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.     

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).     

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.     

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.     

Problems in searching for new solid-state UV-and VUV-active media: The role of photodynamic processes

The impact of photodynamic processes induced by pump radiation in crystals doped with rare-earth (RE) ions on the possibility of generating stimulated radiation in the UV and VUV spectral ranges is analyzed. It is shown that, in addition to objective factors, one of the main causes preventing the lasing effect from being obtained using the interconfigurational 4?^n?15d-4? ⁿ transitions of RE ions is insufficient consideration of the photodynamic processes involved in experiments. It is proposed to correct laser test techniques and “pumpprobe” experiments aimed at investigating active media appropriate for lasing in the UV and VUV ranges. Extended criteria oriented to search for new solid-state UV and VUV active media are formulated.     

Radiative decays of doubly excited states of oxygen,carbon, and nitrogen ions

Systematic calculations of the probabilities and energies of radiative transitions in doubly excited 3l3l′, 3l4l′, and 4l4l′ states of oxygen, carbon, and nitrogen ions have been carried out within the Hartree-Fock approximation. The emission spectra are obtained, and analysis of the changes in the spectral characteristics with a change in the charge and the number of additional electrons in the ground state of the initial ion is performed. The data obtained are used to interpret the X-ray spectra of the atmospheres of planets and comets.     

Determination of the effective nuclear charge for free ions of transition metals from experimental spectra

The refined set of values of the effective nuclear charge (\(\bar Z_{ef} \)) and the set of one-electron spin-orbital constants (ξ _3d ^teor ) are obtained for ions of transition metals with the help of a semiempirical method of calculation of the spectrum of free ions with allowance for the spin-orbital interaction. The effective nuclear charge, which is a variable theoretical parameter, was determined from a comparison of theoretically calculated ion absorption spectra with experimental ones. The form of the potential for the calculation of the spin-orbital constant was chosen such that the calculated value ξ _3d ^teor would coincide with the experimental one ξ _3d ^exp . The calculated set of values \(\bar Z_{ef} \), ξ _3d ^teor } can be used in semiempirical calculations of energy levels of 3d ions (ions with an incomplete 3d shell).     

Effective Electrostatic Interactions Between Two Overall Neutral Surfaces with Quenched Charge Heterogeneity Over Atomic Length Scale

Using Monte Carlo results as a reference, a classical density functional theory (CDFT) is shown to reliably predict the forces between two heterogeneously charged surfaces immersed in an electrolyte solution, whereas the Poisson–Boltzmann (PB) theory is demonstrated to deteriorate obviously for the same system even if the system parameters considered fall within the validity range of the PB theory in the homogeneously charged surfaces. By applying the tested CDFT, we study the effective electrostatic potential of mean force (EPMF) between two face–face planar and hard surfaces of zero net charge on which positive and negative charges are separated and considered to present as discontinuous spots on the inside edges of the two surfaces. Main conclusions are summarized as follows: (i) strength of the EPMF in the surface charge separation case is very sensitively and positively correlated with the surface charge separation level and valency of the salt ion. Particularly, the charge separation level and the salt ion valency have a synergistic effect, which makes high limit of the EPMF strength in the surface charge separation case significantly go beyond that of the ideal homogeneously charged surface counterpart at average surface charge density similar to the average surface positive or negative charge density in the charge separation case. (ii) The surface charge distribution patterns mainly influence sign of the EPMF: symmetrical and asymmetrical patterns induce repulsive and attractive (at small distances) EPMF, respectively; but with low valency salt ions and low charge separation level the opposite may be the case. With simultaneous presence of both higher valency cation and anion, the EPMF can be repulsive at intermediate distances for asymmetrical patterns. (iii) Salt ion size has a significant impact, which makes the EPMF tend to become more and more repulsive with the ion diameter regardless of the surface charge distribution patterns and the valency of the salt ion; whereas if the 1:1 type electrolyte and the symmetrical patterns are considered, then the opposite may be the case. All of these findings can be explained self-consistently from several perspectives: an excess adsorption of the salt ions (induced by the surface charge separation) serving to raise the osmotic pressure between the plates, configuration fine-tuning in the thinner ion adsorption layer driven by the energy decrease principle, direct Coulombic interactions operating between charged objects on the two face-to-face plates involved, and net charge strength in the ion adsorption layer responsible for the net electrostatic repulsion.     

Study of background processes with the formation of neutrons in nuclear reactions in the energy range of 26–32 kev

The nature of background processes accompanying astrophysical nuclear reactions induced by hydrogen, helium, and neon ions in deuterated targets with small cross sections has been studied in calculations and experiments. The experiments have been performed at a Hall pulsed plasma accelerator in the ion energy range of 26–32 keV. The yield of background neutrons and γ-quanta with energies below 4 MeV in the proton-induced D(p, γ)³He reaction is primarily due to the presence of a natural impurity of gaseous deuterium in gaseous hydrogen and the chain of D(D, ³He)n → (n, γ) or (n, n'γ) reactions. A small contribution comes from the chain of D(¹H, ¹H)D → D(D, ³He)n → (n, γ) or (n, n'γ) reactions. It has been shown that background neutrons and γ-quanta from the D(4He, γ)6Li reaction are entirely due to the chain of D(⁴He, ⁴He)D → D(D, ³He)n → (n, γ) or (n, n'γ) reactions. It has been shown that the yield of neutrons and γ-ray photons detected at the interaction of neon ions with deuterated targets is also entirely due to the chain of elastic- scattering reactions of neon ions on deuterons in the target and to subsequent inelastic processes of interaction of deuterons accelerated at elastic scattering with other deuterons of the target. The main contribution to the yields of background neutrons and γ-quanta comes from doubly charged neon ions. The main conclusion is that the explanation of the yield of neutrons and γ-quanta at the interaction of hydrogen, helium, and neon ions with deuterated targets does not require “exotic” theoretical models.     

Charge state of a transition metal impurity in II–VI semiconductors

The results of calculating the electronic structure of semiconductor compounds A^IIB^VI: 3d(A = Zn; B = S, Se, Te; 3d = Sc-Cu) at a low content of 3d impurities are discussed. The excess charge of an impurity ion with respect to the charge of the zinc ion is determined for the whole series of 3d impurities. It is found that the excess charge gradually varies from +0.6|e| for the scandium impurity to ?0.2|e| for the copper impurity. Photoionization of an impurity ion is simulated by adding a hole or an electron to the impurity center. The added charge is redistributed between the impurity ion and its nearest neighbors, thus decreasing or increasing the total excess charge of the impurity center by a magnitude of ～ 0.2|e|.     

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.     

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.     

Weak ferromagnetism in BiFeO<Subscript>3</Subscript>-based multiferroics

The magnetic properties of the Bi_{1 ? x} Ln _x FeO₃ (Ln is a rare-earth ion), Bi_{1 ? x} A _x FeO_{3 ? x/2} (A is an alkali earth ion), and BiFe_{1 ? x} Ti _x O_{3 + δ} solid solutions in magnetic fields up to 14 T have been studied. The concentration ranges of the existence of the ferroelectric phase described by the space group R3c have been determined. It is shown that the substitution of the rare-earth ions for the Bi³⁺ ions leads to a sharp decrease in the critical fields inducing the metamagnetic transition from a modulated antiferromagnetic state to a weakly ferromagnetic one; however, the modulated structure in the concentration range of the R3c phase is mainly retained. The substitution of the alkali earth ions (x ～ 0.1) for the bismuth ions leads to the total destruction of the modulated structure and to the implementation of the weakly ferromagnetic state within the R3c phase. A homogeneous weakly ferromagnetic state has been revealed when the Ti⁴⁺ ions (x = 0.1) are substituted for the Fe³⁺ ions in the ferroelectric R3c phase.     

Theta Series,Wall-Crossing and Quantum Dilogarithm Identities

Motivated by mathematical structures which arise in string vacua and gauge theories with \({{\mathcal{N}=2}}\) supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi–Yau string vacua, such theta series encode instanton corrections from k Neveu–Schwarz five-branes. The theta series are determined by vector-valued wave-functions, and in this work we obtain the transformation of these wave-functions induced by Kontsevich–Soibelman symplectomorphisms. This effectively provides a quantum version of these transformations, where the quantization parameter is inversely proportional to the five-brane charge k. Consistency with wall-crossing implies a new five-term relation for Faddeev’s quantum dilogarithm \({\Phi_b}\) at b = 1, which we prove. By allowing the torus to be non-commutative, we obtain a more general five-term relation valid for arbitrary b and k, which may be relevant for the physics of five-branes at finite chemical potential for angular momentum.     

Formation of lithium-like boron and nitrogen ions in the <Superscript>4</Superscript><Emphasis Type="Italic">P</Emphasis><Subscript>5/2</Subscript> state in gaseous media

We experimentally determined the fraction of α_v of lithium-like boron B²⁺ and nitrogen N⁴⁺ ions in the ⁴ P _5/2 state having a velocity of 3.6 au that are formed upon capture of two (α₂) electrons by hydrogen-like B⁴⁺ and N⁶⁺ ions and upon capture of one (α₁) electron by helium-like (1s2s)^1,3 S metastable B³⁺ and N⁵⁺ ions in gaseous media (H₂, He, N₂, Ar), as well as upon passage through a celluloid film. In light-element media (H₂, He), α₂ increases proportional to the target thickness T _g and reaches a maximum at T _g ≈ 10¹⁶ atom/cm² (for B ions, α₂ ≈ 0.2 in H₂ and α₂ ≈ 0.4 in He). For boron and nitrogen ions passing through thin layers of heavier gases (N₂, Ne), α₂ depends considerably more weakly on T _g , and, in Ar, becomes practically constant. It is assumed that, since hydrogen and helium do not contain electrons with parallel spins, autoionizing lithium-like ions are formed as a result of successive (one by one) capture of electrons, whereas, in the heavier gases, simultaneous capture of two electrons predominates. At T _g ～ 10¹⁵ atom/cm², the fraction α₁ of boron ions is the highest in He, ～0.15, and the lowest in Ar, ～0.07, being in qualitative agreement with calculations.     

X-ray spectroscopy diagnostics of a recombining plasma in laboratory astrophysics studies

The investigation of a recombining laser plasma is topical primarily because it can be used to simulate the interaction between plasma jets in astrophysical objects. It has been shown that the relative intensities of transitions of a resonance series of He-like multicharged ions can be used for the diagnostics of the recombining plasma. It has been found that the intensities of the indicated transitions for ions with the nuclear charge number Z _n ~ 10 are sensitive to the plasma density in the range N _e ~ 10¹⁶–10²⁰ cm^–3 at temperatures of 10–100 eV. The calculations performed for the F VIII ion have determined the parameters of plasma jets created at the ELFIE nanosecond laser facility (Ecole Polytechnique, France) in order to simulate astrophysical phenomena. The resulting universal calculation dependences can be used to diagnose different recombining plasmas containing helium-like fluorine ions.     

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.     

Energy levels of ions of silver and rhodium isoelectronic sequences with <Emphasis Type="Italic">Z</Emphasis> < 86

The method of extrapolation of the parameter of a model potential for states of one electron (4f, 5s, 5p, 5d, 5f) above the core 1s ²2s ²2p ⁶3s ²3p ⁶3d ¹⁰4s ²4p ⁶4d ¹⁰ and one vacancy (4d ⁹) in the same core is applied to calculate the energy levels in the silver and rhodium isoelectronic sequences with the maximum nuclear charge Z = 86. The energy levels of Ag-and Rh-like ions were used for the calculation of the energies of resonance transitions to the ground state ¹ S ₀ in Pd-like ions. Good agreement between the theoretical and calculated energies of the resonance transitions in Pd-like ions indicates the reliability of the results obtained.     

Effect of the capture and loss of two electrons on the charge distributions of ions

The effect of the processes of capture and loss of two electrons on the width of the equilibrium charge distribution of ions in different materials is studied. These processes increase the width of the equilibrium charge distribution in the energy region of E < 0.1 MeV/nucleon. The effect increases with decreasing ion nuclear charge and reaches 10–15% for boron ions.     

Die Anlagerung von radioaktiven Atomen und Ionen an Aerosolteilchen

The attachment of radioactive atoms and ions to spherical aerosol particles has been studied theoretically. For uncharged atoms the deposition is considered to be solely governed by thermal diffusion. With calculations based on the “limiting-sphere”-method ofArendt-Kallman it is found, that the attached activity is proportional toΦ ² for aerosol particle diametersΦ smaller than 0.1 μm, and proportional toΦ forΦ greater than 1 μm. For charged ions the diffusion process is modified by the influence of electrostatic forces between the diffusing ions and the aerosol particles. In the frequently occurring case of a symmetrically bipolar charged aerosol this influence can be expressed by a functionG _p(Φ), which depends on the diameterΦ and the effective numberp of elementary charges on the aerosol particle. For an aerosol particle diameterΦ greater than 0.1 μm the attached activity is proportional toΦ ^1.1, and forΦ smaller than 0.01 μm it is proportional toΦ ^1.55. The effects of neglecting various terms in the calculation are considered. The distribution of natural radioactivity on atmospheric aerosols has been calculated for various particle size distributions according toJunge. The calculation shows that about 90% of the total natural activity should be attached to particles smaller thanΦ=0.5 μm, and about 35% to particles smaller thanΦ=0.1 μm. The time T_1/2, in which the concentration of the radioactive particles decreases to half the initial value, depends on the concentration of the aerosol particles and on their size distribution. For 10⁴ aerosol particles per cm³ and the size distributions mentioned,T _1/2 varies between 15 and 30 seconds for radioactive ions. For radioactive atomsT _1/2 is greater than it is for ions in the range of aerosol particle diameters belowΦ=0.25 μm, and smaller ifΦ greater than 0.25 μm.