  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_{Coul}=-\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.
