N. L. Manakov

Atoms in a laser field

Abstract The method of quasienergy states (QES) for describing a quantum system in the field of a monochromatic light wave is presented. The perturbation theory for QES and quasistationary (decay) QES is developed. Various methods of obtaining approximate Green functions of valence electrons in atoms used for numerical calculations of the multiphoton-transition cross sections are discussed. On the basis of the developed formalism the variation of the atomic spectrum in an intense field, the multiphoton ionization of atoms and the influence of the light field on electron-atom and atom-atom collision processes are examined.

Analytic formulae for high harmonic generation

Analytic formulae describing harmonic generation by a weakly bound electron are derived quantum mechanically in the tunnelling limit. The formulae confirm the classical three-step model and provide an analytic explanation for oscillatory structures on the harmonic generation plateau.

Interaction of laser radiation with a negative ion in the presence of a strong static electric field

This paper provides a general theoretical description of a weakly bound atomic system (a negative ion) interacting simultaneously with two (generally strong) fields, a static electric field and a monochromatic laser field having an arbitrary elliptical polarization. The zero-range δ-potential is used to model the interaction of a bound electron in a negative ion as well as the interaction of a detached electron with the residual atom. Our treatment combines the quasistationary (complex energy) and quasienergy (Floquet) approaches. This quasistationary, quasienergy state (QQES) formalism is the most appropriate one for analysing a decaying quantum system under the influence of a periodic external perturbation. Existing QQES theory is reviewed and some new results are discussed: the Hellmann-Feynman theorem and the normalization procedure for QQES, and the definition of the dipole moment and the dynamic polarizability for a decaying atomic system (in strong static electric and/or laser fields). These results are illustrated using analytical formulae obtained from an exact solution of the QQES problem for a δ-model potential in two strong fields. Finally, from the imaginary part of the dynamic polarizability we obtain analytic results (to first order in the laser-field intensity) for the photodetachment cross section. Our results are then compared with those of previous theoretical studies.

Multiphoton detachment of a negative ion by an elliptically polarized, monochromatic laser field

The quasistationary quasienergy state approach (QQES) is applied to the analysis of partial (n-photon) decay rates and angular distributions (ADs) of photoelectrons produced by an elliptically polarized laser field. The problem is formulated for a weakly bound electron with an energy E0 in the threedimensional δ-model potential (which approximates the short-range potential of a negative ion) interacting with a strong monochromatic laser field having an electric vector F (ωt) .T he resu lts presented cover weak (perturbative), strong (nonperturbative), and superstrong field regimes as well as a wide interval of frequencies ω extending from the tunnelling (¯ hω �| E0|) and multiphoton (¯ ω |E0|). For a weak laser field, exact equations for the normalization factor and for the Fourier coefficients of the QQES wavefunction at the origin (|r |→ 0) (that are key elements of the QQES approach for a δ-model potential) as well as for the detachment amplitudes are analysed analytically using both standard Rayleigh– Schr¨ odinger perturbation theory (PT) in the intensity, I ,o f the lase rfi eld and Brillouin–Wigner PT expansions involving the exact (complex) quasienergy � . The lowest-order perturbative results for the n-photon ADs are presented in analytic form, and the parametrization of ADs in terms of polarization- and angular-independent atomic parameters is discussed for the general case of elliptical polarization. The major emphasis is on the analysis of an ellipticity induced distortion of three-dimensional ADs and, especially, on the elliptic dichroism (ED) effect, i.e. the dependence of the photoelectron yield in a fixed direction n on the sign of the ellipticity (or on the helicity) of a laser field. The dominant role of binding potential effects for a correct description of ED and threshold effects is demonstrated, and the intimate relationship between atomic ED factors and scattering phases o ft hedetached electron is established for multiphoton detachment, including the above-threshold case.

Some general properties of quasi-energetic spectra of quantum systems in classical monochromatic fields

Some general features of the quasi-energy dependence on the periodic field frequency and amplitude are examined assuming the discrete character of the quasi-energy spectrum. Jump discontinuities are found in the frequency dependence of the quasi-energy and connected with them band structure of the quasi-energies. A notion of mean energy of a system in a periodic field is introduced and relations between the mean energy and the quasi-energy are investigated. As examples the quasi-energy zones for a two-level system and a rigid rotator are calculated.

A new technique in the theory of angular distributions in atomic processes: the angular distribution of photoelectrons in single and double photoionization

Special reduction formulae for bipolar harmonics with higher ranks of internal spherical functions are derived, which will be useful in problems involving multiple expansions in spherical functions. Together with irreducible tensor operator techniques these results provide a new and effective approach, which enables one to extract the geometrical and dynamical factors from the cross sections of atomic processes with polarized particles with an accurate account of all the polarization effects. The angular distribution of polarized electrons and the circular dichroism in photoionization of polarized atoms with an arbitrary angular momentum are presented in an invariant vector form. A specific circular dichroism, which is caused by the correlation of electron and atom orientations, is discussed. The angular distribution of escaping electrons in double photoionization of unpolarized atom is presented in a simple form. A convenient parametrization is proposed for describing the dependence of the photoprocess cross sections on the polarization state of the photon beam.

Elliptic dichroism and angular distribution of electrons in two-photon ionization of atoms

The three-dimensional angular distribution of electrons in two-photon ionization of atoms by an elliptically polarized laser beam, from an initial state with arbitrary angular momentum Ji, is expressed in terms of six frequency-dependent invariant atomic parameters. The specific effect of the field polarization on the angular distribution (the elliptic dichroism, ED) is discussed for the general case of elliptic polarization. The necessary conditions for a non-zero ED are established and its physical origin is explained. The general theory is illustrated by a simple analytical calculation for the -potential model. Numerical calculations of the angular distribution parameters for H and Cs atoms are also performed and the dependence of ED magnitude on the atomic quantum numbers and the photon frequency is discussed for different frequencies.

Sturmian expansions of the relativistic Coulomb Green function

Abstract Sturmian expansion of the Coulomb Green function of the second-and first-order Dirac equations have been derived in both coordinate and momentum spaces.

Vacuum polarization by a Coulomb field. Analytical approximation of the polarization potential

The vacuum polarization by a Coulomb point centre with charge Z is evaluated to the lowest order in alpha ( alpha =e2/c) and to all orders in alpha Z. The results of numerical calculations of the polarization potential V(3+)(r) for a number of values of r and Z are given. The asymptotic expansion of V(3+)(r) for large r and also the analytical approximation of V(3+) as a function of r and Z are obtained. Values of polarization corrections to energy levels of hydrogen-like ions with main quantum numbers n=1 and 2 are given for illustration.

Relativistic electromagnetic susceptibilities of hydrogen-like atoms

Electric and magnetic susceptibilities are calculated in relativistic theory for hydrogen-like atoms. The results are the combination of the hypergeometrical function 3F2 with the unit argument. The case of small alpha Z is investigated. The method of Greens function is used in the calculations.