Perturbed Coulomb potentials in the Klein-Gordon equation via the shifted-l expansion technique

A shifted-l expansion technique is introduced to calculate the energy eigenvalues for the Klein-Gordon (KG) equation with Lorentz vector and/or Lorentz scalar potentials. Although it applies to any spherically symmetric potential, those that include Coulomb-like terms are only considered. Exact eigenvalues for a Lorentz vector or a Lorentz scalar, and an equally mixed Lorentz vector and Lorentz scalar coulombic potentials are reproduced. Highly accurate and rapidly converging ground-state energies for Lorentz vector Coulomb with a Lorentz vector or a Lorentz scaler linear potential, V(r) = -A(1)/r + kr, and V(r) = -A(1)/r and S(r) = kr, respectively, are obtained. Moreover. a simple straightforward closed-form solution for a KG-particle in coulombic Lorentz vector and Lorentz scalar potentials is presented.