V. S. Popov

Energy and momentum spectra of photoelectrons under conditions of ionization by strong laser radiation (The case of elliptic polarization)

Analytical and numerical studies are made into the momentum distribution and energy spectra of photoelectrons emitted during nonlinear ionization of atoms and molecules by laser radiation with elliptic polarization. The dependence of these distributions on the ellipticity ξ of an electromagnetic wave is treated, as well as their evolution upon variation of the Keldysh parameter γ from the region of optical tunneling (γ≪1) to the region of γ≫1, in which the ionization is multiphoton. The quasiclassical approximation is used in the calculations, in particular, the imaginary-time method and the saddle-point method with expansion in the vicinityof the field ellipse.

Strong field ionization rate for arbitrary laser frequencies.

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.

Relativistic version of the imaginary-time formalism

A relativistic version of the quasiclassical imaginary-time formalism is developed. It permits calculation of the tunneling probability of relativistic particles through potential barriers, including barriers lacking spherical symmetry. Application of the imaginary-time formalism to concrete problems calls for finding subbarrier trajectories which are solutions of the classical equations of motion, but with an imaginary time (and thus cannot be realized in classical mechanics). The ionization probability of an s level, whose binding energy can be of the order of the rest energy, under the action of electric and magnetic fields of different configuration is calculated using the imaginary-time formalism. Besides the exponential factor, the Coulomb and pre-exponential factors in the ionization probability are calculated. The Hamiltonian approach to the tunneling of relativistic particles is described briefly. Scrutiny of the ionization of heavy atoms by an electric field provides an additional argument against the existence of the “Unruh effect.”

Quasiclassical theory of atomic ionization in electric and magnetic fields

Abstract 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.

Ionization of atoms in electric and magnetic fields and the imaginary time method

A semiclassical theory is developed for the ionization of atoms and negative ions in constant, uniform electric and magnetic fields, including the Coulomb interaction between the electron and the atomic core during tunneling. The case of crossed fields (Lorentz ionization) is examined specially, as well as the limit of a strong magnetic field. Analytic equations are derived for arbitrary fields ℰ and ℋ that are weak compared to the characteristic intraatomic fields. The major results of this paper are obtained using the “imaginary time” method (ITM), in which tunneling is described using the classical equations of motion but with purely imaginary “time.” The possibility of generalizing the ITM to the relativistic case, as well as to states with nonzero angular momentum, is pointed out.

ON MATCHING CONDITIONS IN THE WKB METHOD

Abstract 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.

Multiphoton ionization of atoms and ions by high-intensity X-ray lasers

Coulomb corrections to the action function and rate of multiphoton ionization of atoms and ions in a strong linearly polarized electromagnetic field are calculated for high values of the Keldysh adiabaticity parameter. The Coulomb corrections significantly increase the ionization rate for atoms (by several orders of magnitude). An interpolation formula proposed for ionization rate is valid for arbitrary values of the adiabaticity parameter. The high accuracy of the formula is confirmed by comparison with the results of numerical calculations. The general case of elliptic polarization of laser radiation is also considered.

RELATIVISTIC VERSION OF THE IMAGINARY TIME METHOD

Abstract 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.

Contribution to the theory of Lorentzian ionization

The probability wL of Lorentzian ionization, which arises when an atom or ion moves in a constant magnetic field, is calculated in the quasiclassical approximation. The nonrelativistic (v≲e2/ℏ=1, v is the velocity of the atom) and ultrarelativistic (v→c=137) cases are examined and the stabilization factor S, which takes account of the effect of the magnetic field on tunneling of an electron, is found.

The imaginary-time method for relativistic problems

A relativistic version of the imaginary-time method is presented. The method is used to calculate the probability w of ionization of a bound state by electric and magnetic fields of various configurations (including the case when the binding energy Eb is comparable to mc2). The formulas cover as limiting cases both the ionization of nonrelativistic bound systems (atoms and ions) and the case Eb=2mc2, when w equals the probability of electron-positron pair production from the vacuum in the presence of a strong field.