Relativistic tunneling effect under ionization of multiply charged ions in multi-petawatt laser beams

The possibility of observing the relativistic tunneling effect under the ionization of multiply charged ions of heavy atoms in the field of multi-petawatt laser beams is discussed. An approximate analytical formula is obtained that makes it possible to estimate the change in the ionization rate of deep levels under the influence of a strong quasi-static electromagnetic field under conditions close to saturation. It is shown that the Zeeman level shift and the relativistic curvature of the sub-barrier electron trajectory in the magnetic field of a laser wave lead to the corrections in the ionization probability that are close in magnitude. These corrections become significant only at laser radiation intensities of at least 2 × 10²³ W/cm², which are expected to be attained at multi-petawatt laser facilities, including the XCELS facility. The principal scheme of the experimental observation of the deviation of the ionization rate from the values predicted by the nonrelativistic theory is discussed.