A simple, analytical, nonrelativistic ionization rate formula for atoms and positive ions in intense ultraviolet and x-ray electromagnetic fields is derived. The rate is valid at arbitrary values of the Keldysh parameter and confirmed by results from ab initio numerical solutions of the single active electron, time-dependent Schrödinger equation. The proposed rate is particularly relevant for experiments employing the new free electron laser sources.

The probability of electron-positron pair creation by a focused laser pulse is calculated. For description of the focused laser pulse we use a 3-dimensional model of the electromagnetic field which is based on an exact solution of Maxwell equations. There exists two types of focused waves: e-and h-polarized waves with only either electric, or magnetic vector being transverse respectively. It is shown that pair production is possible only in e-polarized electromagnetic wave. The dependence of the pair production probability on the intensity of the laser pulse is obtained. It is argued that there exists a natural physical limit for attainable focused laser pulse intensities. This limit is posed by the pulse energy loss due to the effect of pair creation.

Problem is considered of spontaneous creation of electron-positron pairs from the vacuum induced by external electric field, that is homogeneous and depends on time in an arbitrary way. The Heisenberg equations of motion are obtained for the creation-annihilation operators. The solution is a linear canonical transformation. The problem is reduced to a set of differentialequationsforthe second-order matrices determining this transformation. A consequence of the CP symmetry of the Dirac equation with an external electric field is that the efe-pair is created from the vacuum in a state with total spin 1. The cane when the variating electric field conserves its direction, is considered in more detail. In this caae the equations are much simplified and may be reduced to the Riccati equation or to problem of oscillator with variable frequency, so the problem is equivalent to the one-dimensional quanta1 problem of a barrier penetration. Two approximate methods to calculate the pair creation probabilities are discussed: the quasiclassical approach and the antiadiabatical method, applicable for sharp variations of the external field. Numerical estimates are obtained for the number of efe-pairs produced by the field E(1) = E cos wt. Group-theoretical aapecta of the problem are also considered.

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