Screened self-energy correction to the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript>-2<Emphasis Type="Italic">s</Emphasis> transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for 1s² 2p_3/2 and 1s² 2s states of Li-like ions with nuclear charge numbers in the range Z = 12?100. The evaluation is carried out to all orders in the nuclear strength parameter Zα. This investigation concludes our calculations of all two-electron QED corrections for the 2p_3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.     

Double <Emphasis Type="Italic">K</Emphasis>-shell ionization of atoms by a single photon

We investigate the double K-shell ionization of heliumlike ions by a single photon. A fast convergence of QED perturbation theory with respect to the parameter 1/Z is demonstrated in the entire nonrelativistic domain for moderate nuclear charge numbers Z≥2. The ratio of double-to-single photoionization cross sections is calculated for light heliumlike ions, taking into account the leading orders of 1/Z and αZ expansions. A comparison of our results with the available experimental data for a number of neutral atoms is presented.     

Effect of the nuclear charge of a fast structural ion on its internal effective stopping in collisions with atoms

The energy losses of fast structural ions in collisions with atoms have been considered in the eikonal approximation. The structural ions are ions consisting of a nucleus and a certain number of electrons bound to it. The effect of nuclear charge Z of the ion on its effective deceleration κ^(p) (energy losses associated with excitation of only intrinsic ion shells) has been analyzed. It is shown that the allowance for the interaction of an atom with the ion nucleus for Z _a Z/v > 1, where Z _a is the charge of the atomic nucleus and v is the velocity of collisions in atomic units, considerably affects the value of κ^(p), which generally necessitates taking into account nonperturbatively the effect of both charges Z _a and Z on κ^(p).     

Screening of strongly charged macroparticles in liquid electrolyte solutions

A modified Poisson-Boltzmann model has been proposed which makes it possible to describe the screening of strongly charged macroparticles in liquid electrolyte Z: Z solutions in the case when parameter B= ZeQ₀/εRT?1(Q₀ is the surface electric charge, T is the temperature, ε is the solution permittivity, and Z is the valence of ions) provided that the solution is dilute: κR ≡ (8πZ²e²n_i0/εT)^1/2R?1 (n_i0 is the equilibrium number density of ions). It is assumed that the charge Q₀ of a macroparticle appears as a result of adsorption of ions of a certain polarity on its surface. Quantitative criteria of division of dissolved ions into capable and incapable of adsorption are formulated. For aqueous solutions, the adsorption mechanism always leads to values of B ? 1. It is shown that the charge inversion effect predicted by other authors on the basis of different models must be observed for such solutions for all Z ≥ 1. The effect of Brownian movement of macroparticles on their screening is considered. It is shown that viscous forces emerging during such movement lead to peripheral destruction (“washing out”) of the screening ionic shell of macroparticles and, as a result, to violation of their electroneutrality. This results in the emergence of two types of oppositely charged compound particles with small radii close to R and with radii much larger than R, the charge polarity of the latter being opposite to the polarity of Q₀. It is found that both types of ions of compound particles obey the “law of distribution” of the mean energy of their electric field, expressed by formula (29). The problem of ionic screening of gas bubbles accompanied by the formation of bubstons (bubbles stabilized by ions) is considered separately. It is shown that the bubston radius R in pure water and in aqueous solutions of electrolytes is equal to 14 nm irrespective of the ion number density n_i0. The value of n_i0 determines the number density n _b of bubstons themselves, which are formed spontaneously under equilibrium conditions.     

Two-loop self-energy correction in a strong Coulomb nuclear field

The two-loop self-energy correction to the ground-state energy levels of hydrogen-like ions with nuclear charges Z≥10 is calculated without the Zα expansion, where α is the fine-structure constant. The data obtained are compared with the results of analytical calculations within the Zα expansion; significant disagreement with the analytical results of order α²(Zα)⁶ has been found. Extrapolation is used to obtain the most accurate value for the two-loop self-energy correction for the 1s state in hydrogen.     

Cross sections of electron capture by Boron ions in gaseous media

We study the cross sections σ_{i, i?1}, σ_{i, i?2}, and σ _{i, i?3} of capture of one, two, and three electrons by boron ions with charges i=1?5 and velocities V=(1.83?5.50)V₀ in gaseous media with atomic numbers Z_t varying from 1 to 54. The oscillatory form of the Z_t dependence of electron capture cross section by boron ions, which has been established for lighter ions, is confirmed.     

Special features of the structure of the beta-stability line for nuclei

The mass-number (A) dependence Z _β(A) for nuclei lying on the beta-stability line (BSL) is calculated for A and Z values in the ranges of A = 2–258 and Z = 1–100, respectively. The calculated values are compared with experimental data. The deviations ΔZ = Z _expt ? Z _β are analyzed. This analysis of ΔZ reveals that there are three regions of A values in which the A dependence of ΔZ is parabolic. The possible forms of the A dependence of ΔZ are analyzed, and it is shown that the majority of nuclei belong to several parabolas simultaneously.     

Features of the Emission Spectra of Ni-Like Ions. Application to Calculating the Wavelengths of Self-Photo-Pumped X-Ray Lasers

The energy levels and probabilities of radiative transitions to the ground state of Ni-like ions with Z = 36–51 are calculated. The energies of the upper working level 3d_3/24f_5/2 [J = 1] and the lower working level 3d_3/24d_3/2 [J = 1] of self-photo-pumped X-ray lasers along the sequence of Ni-like ions are studied. It is shown that, at the points of intersection of levels of the same parity, a strong interaction of these levels takes place, which leads to a redistribution of the oscillator strengths of the radiative transitions from these levels. Near the intersection points, the emission spectra change abruptly with variation in the nuclear charge Z.     

Self-consistent expansion of a multicomponent plasma into a vacuum

The problem of the one-dimensional collisionless expansion of a multicomponent plasma into a vacuum is considered. In the hydrodynamic approximation, an approximate analytical solution for an arbitrary set of ion species with masses M₁,..., M_n and charge numbers Z₁e, Z₂e,..., Z_ne is found by using the technique of self-similar variables employed by Gurevich, Pariiskaya, and Pitaevskii for the case of single-species ions. A numerical iterative algorithm is developed in which the analytical solution is used as a first approximation.     

Probabilities of forbidden magnetic-dipole transitions in the hydrogen atom and hydrogen-like ions

Explicit formulasfor strongly forbidden magnetic-dipole transitiions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived. The expressions for transition probabilities are presented in the form W _{n′jl; njl} ^(M1) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, and Z is the nuclear charge; the constants D _n′n ^lj are presented in an analytical form. Before now, only the D ₂₁ ^01/2 coefficient corresponding to the 1s _1/2–2s _1/2 transition was known in explicit form. The results obtained can be used in designing an experiment on parity violation in the hydrogen atom.     

New Bounds on the Maximum Ionization of Atoms

We prove that the maximum number N _c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z ^1/3. This improves Lieb’s upper bound N _c  < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, \({\limsup_{Z \to \infty}N_c/Z \le 1.22}\).     

Die Coulomb-Energien leichter Atomkerne

A compilation of the known data on Coulomb energy differences of isobaric doublets and isobaric triplets is given. Plots of the Coulomb energy differences versus¯Z/A ^1/3 with¯Z=(Z ₁+Z ₂)/2 show an analogous shell structure behaviour for the three series with 2¯Z=A?1,A andA+1 (T=1, 1/2 and 1), i.e. discontinuities at the closed shells atA=4, 16 and 40 and the closed subshell atA=32 and oscillations mainly being due to Coulomb proton-proton pairing energy. A positive energy shift of the lowest states withT=1 of all self-conjugate nuclei withA=4n+2 seems to be indicated by the experimental data. A semi-empirical formula is given that describes the data.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

<Emphasis Type="Italic">g</Emphasis> factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s ² 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.     

Dynamical screening of AMM and QED effects for large-<Emphasis Type="Italic">Z</Emphasis> hydrogen-like atoms

The effective interaction ΔU_AMM of the anomalous magnetic moment (AMM) of an electron with the Coulomb field of an extended nucleus is analyzed. As soon as the q² dependence of the electron formfactor F₂(q²)is taken into account from the beginning, the AMM is found to be dynamically screened at small distances of r ? 1/m. The ΔU_AMM effects on the low-lying electronic levels of a superheavy extended nucleus with Zα > 1are analyzed using the nonperturbative approach. The growth rate of the ΔU_AMM contribution with increasing Z is shown to be essentially nonmonotonic. At the same time, the energy shifts of electronic levels in the vicinity of the threshold of the lower continuum monotonically decrease in the region Z ?Z_cr,1s. The latter result is generalized to the whole self-energy contribution to energy shifts of electronic levels, thus also referring to the possible behavior of QED radiative effects with virtual-photon exchange, considered beyond the framework of the perturbative expansion in Zα.     

Probing of <Emphasis Type="Italic">Z</Emphasis>γγ production sensitivity to anomalous quartic gauge couplings at LHC experiments with √ <Emphasis Type="Italic">s</Emphasis> =13 TeV

Sensitivity to anomalous ZZγγ and Zγγγ couplings in Zγγ production was probed for the ATLAS experiment at Large Hadron Collider. Zγγ process with anomalous couplings simulation in ppcollisions with √ s = 13 TeV was performed using VBFNLO MC generator. The expected limits on the Effective Field Theory parameters f _T0/Λ4, f _T5/Λ4, f _T9/Λ4, f _M2/Λ4, f _M3/Λ4 were extracted for 5 fb^?1 integral luminosity using the distribution on the invariant mass of Zγγ from the combination of charged leptonic decay channels of Z boson (Zγγ → μ⁺μ^?γγ and Zγγ → e⁺e^?γγ).     

Nonperturbative effects of vacuum polarization for a quasi-one-dimensional Dirac–Coulomb system with <Emphasis Type="Italic">Z</Emphasis> &gt; <Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">cr</Emphasis></Subscript>

Major nonperturbative properties of the vacuum charge density ρ _VP (x) and vacuum-polarization energy ξ _VP are considered for an overcritical Coulomb source with Z > Z _cr in 1 + 1 D. We demonstrate that, for a broad range of external-field parameters, vacuum energy may significantly deviate from the perturbative quadratic increase and even decrease towards deeply negative values due to vacuum polarization in the overcritical region.     

Optical properties of lithium niobate and lithium tantalate crystals with impurities and defects

The photoinduced and Raman scattering in lithium niobate and lithium tantalate crystals with impurities and defects have been studied. An exciting laser beam propagated either along the ferroelectric Z axis or perpendicular to it. The conditions for exciting transverse and longitudinal polar optical modes in Raman spectra are established. The regularities of the excitation of Raman spectra in several polarization geometries (X(ZZ)Y, Z(XX, Y Y)Z, Z(XX, Y Y)Z, X(ZX)Y, X(ZX)X and X(ZX)X) have been investigated. Additional (extra) spectral lines are interpreted as a manifestation of a biphonon enhanced by the Fermi resonance and the result of violation of selection rules for pseudoscalar modes of the A ₂ type due to the reduction of the point symmetry group caused by the presence of impurities and defects in real crystals. The conditions for exciting coherent longitudinal and transverse modes in lithium niobate and lithium tantalate single crystals upon stimulated Raman scattering are analyzed. The temperature evolution of the spectra recorded in the X(ZZ)Y geometry near the ferroelectric phase transition point is explained based on the concept of effective soft mode and analysis of the isofrequency opalescence effect. Strong photoluminescence is found in copper-doped lithium niobate crystals.