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Analytical expressions and numerical results describing ionization of atoms by intense linearly polarized ultrashort laser pulses are obtained in the frame of the Keldysh approach. Photoelectron spectra and total ionization probabilities are presented for several analytical models of a single-cycle laser pulse. In particular, strong left–right asymmetry of the spectra is shown for the case of odd pulses.

A Coulomb correction to the rate of multiphoton ionization of atoms and positive ions in intense high-frequency laser fields is found using the imaginary time method for a subbarrier trajectory and Kapitza method for description of motion in a rapidly oscillating field. The obtained results cover the domain of parameters opposite to the well-studied low-frequency tunneling limit. We show that the Coulomb correction enhances the ionization rate up to several orders in magnitude. Application of the obtained results for description of multiphoton ionization in intense ultraviolet laser pulses is briefly discussed.

Relativistic generalization of the semiclassical theory of tunnel and multiphoton ionization of atoms and ions in the field of a high-intensity electromagnetic wave (Keldysh theory) with linear and elliptic polarizations is developed. The exponential factor in the ionization rate of relativistic bound state is calculated for arbitrary values of the adiabaticity parameter γ . In the case of low-frequency laser radiation, γ ≪ 1 , the asymptotically exact formula is derived for the ionization rate of atomic s -level, including the Coulomb, spin and adiabatic corrections and the pre-exponential factor. The ionization rate of the ground state of a hydrogen-like atoms (ions) with Z ≲ 100 is calculated, depending on laser intensity and ellipticity of radiation.

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.

We present the theoretical calculation of photodetachment rate of loosely bound atomic states in an intense circularly polarized monochromatic laser field. Different calculation methods are used: the perturbation theory with respect to laser field intensity, the semiclassical approximation and the exact numerical solution of transcendental equation for complex quasienergy of an atomic level. In the last case we use the regularization method for divergent integrals with Gamow wave function proposed by Zel'dovich. We present the comparison of semiclassical and exact results and discuss the accuracy of semiclassical approximation in the theory of ionization. Results are applied for the calculation of photodetachment rate for negative ions of hydrogen and alkali metals.

We present the relativistic version of the imaginary time method (ITM). The ionization probability w of the bound state under the action of electric and magnetic fields (for the case when the binding energy Eb is comparable with mc2) has been calculated using the ITM. The formulae obtained cover both the ionization of nonrelativistic bound systems (atoms, ions) and the case of Eb = 2mc2, when w is compared with the probability of electron-positron pair production from vacuum in a strong field.

Using the “imaginary time” method we have calculated (in the quasiclassical approximation) the probability of ionization of the atomic s-state in static electric and magnetic fields. The Coulomb interaction between the emitted electron and the atomic remainder is taken into account. The results obtained are valid for external fields T and H which are smaller than characteristic atomic fields. The case of mutually orthogonal fields (the Lorentz ionization) is carefully studied.

Using the 1 n - expansion , we obtain analytic formulae for the bound state radial wave functions, including its asymptotic coefficients at r → 0 and r → ∞, for an arbitrary smooth potential V(r). The formulae are asymptotically exact in the limit nr → ∞ (n = nr + l + 1 is the principal quantum number and the expansion parameter is 1 n ). Comparison with exact solutions and numerical calculations for the power-law and short-range potentials show that the applicability region of these formulae is usually prolonged up to small quantum numbers, n ∼ 1. With growing nr, the accuracy of the formulae decreases, but the WKB method becomes applicable in this case.

The modified matching conditions for quasiclassical wave functions on both sides of a turning point for the radial Schrodinger equation have been obtained. They differ significantly from the usual Kramers condition which holds for the one-dimensional case. Namely, the ratio C 2 C 1 in the subbarrier and the classical allowed regions is not a universal constant ( C 2 C 1 = 1 2 , as usual), but depends on the values of the orbital angular momentum l, energy E and on the behaviour of the potential V(r) at r → 0. The comparison with exact and numerical solutions of the Schrodinger equation shows that the modified matching conditions not only make the quasiclassical approximation in the subbarrier region asymptotically exact within the n → ∞ limit, but also considerably enhances its accuracy even in the case of small quantum numbers, n ∼ 1. The power-law, funnel and short-range potentials are considered in detail.