Ionization by intense laser radiation under the action of quantizing magnetic field

A transcendental equation for the complex energy has been obtained on a basis of an exactly solvable $3D$ model for a short-range potential and the Green's function in an intense electromagnetic field combining a constant magnetic field and the field of a circulary polarized wave. Parameters of the quasistationary states of an electron in the $\delta$-potential with consideration for an intense external field of complicated configuration have been calculated. Possible stabilization of the decay of a spinor and a scalar particles in the bound state by means of an intense magnetic field has been cleared up. It is argued that with consideration for the results obtained, the commonly accepted idea of the stabilizing role of a strong magnetic field in the atom ionization should be revised.