{\kappa} state solutions for the fermionic massive spin-1/2 particles interacting with double ring-shaped Kratzer and oscillator potentials

摘要

In recent years, an extensive survey on various wave equations ofrelativistic quantum mechanics with different types of potential interactionshas been a line of great interest. In this regime, special attention has beengiven to the Dirac equation because the spin-1/2 fermions represent the mostfrequent building blocks of the molecules and atoms. Motivated by theconsiderable interest in this equation and its relativistic symmetries (spinand pseudospin) in the presence of solvable potential model, we attempt toobtain the relativistic bound states solution of the Dirac equation with doublering-shaped Kratzer and oscillator potentials under the condition of spin andpseudospin symmetries. The solutions are reported for arbitrary quantum numberin a compact form. the analytic bound state energy eigenvalues and theassociated upper- and lower-spinor components of two Dirac particles have beenfound. Several typical numerical results of the relativistic eigenenergies havealso been presented. We found that the existence or absence of the ring shapedpotential potential has strong effects on the eigenstates of the Kratzer andoscillator particles with a wide band spectrum except for thepseudospin-oscillator particles where there exist a narrow band gap.