Decay of a weakly bound level in a monochromatic electromagnetic field and a static magnetic field

We consider an electron that is bound by a zero-range potential and a constant magnetic field and which becomes disturbed by a monochromatic laser beam with elliptical polarization. The exact solution of the Schrödinger equation for an electron in the presence of an arbitrary electromagnetic wave and a static magnetic field is obtained. Exact expressions have been found for the complex energy, whose real and imaginary parts yield the level position and the width of an electron in a zero-range force field, a constant magnetic field, and a monochromatic electromagnetic field. These expressions have been analyzed in details for the case of a circularly polarized laser light.