Simple analytical representation for Delbrück scattering amplitudes at high energies

We use a new representation for the semiclassical Green’s function of the Dirac equation in the Coulomb field to find an exact (in the parameter Zα) expression for the amplitudes of small-angle Delbru ck scattering of high-energy photons. The values of these amplitudes agree with those obtained in earlier calculations, but the structure of the expressions is much simpler than that of previously known representations, which makes numerical calculations much easier. Zh. éksp. Teor. Fiz. 116, 78–84 (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)     

The polarization of radiation in single crystals in the semiclassical approach

The radiation emission spectra of polarized photons emitted from charged particles in single oriented crystals are obtained in Bayer-Katkov-Strakhovenko semiclassical approach. The results of numerical calculations are presented in the region of small angles of incidence for which the coherent theory fails but the magnetic bremsstrahlung region is not yet achieved. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 171–175 (10 February 1999)     

Differential thermopower of a superlattice in a strong electric field

The effect of an electric field on the differential thermopower α(E) of a one-dimensional superlattice is investigated in the semiclassical approximation. A nonmonotonic temperature dependence of α(0) is established for a degenerate electron gas. It is shown that, in principle, an electric field can be used to control the thermoelectric properties of superlattices. Fiz. Tverd. Tela (St. Petersburg) 41, 1314–1316 (July 1999)     

Parametric instability and Hamiltonian chaos in cavity semiclassical electrodynamics

We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high-Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow, in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode. The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first in the area of the fundamental parametric resonance, δ/2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance, generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high-Q microwave cavity are possible objects for observing parametric instability and dynamical chaos. Zh. éksp. Teor. Fiz. 115, 740–753 (February 1999)     

Study of η -production reaction πp → ηn in the near-threshold region⋆

The differential cross-sections (DCS) of the η -production reaction π^- p → ηn are measured at momenta of incident π^- mesons (700, 710 and 720MeV/c) close to the threshold of this reaction. The experiment is carried out at the pion channel of the PNPI synchrocyclotron (with the momentum spread of the pion beam equal to 1.5%) using the Neutral Meson Spectrometer (NMS) designed and created at the Meson Physics Laboratory for detecting two photons from the decay η → 2γ . This spectrometer consisting of two electromagnetic total absorption calorimeter (24 CsI(Na) crystals in each calorimeter) allowed to obtain the DCS in the whole angular range from 0^° to 180^° in the c.m.s. It is shown that at 700MeV/c the DCS angular dependence is isotropic, indicating on the S -wave character of the η -production process while at higher momenta a significant contribution of the D -wave has led to the anisotropic angular dependence having a bowl-like shape.     

Interference in Phase Space of Squeezed States for the Time-Dependent Hamiltonian System

We showed that the idea of Schleich and Wheeler (1987, Nature 326, 574) for the semiclassical approach of the interference in phase space of harmonic oscillator squeezed states can be extended to that of general time-dependent Hamiltonian system. The quantum phase properties of squeezed states for the general time-dependent Hamiltonian system are investigated by using the quantum distribution function. The weighted overlaps A _n and phases θ _n for the system are evaluated in the semiclassical limit.     

Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models

The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and boron nitride. The main focus is on wave effects – such as Berry phase and Maslov index – occurring at order (^h/_2p)\hbar in the semiclassical quantization and producing non-trivial shifts in the resulting Landau levels. Specifically, we show that the index shift appearing in the Landau levels is related to a topological part of the Berry phase – which is basically a winding number of the direction of the pseudo-spin 1/2 associated to the coupled bands – acquired by an electron during a cyclotron orbit and not to the complete Berry phase, as commonly stated. As a consequence, the Landau levels of a coupled band insulator are shifted as compared to a usual band insulator. We also study in detail the Berry curvature in the whole Brillouin zone on a specific example (boron nitride) and show that its computation requires care in defining the “k-dependent Hamiltonian” H(k), where k is the Bloch wavevector.     

Polarization of the vacuum in a relativistic hydrogenlike atom: The Lamb shift

This paper examines the shift of energy levels in a hydrogenlike atom induced by vacuum polarization effects. The contribution of free polarization is found for the ground state and several excited states in a closed analytical form. For the first time an expression is derived for the radiative correction to the energy in the form of an explicit function of the parameter Zα. The results are valid for states nl _j with the largest values of orbital and total angular momenta (l=n−1 and j=l+1/2). The final expression, found in terms of generalized hypergeometric functions, is a function of three variables, Zα, n, and the ratio of the particle masses on the orbit and in the vacuum loop, i.e., the result is valid for ordinary atoms and for muonic atoms. Several useful asymptotic expressions are also derived. Zh. éksp. Teor. Fiz. 116, 1575–1586 (November 1999)     

Investigation of the reaction D(e, pp)e′ π − on a tensorpolarized deuterium target at high proton momenta

The differential cross section of the reaction D(e,pp)e′ π ⁻ is measured in the range of proton momenta 300–720 MeV/c and proton emergence angles 64–83° for invariant masses of the pp system ranging from 2m _p to 2220 MeV/c ². The measured values of the cross section are found to differ substantially from single-particle model calculations. The components of the analyzing power for this reaction are measured. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 730–736 (25 May 1998) Deceased.     

Induced emission from a sodium Rydberg atom in a microwave cavity

Results are presented from an experiment on the observation of an induced microwave transition 37P-37S in sodium Rydberg atoms under the action of 30 thermal photons in a microwave cavity. The measured value of the transition rate (4±1.5)×10⁴ s⁻¹ agrees with the calculated value. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 413–416 (25 March 1999)     

Resonant two-photon absorption in a tetragonal CdP2

Kinetic, spectral, intensity, angular, and polarization of resonant two-photon absorption (TPA) in β-CdP₂ has been investigated. Resonant TPA was observed for which the total energy of the two photons was 2.60 eV. It is shown that resonant TPA takes place via a real intermediate level d ₃ in the band gap at the depth E _c-0.86 eV. The electron transverse relaxation time for resonant TPA, the cross section for absorption of laser photons in d ₃→C transitions, the equilibrium population of d ₃ centers in a doped n-type sample, and the resonant TPA constant were determined as 4.3×10⁻¹⁴ s, 1.25×10⁻¹⁷ cm², 0.95, and 0.028 cm/MW, respectively. Fiz. Tverd. Tela (St. Petersburg) 40, 1252–1256 (July 1998)     

Multilevel rotational transitions in the intermediate stage of three-photon ionization of molecules

Ionization and dissociation of diatomic molecules induced by a weak field (after preliminarily populating an intermediate level) and by intense, linearly polarized monochromatic radiation have been studied. Field-induced mixing of rotational components of various electronic-vibrational states of molecules (such as CO, NO, etc.) at field strength f∼10⁻⁴–10⁻⁵ atomic units can lead to migration among states with different angular momenta J. Therefore, ions with rotational momenta J ⁺ much higher than those prescribed by selection rules for three-photon absorption can be formed from molecules in the ground state. The possibility of selective formation of ions with J ⁺≫1 and zero projection of the angular momentum on the polarization vector of the external electromagnetic radiation has been investigated. Zh. éksp. Teor. Fiz. 111, 1624–1632 (May 1997)     

Quantum-nondemolition measurement of the number of photons in a microcavity

A new scheme for quantum-nondemolition measurement of the number and statistics of photons in a microwave cavity on the basis of interferometry of strongly-controlled V atoms which interact by a dispersion interaction with a cavity mode at a different transition is proposed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 58–63 (10 July 1997)     

Electroproduction of an isobar as a background from the beam-residual-gas interaction in φ factories

It is shown that the electroproduction of the isobar Δ(1232) occurs in φ factories when the beams interact with the residual gas. In one effective year (10⁷ s) the decay of this isobar over an interaction length of one meter gives ∼10⁷ pions, moving predominantly in a direction transverse to the axis of the beams, with a resonance energy distribution having a 120-MeV wide peak near 265 MeV. Formulas required for modeling the process under discussion, giving the distributions over the momentum transfer, angles, energies, and momenta of the decay products are presented. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 295–300 (25 February 1997)     

Thick-target X-ray bremsstrahlung spectra produced in 6.5 keV and 7.5 keVe--Hf collisions

The absolute doubly differential cross-sections (DDCS) for production of the thick-target X-ray bremsstrahlung spectra in collisions of 6.5 keV and 7.5 keV electrons with thick Hf target are measured. The X-ray photons are counted by a Si(Li) detector placed at 90° to the electron beam direction. The bremsstrahlung spectra are corrected for various ‘solid-state effects’ namely, electron energy-loss, electron back-scattering, and photon-attenuation in the target, in addition to the correction for detector’s efficiency. The DDCS values after correction, are compared with the predictions of a most accurate thin-target bremsstrahlung theory [H K Tseng and R H Pratt,Phys. Rev. A3, 100 (1971); Kisselet al, Atomic Data Nucl. Data Tables 28, 381 (1983)]. Also, a dependence of the absolute DDCS on atomic numberZ of the targets (₄₇Ag,₇₉Au and₇₂Hf) at 7.0 keV and 7.5 keV electron energies has been studied. The agreement between experiment and theory is found to be satisfactory within 27% systematic error of measurements. However, an apparent systematic difference between experiment and theory in the region of low-energy photons has been explained qualitatively by considering the fact that the hexagonal atomic structure of Hf offers possibly a greater magnitude of ‘solid-state effects’ in respect of blocking the low-energy bremsstrahlung photons from coming out of the target surface than does the cubic-face centered structure of Ag and Au target in similar conditions of the experiment.     

A note on conserved charges of asymptotically flat and anti-de Sitter spaces in arbitrary dimensions

The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces in arbitrary dimensions. This paper provides a systematic and explicit Hamiltonian derivation of the energy and the angular momenta of both asymptotically flat and asymptotically AdS spacetimes in any dimension D  ≥  4. This requires as a first step a precise determination of the asymptotic conditions of the metric and of its conjugate momentum. These conditions happen to be achieved in ellipsoidal coordinates adapted to the rotating solutions. The asymptotic symmetry algebra is found to be isomorphic either to the Poincaré algebra or to the so(D − 1,2) algebra, as expected. In the asymptotically flat case, the boundary conditions involve a generalization of the parity conditions, introduced by Regge and Teitelboim, which are necessary to make the angular momenta finite. The charges are explicitly computed for Kerr and Kerr–AdS black holes for arbitrary D and they are shown to be in agreement with thermodynamical arguments. The author is a FRIA-FNRS bursar (National Fund for Scientific Research, Belgium).     

New method for detection of exciton Bose condensation using stimulated two-photon emission

An investigation is reported of stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation numbers of exciton states with momenta p≠0. Raman light scattering (RLS) accompanied by a similar two-exciton recombination (or production of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, so their detection can be used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted to optical phonons with frequency ω ₀ ^s , whose occupation numbers are negligible, and the incident light frequency satisfies ω<2Ω, where Ω_=Ω−ω ₀ ^s is the difference frequency and Ω is the light frequency corresponding to the recombination of an exciton with zero momentum, stimulated two-photon emission and RLS with coherent two-exciton recombination give rise to a line at 2Ω_ −ω and an anti-Stokes component at ω+2Ω_, respectively. For ω2Ω_ the RLS spectrum contains Stokes and anti-Stokes components at frequencies ω±2Ω_, whereas stimulated two-photon emission is impossible. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line at 2Ω_−ω, corresponding to the stimulated two-photon emission accompanied by coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu₂O. Zh. éksp. Teor. Fiz. 115, 1353–1376 (April 1999)     

Two-photon fluorescence spectrum in an atom + dielectric microsphere system

A strong resonant interaction of a two-level atom with a dielectric microsphere is studied on the basis of quantum electrodynamics. The initial condition considered is one in which the atom is initially excited and the resonant mode of the microsphere has been excited by a single photon. The spectrum of two emitted photons depends strongly on the method used to excite the microsphere, i.e., on the spatial distribution of the photon energy. The most characteristic feature of the two-photon fluorescence spectrum is a strong energy correlation of the emitted photons. This correlation is expressed in the fact that the energies of the emitted photons are related by the equation of an ellipse (ω+ω ₂−2ω _vA )²+3(ω ₁−ω ₂)²= 4Ω _Rabi ² . The relation between the results obtained and the predictions of the theory of dressed states is discussed. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 192–197 (10 August 1999)