Research with lasers of extremely high intensity has been proposed in terms of tunneling and the “Schwinger Limit”, which refers to breakdown of the vacuum into electron-positron pairs caused by a static or quasistatic electric field. The difficulty is that lasers produce transverse fields, wherein the electric and magnetic fields form a mutually orthogonal triad with the direction of propagation. Tunneling, including the Schwinger Limit, relates to longitudinal fields, in which the direction of the electric field vector is the only preferred direction. Transverse fields propagate indefinitely without inputs from source or current distributions. By contrast, longitudinal fields require continuing contributions from external source or current distributions. Failure to distinguish between longitudinal and transverse fields is consequential in that some proposed applications of very high intensity lasers pertain only to tunneling processes, but not to laser fields. A related difficulty is the flawed notion that tunneling constitutes a low-frequency limit of laser-induced processes. A counter-indication is that the ponderomotive potential of a charged particle in a laser field is proportional to the inverse square of the field frequency. Thus there is no possible approach to a zero-frequency laser field. The Göppert-Mayer gauge transformation of atomic physics makes possible a limited correspondence between transverse and longitudinal fields. The correspondence fails at both high and, most importantly, at low field frequencies. Vacuum pair production does not require the Schwinger Limit, but can be achieved at much lower intensities.
Different types of relativistic effects in atomic photoionization are shown to have frequency-dependent onset intensities. These phenomena can be explored analytically with the Strong-Field Approximation (SFA), which becomes accurate without need for rescattering corrections when intensities are high enough to be relativistic. Specially interesting results are that electron spin-flip amplitudes and virtual pair creation become important at intensities often not considered to be relativistic. The stabilization effect wherein transition rates decline with increasing intensity is strongly enhanced by relativity when the laser is linearly polarized. With linearly polarized light, photoelectron spectra exhibit a strong displacement towards the 'hotter' or higher-energy end of the spectrum; and both spectra and total transition rates, if calculated nonrelativistically, can be seriously in error for laser intensities I greater than 1 a.u. at typical intense-laser frequencies.
A simple analytical approximation is obtained for ionization rates of atoms exposed to a strong, linearly polarized plane-wave field. Coulomb interaction between the ejected electron and the atomic core is taken into account in the frames of semi-classical perturbation theory. In the previous paper we introduced an analytical simple solution for an unbound electron in the simultaneous presence of a Coulomb potential and a circularly polarized plane-wave electro-magnetic field. Here we consider the Coulomb-Volkov correction in the case of a linearly polarized field using so called strong field approximation (SFA).