Relativistic Energies and Scattering Phase Shifts for the Fermionic Particles Scattered by Hyperbolical Potential with the Pseudo(spin) Symmetry

K J Oyewumi,O J Oluwadare

doi:10.1155/2017/1634717

Abstract

In this paper, we studied the approximate scattering state solutions of the Dirac equation with the hyperbolical potential with pseudospin and spin symmetries. By applying an improved Greene-Aldrich approximation scheme within the formalism of functional analytical method, we obtained the spin-orbit quantum numbers dependent scattering phase shifts for the spin and pseudospin symmetries. The normalization constants, lower and upper radial spinor for the two symmetries, and the relativistic energy spectra were presented. Our results reveal that both the symmetry constants (Cps and Cs) and the spin-orbit quantum number κ affect scattering phase shifts significantly.

Highlights

Scattering theory is very central to the study of several fields such as atomic, nuclear, high energy or condensed matter physics
Complete information about the quantum systems can only be obtained by investigating scattering state solutions of relativistic and nonrelativistic equations with quantum mechanical potential model
Several authors in quantum mechanics have strictly followed different approaches to study the scattering state solutions of the relativistic and nonrelativistic wave equations for central and noncentral potential models [8,9,10,11,12,13,14,15]. They have reported the calculations on phase shifts, transmission and reflection coefficients, resonances, normalized radial wave functions and properties of S-matrix for potential models of their interest

Summary

Introduction

Scattering theory is very central to the study of several fields such as atomic, nuclear, high energy or condensed matter physics. Several authors in quantum mechanics have strictly followed different approaches to study the scattering state solutions of the relativistic and nonrelativistic wave equations for central and noncentral potential models [8,9,10,11,12,13,14,15]. In their works, they have reported the calculations on phase shifts, transmission and reflection coefficients, resonances, normalized radial wave functions and properties of S-matrix for potential models of their interest.

The Basic Equations

Relativistic Scattering State Solutions

Discussion and Conclusion

Disclosure