordon equation (spin zero particle) and Dirac equation (spin ½ particle) at high energy, much interest in providing analytic solutions to the relativistic equations in many fields of Physics and Chemistry for different central and non central potentials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The quantum structure based to the ordinary canonical commutations relations in both Schrödinger and Heisenberg (the operators are depended on time) pictures, respectively (Natural units (3) here Ĥ denote to the ordinary quantum Hamiltonian operator.…”

“…The quantum structure based to the ordinary canonical commutations relations in both Schrödinger and Heisenberg (the operators are depended on time) pictures, respectively (Natural units (3) here Ĥ denote to the ordinary quantum Hamiltonian operator. In addition, for spin ½ particles described by the Dirac equation, experiment tells us that must satisfy Fermi Dirac statistics obey the restriction of Pauli, which imply to gives the only non-null equal-time anti-commutator for field operators as follows: [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Revised: 2016-11-16 doi:10.18052/www.scipress.com/IFSL. 10.8 Accepted: 2016-11-30 2016SciPress Ltd., Switzerland Online: 2016 SciPress applies the CC- .…”

A New Approach for Parameters of Nucleon-Nucleon Scattering at Low Energies in One and Two Dimensions

“…With the equation (16) leads to the generalized form of hypergeometric type given in equation (7): (19) where (20) Comparing equation (19) with equation (7) yields the corresponding polynomials as follows: (21) Substituting these polynomials in equation (13), π(s) can be achieved as: (22) with (23) 4 Volume 3 and (24) The constant K is determined according to the rule that the expression under the square root must be square of a polynomial and since in equation (15) must have a negative derivative, the most appropriate answer for π(s) i:…”

“…The Woods-Saxon potential which is one of the most important and acceptable central potentials in nuclear physics is defined as [21]:…”

Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model

“…This model receives great attention for it plays an important role in high energy and particle physics, atomic physics, chemical physics, gravitational plasma physics and solid state physics. In solid state physics and atomic physics, its named the Thomas-Fermi or screened Coulomb potential while in plasma physics it is known as the DebyeHückel potential [11,12].…”