Exact two-loop vacuum polarization correction to the Lamb shift in hydrogenlike ions

We present a calculation scheme for the two-loop vacuum polarization correction of order to the Lamb shift of hydrogenlike high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in . By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuum polarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell electron states in hydrogenlike Lead and Uranium are presented. Received: 10 August 1997 / Revised: 31 October 1997 / Accepted: 18 November 1997     

Am原子及其离子Amq+(q=1~6)的K,L,M-X射线跃迁能和跃迁几率的理论研究(英文)

使用基于Dirac-Hartree-Fock方法的Grasp2K程序包,计算了Am原子及离子的K,L,M-X射线的跃迁能和跃迁速率。在计算中,包括了Breit相互作用、真空极化和自能等重要效应。目前研究结果与已有的其他实验和理论结果相对误差约为0.04%。此外,我们还首次计算了从Am1+到Am6+离子的K,L,M-X射线的跃迁能和跃迁速率。相对于中性原子,来自低离化态的跃迁能相对于中性的相应跃迁线的能量仅有轻微的偏移,这反映出外层电子几乎不影响内壳层的跃迁性质。Transition energies and rates of K, L, and M X-ray lines from electric-dipole transition of americium have been calculated using GRASP2K code based on the Dirac-Hartee-Fock method. The effects of the Breit interaction, vacuum polarization and self energy were taken into account. It is found that the present results agree within 0.04% with other experimental and theoretical values. Furthermore, we also calculated transition energies and rates of the K-, L-, and M-shell hole states of americium ions with charge states Am1+-Am6+ for the first time. It is found that the transition energies and rates change slightly relative to the corresponding results of americium atoms, which indicates that the outermost electrons can hardly affect inner-shell transition properties.     

Application of radiative electron capture for the diagnostics of spin-polarized ion beams at storage rings

It is proposed to apply the radiative electron capture into high-Z projectiles as a probe process for measuring the spin polarization of the hydrogenlike ions at storage rings. We argue that such polarization measurements are possible since the linear polarization of emitted x-ray photons is greatly sensitive to the spin states of incoming ions with nuclear spin I > 1/2. In particular, for K-shell electron capture into the hydrogenlike ions, the linear polarization of light as measured out of the reaction plane is found to be proportional to the degree of ion polarization. Detailed computations for the dependence of the photon polarization on the ion spin states and projectile energies are carried out for the electron recombination into hydrogenlike Bi 82+ ions.     

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)     

Generalized Kolbenstvedt model for electron impact ionization of K-, L- and M-shell atoms

The recently modified Kolbenstvedt (MKLV) model [Eur. Phys. J. D 37, 361 (2006)], developed for electron impact ionization (EII) of the K-shell atomic targets, has been extended to generalize its two parameters in terms of the electronic orbitals nl. The generalized MKLV (GKLV) with two sets of the species independent parameters for the same nl, one set for the ionization of inner orbits and another for the outermost orbit, is found profoundly successful in accounting for the EII cross section data of the K, L and M-shell neutral atoms with atomic numbers Z = 1-92 for the incident energies up to 1000 MeV in a consistent manner.     

Quantitative Brewster angle microscopy measurements of chiral symmetry breaking and chiral boundaries in fatty acid Langmuir monolayers

Brewster angle microscopy (BAM) measurements of the low temperature region of the phase diagram of eicosanoic acid monolayers at an acidic subphase are performed. The existence of a new chiral I phase intervening between the L₂ and L ₂ ' phase recently discovered by Durbin et al. [M.K. Durbin, A. Malik, A.G. Richter, R. Ghastkadvi, T. Gog, P. Dutta, J. Chem. Phys. 106, 8216 (1997)] using grazing incidence X-ray diffraction (GIXD) is confirmed. Chiral symmetry breaking within the monolayers creates characteristic boundaries separating domains of opposite handedness. These disclination lines are associated with a jump in the tilt azimuth of the director, while the underlying hexatic orientation is continuous across the boundary. The disclination lines are observed with the Brewster angle microscope and analyzed as a function of surface pressure. The jump in tilt azimuth is determined. Agreement with an extended Landau theory proposed by Durbin is achieved. Received: 26 January 1998 / Revised: 3 August 1998 / Accepted: 7 August 1998     

低损耗玻璃光波导的溶胶-凝胶法制备

By means of the relation of ionicity and the ionization energies of hydrogenlike atoms, the soft X-ray spectra are calculated for the hydrogenlike sodium, magnesium and aluminium atoms. The calculated results are in good agreement with the experiments.     

Multiconfiguration Dirac-Fock calculation of transition energies in highly ionized bismuth, thorium, and uranium

Structure and QED effects for and levels are calculated for lithiumlike U⁸⁹⁺ trough neonlike U⁸²⁺, lithiumlike Th⁸⁷⁺ trough neonlike Th⁸⁰⁺ and lithiumlike Bi⁸⁰⁺ trough neonlike Bi⁷³⁺. The results of the first two sets are compared with recent measurements of the transition energy in 3 to 10-electron ions. Good agreement with experiment is found for most of the observed lines. Forty-one possible transitions are calculated for each ion in the eight ionization states, in the experimental energy range. Twenty-eight of these transitions have not been observed, nor calculated previously. We also calculate transition rates, branching ratios, excitation and ionization cross sections and confirm that the thirteen experimental o bserved transitions correspond to the ones with highest relative intensities. However, we find nineteen more transitions that could be measured in a more sensitive experiment. Received: 5 November 1997 / Accepted: 8 December 1997     

Measurement of angular dependence of M X-ray production cross-sections in Re,Bi and U at 5.96 keV

The M X-ray production differential cross sections in Re, Bi and U elements have been measured at the 5.96 keV incident photon energy in an angular range 135°–155°. The measurements were performed using a ⁵⁵Fe source and a Si(Li) detector. The present results contradict the predictions of Cooper and Zare [Atomic Collision Processes, Gordon and Breach, New York (1969)] and experimental results of Kumar et al. [J. Phys. B: At. Mol. Opt. 34, 613 (2001)]. that, after photoionization of inner shells, the vacancy state has equal population of magnetic substates and the subsequent X-ray emission is isotropic, but confirm the predictions of the calculations of Flügge et al. [Phys. Rev. Lett. 29, 7 (1972)] and experimental results of Sharma and Allawadhi [J. Phys. B: At. Mol. Opt. 32, 2343 (1999)] and Ertugrul [Nucl. Instrum. Meth. B 119, 345 (1996)]. Total M X-ray production cross sections from the decay at the 5.96 keV photon energies are found to be in good agreement with the calculated theoretical results using the theoretical values of M shell photoionization cross section.     

The and transitions in the oxygen isoelectronic sequence

Multiconfiguration Dirac-Fock results are reported for the and transitions in the oxygen-like sequence for Z =9,...,18. Both transition energies and transition rates are included. Received: 29 June 1998 / Accepted: 1st July 1998     

Low frequency dielectric permittivity of quasi-one-dimensional conductor (TMTTF)2Br

Conductivity and permittivity of the organic transfer salt (TMTTF)₂Br have been measured at low frequencies (10²-10⁷ Hz) between room temperature down to 4 K. The real part of the permittivity, , is shown to grow below the temperature at which the conductivity is maximum due to charge localization of Mott-Hubbard type. reaches a maximum of 10⁵-10⁶ at 35 K-50 K depending on the samples. Decreasing temperature below , sharply decreases down to helium temperature through the antiferromagnetic phase transition at T _N = 15 K. We explain the magnitude, the temperature and frequency dependence of as resulting from short range charge density wave states in the temperature range where charge localization occurs. This interpretation is supported by recent X-ray scattering measurements. Received: 10 October 1997 / Revised: 28 February 1998 / Accepted: 3 March 1998     

Elastic scattering of low-energy electrons by NO

We report elastic integral, momentum transfer and differential cross sections for electron scattering by N₂O for energies up to 50 eV. These results were obtained at the static-exchange approximation with the Schwinger Multichannel Method with Pseudopotentials [M.H.F. Bettega, L.G. Ferreira and M.A.P. Lima, Phys. Rev. A 47, 1111 (1993)]. In general our results show good agreement with experimental data and with other theoretical results but some discrepancies are found. We have also found a shape resonance around 4 eV in agreement with previous calculations using the R-matrix Method of Sarpal et al. [J. Phys. B 29, 857 (1996)]. On the other hand, the existence of a resonance at about 13 eV, clearly seen by the Schwinger Variational Iterative Method [Michelin et al., J. Phys. B 29, 2115 (1996)], can not be confirmed by our calculations. At this energy, our cross sections show a broad bump with no clear resonant behavior given by the eigenphase sum. Received: 13 November 1997 / Revised: 13 March 1998 / Accepted: 9 April 1998     

Photoionization of argon, krypton and xenon clusters in the inner valence shell region

Photoionization of rare gas clusters in the innervalence shell region has been investigated using threshold photoelectron and photoion spectrometers and synchrotron radiation. Two classes of states are found to play an important role: (A) valence states, correlated to dissociation limits involving an ion with a hole in its innervalence ns shell, (B) Rydberg states correlated to dissociation limits involving an ion with a hole in its outervalence np shell plus an excited neutral atom. In dimers, class A states are “bright”, that is, accessible by photoionization, and serve as an entrance step to form the class B “dark” states; this character fades as the size of the cluster increases. In the dimer, the “Mulliken” valence state is found to present a shallow potential well housing a few vibrational levels; it is predissociated by the class B Rydberg states. During the predissociation a remarkable energy transfer process is observed from the excited ion that loses its innershell electron to its neutral partner. Received: 10 February 1998 / Revised: 17 July 1998 / Accepted: 31 July 1998     

Rare-gas-induced broadening and shift of two-photon transitions to intermediate Rydberg states of atomic thallium*

Results of broadening and shift measurements of Doppler-free two-photon lines for transitions from the ground state to the Rydberg states with intermediate principle quantum numbers of atomic thallium perturbed by rare gases are reported. The rates show a distinct behaviour in this range of principle quantum numbers and significant dependence on the total angular momentum of the upper nP state. The experimental results are compared with calculations using a Van der Waals potential and a superposition of polarization and Fermi potentials. Additionally, broadening and shift rates of the transition Tl 6P _3/2 -9P _3/2 have been measured for quadrupolar as well as for mainly scalar excitation. The rates for both kinds of excitation coincide within the limits of error reflecting the small perturbation of the 6P _3/2 state compared to that of the upper 9P _3/2 state. Received: 6 August 1997 / Revised in final form: 29 November 1997 / Accepted: 11 December 1997     

Investigations on the soft-mode mechanism of the ferroelectric phase transition in

Dielectric and Raman spectroscopic measurements have been performed to investigate the ferroelectric phase transition in . Single crystals were grown by the zone melting method. The frequency dependence of the dielectric permittivity from 1 MHz to 1 GHz has been studied in a temperature range between 265 and 285 K. A Debye like dielectric dispersion was found, showing a critical slowing down around K. Polarized Raman spectra have been taken between 220 and 310 K. Two softening modes have been found, one of A- and another one of B / B g-symmetry. The phase transition mechanism in can be classified as partially order-disorder and partially displacive, confirming former structural results. It resembles strongly that of monoclinic . Received: 7 April 1998 / Revised: 5 June 1998 / Accepted: 16 June 1998     

Isotope shifts and hyperfine structure in the transitions in calcium II

The isotope shift and hyperfine structure in the three - transitions in Ca II have been studied by fast ion beam collinear laser spectroscopy for all stable Ca isotopes. The metastable 3d states were populated within the surface ionization source of a mass separator with a probability of about 0.1%. After resonant excitation to the 4p levels with diode laser light around 850 nm the uv photons from the transitions to the ground state were used for detection. Hyperfine structure parameters A and B for the odd isotope ⁴³Ca, as evaluated from the splittings observed, agree well with theoretical predictions from relativistic many-body perturbation theory. Field shift constants and specific mass shift constants were extracted from the measured isotope shifts and are discussed in comparison with expectation values from theory. Received: 19 September 1997 / Revised: 5 December 1997 / Accepted: 27 January 1998     

Single crystal study of the one dimensional Ca Co O compound: five stable configurations for the Ising triangular lattice

Single crystals of the one-dimensional phase Ca₃Co₂O₆ of several mm length have been grown. The magnetic study of such a crystal confirms the previous observations on polycrystalline samples: it consists of a triangular lattice of ferromagnetic [Co₂O₆] chains ( K) antiferromagnetically coupled ( K). The dynamic of these chains array, probed by AC susceptibility, is very slow as shown from the large shift of the freezing temperature from 12 K to 16.5 K as the excitation frequency increases by three orders of magnitude (10⁰ to 10³ Hz). The origin of this effect is believed to be the result of different arrangements with close energies for the chain ferromagnetic moments on the triangular lattice. Five stable magnetic configurations have been evidenced by the magnetization as a function of applied field curves registered at 2 K. Their relative magnetizations correspond to m =1/4, 1/2, 1, 2, 3 where m =3 represents the ferromagnetic ordering of three chains on the same triangle, each chain having a m =1 magnetization. A magnetic phase diagram is finally proposed. Received 7 December 1999     

Sisyphus cooling of rubidium atoms on the line: The role of the neighbouring transitions

We study one-dimensional Sisyphus cooling on the transition of ⁸⁷ Rb atoms in the electric field created by two counter-propagating linearly polarized laser beams with an angle of between the polarization directions. The neighbouring F '=0 and F '=2 excited states are found to play an important role in the cooling mechanism, e.g., by inhibiting a significant population of the velocity-selective dark state. Our experimental data, such as temperatures and probe absorption coefficients, agree well with the results of quantum Monte-Carlo wavefunction simulations. Received 26 November 1998 and Received in final form 20 April 1999     

Inelastic processes in collisions of multicharged fast ions with atoms

We use the eikonal approximation to develop a general formula for the cross sections of inelastic collisions of multicharged fast ions (including relativistic ions) with atoms that is applicable within a broad range of collision energies, has the standard nonrelativistic limit, and becomes, in the ultrarelativistic case, the well-known result that follows from the exact solution of the Dirac equation. As an example we study the excitation and ionization of a hydrogenlike atom, the single and double excitation and ionization of a heliumlike atom, and multiple (up to the eighth order) ionization of the neon atom and (up to eighteenth order) ionization of the argon atom. We derive simple analytical expressions for the inelastic cross sections and establish recurrence relations linking the cross sections of ionization of different orders. Finally, we compare our results with the experimental data. Zh. éksp. Teor. Fiz. 114, 1646–1660 (November 1998)     

The shapes of Auger decay lines in photoelectron satellite spectra

The theory of the shapes of Auger decay lines of satellite two-hole-one particle states accompanying photoionization based on the Green's function method is developed. The lineshapes of Auger decay of satellite states [2 s 2 p ]( ^1,3 P )3 s ( ² P ), [2 s 2 p ]( ¹ P )4 s ( ² P ) and [3 s 3 p ]( ³ P )4 s ( ² P ) in valence p-photoelectron spectra of Ne and Ar atoms are calculated (hole states are indicated by square brackets throughout). It is shown that in some cases the Auger lineshapes reproduce the shape of the photoelectron satellite line, but in other cases Auger line may be narrower then the photoelectron line and may have opposite direction of asymmetry. The theoretical results are in agreement with experimental low-energy Auger spectra. Received: 25 May 1998 / Accepted: 2 October 1998