Spherical Model of the Stark Effect in External Scalar and Vector Fields

Abstract

The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of quasistationary level are generalized by taking into account the relativistic effects, spin and Lorentz structure of interaction potentials. The relativistic quasi-classical theory of ionization of the Coulomb system ($V_C=-\xi/r$) by radial-constant long-range scalar ($S_{l.r.}=(1-\lambda)(\sigma r+V_0)$) and vector ($V_{l.r.}=\lambda(\sigma r+V_0)$) fields is constructed. In the limiting cases the approximated analytical expressions for the position $E_r$ and width $\Gamma$ of below-barrier resonances are obtained. The strong dependence of the width $\Gamma$ of below-barrier resonances on both the bound level energy and the mixing constant $\lambda$ is detected. The simple analytical formulae for asymptotic coefficients of the Dirac radial wave functions at zero and infinity are also obtained.