High-order perturbation theory for the hydrogen atom in a magnetic field

The states of a hydrogen atom with principal quantum numbers n⩽3 in a constant uniform magnetic field ℋ are studied. Coefficients in the expansion of the energy of these states in powers of ℋ² up to the 75th order are obtained. Series for the energies of the states and the wave functions are summed to values of ℋ on the order of the atomic magnetic field. A generalization of the moment method upon which these calculations are based can be used in other cases in which a hydrogen atom is perturbed by a potential with a polynomial dependence on the coordinates. Zh. éksp. Teor. Fiz. 113, 550–562 (February 1998)     

Diffraction of the wave packet of a three-level Λ atom in the field of a multifrequency standing light wave

The diffraction of the wave packet of a three-level atom in a multifrequency optical radiation field is studied. A new type of coherent beam splitter for atoms that employs the scattering of a wave packet in the field of four standing light waves with different spatial shifts is proposed on this basis. It is shown that this interaction scheme makes it possible to obtain large splittings (>100ℏk) of the wave packet of a three-level Λ atom in momentum space into only two coherent components. In addition, the atoms in these coherent components are in long-lived atomic states, which substantially simplifies the experimental implementation of such a splitter. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 386–391 (25 September 1997)     

Subbarrier conversion in 125Te45+

We discuss the process of resonant subbarrier internal conversion of γ rays, where the converted electron is transferred to one of the atomic orbitals. For the first time we study how this process is affected by residual interactions: the splitting of the atomic terms in the total angular momentum of the atom, configuration mixing, and the magnetic interaction between the electrons of the atom. The calculations are done by the relativistic multiconfiguration Dirac-Fock method with allowance for the Breit interaction for the M1 transition with an energy of 35 492 eV in multiply charged ions of ¹²⁵Te. We show that allowing for the residual interaction is obligatory if we want to calculate the conversion rate in the vicinity of a resonance correctly. Zh. éksp. Teor. Fiz. 116, 1565–1574 (November 1999)     

Perturbation of atomic energy levels by a metal surface

The energy level shifts of one-electron atomic particles H, He⁺, Li⁺⁺, etc. which interact with a metal surface have been investigated. In the approximation of image charges, an operator describing perturbations of atomic levels has been obtained. By numerically solving the Schro dinger equation, we have calculated energy levels of H(1s), H*(n=2), and C⁵⁺(n) as functions of the distance between an atom and surface. Asymptotic behavior of atomic levels at large distances from the surface has been studied. The linear Stark effect for excited states, which was earlier mentioned by A. V. Chaplik, has been found and investigated in detail. Zh. éksp. Teor. Fiz. 116, 236–256 (July 1999)     

The polarization-angular structure and elliptical dichroism of the cross sections for three-photon bound-bound transitions in atoms

Using the electric dipole approximation, we present, in invariant form, the cross section of an arbitrary three-photon transition between the discrete states of an atom with total angular momenta J _i and J _f. The cross section contains scalar and mixed products of the photon polarization vectors, and invariant atomic parameters dependent only on the photon frequencies. We determine the number of independent atomic parameters at fixed values of J _i and J _f and obtain their explicit expressions in terms of the reduced composite dipole matrix elements. The polarization dependence of the cross sections is expressed in terms of the degrees l and ξ of linear and circular photon polarizations. We analyze the phenomenon of dissipation-induced circular dichroism in three-photon processes, i.e., the difference Δ of the cross sections for opposite signs of the degree of circular polarization of all the photons. We study in detail the case of two identical photons and the phenomenon of elliptical dichroism, when Δ∼lξ holds and dichroism occurs only when the photons are elliptically polarized, with 0<|ξ|<1. Finally, we discuss the dissipation-induced effects of atom polarization in three-photon processes involving linearly polarized or unpolarized photons. Zh. éksp. Teor. Fiz. 111, 1984–2000 (June 1997)     

Born Reciprocity and the 1/r Potential

Many structures in nature are invariant under the transformation pair, (p,r)→(b  r,−p/b), where b is some scale factor. Born’s reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale b≡mΩ. We find that an Ω∼1.5×10⁻¹⁵ s⁻¹ has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.     

Annihilation of a relativistic positron and K-electron to yield a photon and second K-electron

We study the annihilation of a fast positron and a K-electron resulting in the emission of a photon and a second K-electron. It is assumed that all electrons and positrons move in the Coulomb field of the nucleus and that the Coulomb parameter αZ is much less than unity (α=1/137 is the fine-structure constant and Z is the atomic number). The electron-electron interaction, which is responsible for the ejection of the electron by the atom, is taken into account in the first order of perturbation theory. We calculate the differential and total cross sections of the process and construct the ratio of the cross sections of double and single ionization as a function of the energy of the incident positron. Finally, we establish the high-energy limit of this ratio, equal to 0.34/Z ². Zh. éksp. Teor. Fiz. 113, 786–804 (March 1998)     

Time reversal during magnetization of gas atoms by a resonant light pulse

The optically induced magnetic moment of a stationary atom is calculated as a function of time and the resonance detuning ω-ω _ba to within a constant factor having the dimensions of a magnetic moment based on the symmetry of an atom in the field of a resonant light pulse and symmetry with respect to time reversal including the initial conditions. The even dependence of the optically induced magnetic moment on ω-ω _ba for an elliptically polarized pulse with an isotropic initial state of the atom and its odd dependence on ω-ω _ba in the case of a linearly polarized pulsed with an anisotropic initial state in the atom’s alignment are shown to be consequences of symmetry with respect to time reversal and the initial conditions. This behavior is retained even after passage of the light pulse, when the resulting relaxation destroys the time reversal symmetry. The optically induced magnetization of an atomic gas is found to have analogous properties. Zh. éksp. Teor. Fiz. 112, 453–469 (August 1997)     

Ionization of a two-electron atom in a strong electromagnetic field

A one-dimensional model of a helium atom in an intense field of a femtosecond electromagnetic pulse has been constructed using the Hartree technique. “Exact” calculations have been compared to the approximations of “frozen” and “passive” electrons. A nonmonotonic dependence of the single-electron ionization probability on the radiation intensity has been detected. Minima in the ionization probability are due to multiphoton resonances between different atomic states due to the dynamic Stark effect. We suggest that the ionization suppression is due to the interference stabilization in this case. Zh. éksp. Teor. Fiz. 112, 470–482 (August 1997)     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

Characteristics of the backscattering of moderate-energy electrons by solids having different atomic numbers

The coefficient of backscattering of primary electrons is discussed as a function of their energy and atomic number Z. The amplitude of the wave function obtained in the first Born approximation and the Thomas-Fermi atom model are used to calculate the constant for screening of the electric field of the nucleus by atomic electrons. The theoretically calculated integral backscattering coefficients of primary electrons are compared with the experimental values in the range 12<Z<92 for primary electron energies of 10 and 40 keV. Possible applications of these results are indicated. Zh. Tekh. Fiz. 69, 40–45 (June 1999)     

Effect of time reversal in the magnetization of an atom by a resonant light pulse

It is shown that the even dependence of the light-induced magnetic moment on the detuning ω-ω _ba from resonance in the case of a circularly polarized pulse and an isotropic initial state of the atom and the odd dependence on ω-ω _ba in the case of a linearly polarized pulse and an anisotropic initial state in the form of alignment of the atom are consequences of the symmetry under time reversal t→−t and of the initial conditions at time t=0. In a number of cases, this fundamental law makes it possible to determine the vector properties of a light-induced magnetic moment and its dependence on the time t and ω-ω _ba without solving the equation for the density matrix in detail and without calculating the sum over the projections of the angular momenta in the formula for the magnetization of an atom by light. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 231–236 (10 February 1997)     

Double atomic photoeffect in the relativistic domain: Angular and energy distributions of photoelectrons

We study the double ionization of the atomic K-shell by a single photon in the relativistic energy domain. The differential and total cross sections of the process are calculated. It is shown that the ratio of the cross sections of double and single ionization increases with the photon energy, tending to the limit 0.34/Z ², where Z is the atomic number or the nuclear charge. The formulas are found to be valid for Z≫1 and αZ≪1, where α=1/137 is the fine-structure constant. Zh. éksp. Teor. Fiz. 114, 1537–1554 (November 1998)     

Contribution to the theory of Lorentzian ionization

The probability w _L 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≲e ²/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. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 391–396 (10 March 1997)     

Large-scale amplification of a magnetic field by turbulent helicity fluctuations

In this paper the procedure of large-scale averaging of the magnetic-field diffusion equation with the α-term curlα(r,t)B(r,t) is used to show that a nonuniform distribution of the turbulent helicity fluctuations (more precisely, the fluctuations of the coefficient α) with a zero average value gives rise to large-scale amplification of the initial magnetic field. A detailed study is carried out of the dependence of the resulting large-scale α effect on the characteristics of the correlator 〈〈α(r, t)α(r″,t″)〉〉 in a rotating medium with a nonuniform distribution of the angular velocity ω=ω(ρ,z) (ρ is the distance for the rotation axis z). The effect of helicity fluctuations and the diffusion coefficient on the turbulent diffusion process is also investigated. Zh. éksp. Teor. Fiz. 116, 85–104 (July 1999)     

Fine structure of splitting of the separatrix of a nonlinear resonance

This report is a continuation of an analysis, initiated elsewhere V.V. Vecheslavov and B. V. Chirikov, Zh. éksp. Teor. Fiz. 114, 1516 (1998) [JETP 86, 823 (1998)], of the effect of splitting of the separatrix of a nonlinear resonance for the model of standard mapping, based on results of direct measurements of the splitting angle α(K), where K is the system parameter. Measurements were made in the previously used wide range 0.1≳α≳10⁻²⁰⁸ (1⩾K⩾0.0004), but with significantly higher relative (better than 10⁵⁰) and average (∼10⁻⁵⁵) accuracy. This procedure made it possible to substantially refine the effects observed in Ref. 1 and construct qualitatively new empirical dependences providing reliable extrapolation of the data obtained for the angle and the invariant in the intermediate asymptotic limit K≲10⁻² beyond the limits of the investigated region. The results obtained by us can be useful for further development of the theory of separatrix splitting and formation of the stochastic layer of a nonlinear resonance. Zh. éksp. Teor. Fiz. 116, 336–346 (July 1999)     

Effect of focusing of primary electrons on their reflection from a crystal and on the associated Auger emission

The orientational dependence for different groups of secondary electrons — quasi-elastically scattered, inelastically reflected with excitation of a plasmon and with ionization of the core level M _4.5, and the Auger electrons M _4.5 VV — are measured in the primary electron energy range 0.6–1.5 keV. The data are obtained for a Nb (100) single crystal by varying the azimuthal angle of incidence of the primary beam, with complete collection of secondaries. A relationship is established between the processes of focusing and defocusing of the electrons that have penetrated into the crystal in the 〈110〉 and 〈133〉 directions, which differ substantially in the atomic packing density. Specific details of the Auger orientation effect, due to the focusinginduced variation of the flux density of the reflected electrons, are identified and explained. The contributions, both of anisotropy of ionization of the core level and of variation of the backscattering intensity, to the angular dependence of Auger emission and reflection with ionization loss are estimated. The possibilities of using such orientational dependences for an element-sensitive analysis of the local atomic structure of surfaces are assessed. Zh. Tekh. Fiz. 67, 117–123 (August 1997)     

Anomalous behavior of the structural parameters of YBa2Cu4O8 single crystals at the transition to the superconducting state

High-precision x-ray crystallographic studies of YBa₂Cu₄O₈ single crystals (T _c =70 K) are performed at eight temperatures in the interval 20–295 K. It is found that a number of structural parameters exhibit anomalous behavior near the superconducting transition of the crystal. A characteristic effect near the phase transition is the displacement of the O1 bridge atom that joins the Cu1 atom of the cuprate chain to the Cu2 atom of the cuprate plane. The shift of this oxygen toward the Cu2 atom is indicative of a change in the Cu2-O1 chemical bond and of charge transfer to the cuprate plane in the process of the transition of the crystal to the superconducting state. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 7, 502–506 (10 October 1997)     

Resonant scattering of three-level Rydberg atoms in a microwave field

We examine the theory of potential scattering of Rydberg atoms in a microwave field. The model of a three-level atom is employed to calculate the radiative force emerging in the resonant coherent interaction with the microwave field for the case of a two-photon resonance and high intensities, using the method of quasienergies of the system consisting of the atom and the field. We determine the probabilities of Landau-Zener transitions in the spatial regions where under two-photon resonance conditions the quasienergies of the atoms approach one another by a small quantity. We also study the dynamics of the variation of the spatial profile of a beam of Rydberg atoms caused by resonant scattering. Finally, we give the results of the first experimental observation of the variation of the transverse beam profile when Rydberg atoms pass through a nonuniform microwave field formed in a rectangular waveguide and in resonance with the two-photon 36P–37P transition. Zh. éksp. Teor. Fiz. 111, 796–815 (March 1997)     

Characteristics of the coherent excitation of an impurity atom in a photonic crystal

It is shown that when an optically allowed transition is coherently excited in an impurity atom in a photonic crystal under conditions where one of the normal relaxation channels is suppressed by the spectral characteristics of the photonic crystal, new relaxation mechanisms are activated involving a coherent field quantum. These mechanisms substantially alter the dynamics of the atomic system, leading to filling of levels of the impurity atom which do not belong to the coherently excited atomic transition. Under certain conditions this leads to population inversion as a result of an optically allowed transition which does not interact with the coherent pump and at a frequency where no photonic band gaps can exist. Zh. éksp. Teor. Fiz. 116, 1963–1978 (December 1999)