Relativistic Scattering States of the Hellmann Potential

Abstract

The Dirac equation [1] has become the most appealing relativistic wave equation in the eld of mathematical physics for spin-1/2 particles. One of the interesting problems in the Dirac equation is the concept of spin and pseudospin symmetries. These symmetries of the Dirac Hamiltonian were discovered many years ago. However, the spin and pseudospin symmetries have been recently recognized empirically in nuclear and hadronic spectroscopies. The solution of the Dirac equation with mixed potentials for particles such as atoms, nuclei and hadrons play a central role in a realistic nuclear system. In order to investigate the nuclear shell structure, the study of the pseudospin and spin symmetric solutions of the Dirac equation has been an important area of research in nuclear physics. However, spin symmetry is relevant to mesons [2], and the pseudospin symmetry refers to a quasi-degeneracy of single nucleon doublets [3, 4]. Recently, many works have been done to solve the Dirac equation so to obtain the energy equation and the twocomponent spinor wave functions [5 18]. In the recent years, investigation of scattering states properties of nonrelativistic and relativistic wave equations in quantum mechanics has been in great attention. In order to understand the studied quantum system completely, we should study the both bound states and the scattering states for a given quantum system. In the present work, we deal with the solution of scattering state of the Dirac equation for spin and pseudospin symmetries with the Hellmann potential which is the superposition of the Coulomb and Yukawa potentials and de ned as [19]: