Spin and Pseudospin Symmetries with Trigonometric Pöschl-Teller Potential including Tensor Coupling

M Hamzavi,A A Rajabi

doi:10.1155/2013/196986

Abstract

We study approximate analytical solutions of the Dirac equation with the trigonometric Pöschl-Teller (tPT) potential and a Coulomb-like tensor potential for arbitrary spin-orbit quantum number <i >κ</i> under the presence of exact spin and pseudospin (<svg style="vertical-align:-3.50804pt;width:10.2px;" id="M1" height="13.3" version="1.1" viewBox="0 0 10.2 13.3" width="10.2" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,8.863)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" /></g> </svg>-spin) symmetries. The bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. The case of nonrelativistic limit is studied too.

Highlights

The Dirac equation, which describes the motion of a spin1/2 particle, has been used in solving many problems of nuclear and high-energy physics
Within the framework of Dirac equation, pspin symmetry used to feature the deformed nuclei and the super deformation to establish an effective shell-model [2,3,4], whereas spin symmetry is relevant for mesons [5]
The p-spin symmetry refers to a quasidegeneracy of single nucleon doublets with nonrelativistic quantum number (n, l, j = l + 1/2) and (n − 1, l + 2, j = l + 3/2), where n, l, and j are single nucleon radial, orbital, and total angular quantum numbers, respectively [8, 9]

Summary

Introduction

The Dirac equation, which describes the motion of a spin1/2 particle, has been used in solving many problems of nuclear and high-energy physics. Zhou et al solved Dirac equation approximately for Hulthen potential including Coulomb-like tensor potential with arbitrary spin-orbit coupling number κ under spin and pseudospin symmetry limit [10]. Aydogdu and Sever solved approximately for the Woods-Saxon potential and a tensor potential with the arbitrary spin-orbit coupling quantum number κ under pseudospin and spin symmetry [23]. In the presence of the spin and p-spin symmetry, the approximate energy eigenvalue equations and corresponding two-component wave functions of the DiractPT problem are obtained, and effect of tensor potential is shown .

Dirac Equation including Tensor Coupling

Concluding Remarks