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

TL;DR

This paper analyzes scattering phase shifts and energy spectra of fermionic particles in a hyperbolical potential using the Dirac equation, highlighting the influence of symmetry constants and quantum numbers.

Contribution

It provides approximate solutions for scattering states with pseudospin and spin symmetries, including phase shifts and energy spectra, using a functional analytical approach.

Findings

Symmetry constants significantly affect scattering phase shifts.

Energy spectra depend on spin-orbit quantum numbers.

Results demonstrate the impact of pseudospin and spin symmetries on scattering properties.

Abstract

In this paper, we studied the approximate scattering state solutions of the Dirac equation with the hyperbolical potential with pseudospin and spin symmetries. Using a suitable short range approximation 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 (C_ps and C_s) and the spin-orbit quantum number \k{appa} affect scattering phase shifts significantly.