Corrections to the energy levels of a spin-zero particle bound in a strong field

Formulas for the corrections to the energy levels and wave functions of a spin-zero particle bound in a strong field are derived. The general case of the sum of a Lorentz-scalar potential and zero component of a Lorentz-vector potential is considered. The forms of the corrections differ essentially from those for spin-$\frac{1}{2}$ particles. As an example of application of our results, we evaluated the electric polarizability of a ground state of a spin-zero particle bound in a strong Coulomb field.

Figure 1

Polarizability in units ${\left(m\alpha \right)}^{-3}{Z}^{-4}$ as a function of $Z\alpha$.