Universal two-dimensional kinetics of the populations of Rydberg atoms in plasmas

Universal kinetics has been developed for calculating the two-dimensional populations (in the space of principal n and orbital l quantum numbers) of Rydberg atomic states in plasmas. It has been shown that the direct population of the atomic states by three-body and radiative recombination sources should be taken into account, because the radiative cascade is of quantum character. The subsequent two-dimensional radiation-collision cascade is constructed in the framework of the classical approach. The developed model makes it possible to obtain the populations in the form of universal functions of temperature and density. The numerical calculations of the populations of highly excited hydrogen states (n ∝ 100) in low-density plasmas (10³–10¹³ cm^?3) at moderate temperatures (1 eV) indicate a significantly nonequilibrium population both in n and in l, which is important for the diagnostics of astrophysical and laboratory plasmas.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

On the mechanisms of formation of excited hydrogen atoms in a decaying helium-hydrogen plasma

We spectroscopically studied the population of the excited hydrogen atomic states with the principal quantum numbers n=3 and 4 in a decaying plasma produced by a pulsed discharge in a mixture of helium (p=40.4 Torr) with a small amount of hydrogen ([H₂]≈10¹² cm^?3). Experiments on recording the response of the spectral line intensities to a short-duration electron temperature perturbation revealed the contribution of electron-ion recombination to the population of the H*(n=3) states in the early afterglow. The ions produced by collisions of hydrogen molecules with metastable He(2³ S ₁) atoms, whose density decreases relatively rapidly with time in the decaying plasma, were assumed to be involved in this process. No population of the H*(n=4) atomic levels due to electron-ion recombination was found. Our experimental results are consistent with the conclusions of previous studies that excitation transfer during collisions of metastable helium molecules with hydrogen molecules plays a major role in the population of the excited hydrogen atomic states both with n=3 and with n=4 during most of the afterglow.     

Recombination population of excited states of the hydrogen atom in an He-H<Subscript>2</Subscript> plasma

The population of excited states of the hydrogen atom in an afterglow plasma produced by a pulsed discharge in helium (40 Torr) with a small admixture of hydrogen ([H₂] ≈ 10¹² cm^?3) has been studied spectroscopically. The contribution from electron-ion recombination Γ ₃ ^rec to the production rate of atoms H(n = 3) has been separated. On the basis of an experiment in which the response of the spectral line intensities to the perturbation of the electron temperature in the afterglow phase was observed, the dependence Γ ₃ ^rec (T _e ～ T _e ^?(0.9–1.0) has been obtained in the region kT _e = 0.026–0.064 eV.     

Plasma-volume generation of H<Superscript>−</Superscript> ions in a low-voltage xenon-hydrogen discharge. II

A low-voltage xenon-hydrogen discharge is considered theoretically at an interelectrode distance of L = 1 cm and cathode emission current densities of j _s = 2–20 A/cm². Basic parameters of the discharge plasma, in particular, the total hydrogen and xenon densities, are optimized to attain the maximum possible density of negative hydrogen ions \(N_{H^ - } (L)\) at the plasma-anode boundary. The distributions of the plasma parameters over the discharge gap are calculated for optimized regimes. According to calculations, at intermediate cathode emission current densities (j _s ≈ 5–10 A/cm²) in optimized discharge regimes, the density of negative hydrogen ions in the anode region of the plasma is \(N_{H^ - } (L)\) ≈ (1.5–2.5) × 10¹² cm^?3 and the total plasma pressure is p ₀ = 0.5–0.6 Torr.     

Refinement of the structure of hydrogen–vacancy complexes in titanium by the Rietveld method

The VT1-0 titanium alloy (phase α-Ti) with various hydrogen and hydrogen-vacancy concentrations has been studied. The stability of the 32-atom Ti–nV–mH supercell (n is the number of the V vacancies, and m is the number of hydrogen atoms H) with varying numbers of vacancies and hydrogen atoms has been calculated from the first principles. The structural state of the α-Ti phase has been identified by the Rietveld method based on the calculations of the supercell stability and the data on the defect concentration obtained using positron spectroscopy. The complete structural information on the considered states of the α-Ti phase (the lattice parameters, spatial distribution of titanium and hydrogen atoms and vacancies) has been obtained.     

Pressure-produced ionization of nonideal plasma in a megabar range of dynamic pressures

The low-frequency electrical conductivity of strongly nonideal hydrogen, helium, and xenon plasmas was measured in the megabar range of pressures. The plasmas in question were generated by the method of multiple shock compression in planar and cylindrical geometries, whereby it was possible to reduce effects of irreversible heating and to implement a quasi-isentropic regime. As a result, plasma states at pressures in the megabar range were realized, where the electron concentration could be as high as n _e ≈2×0²³ cm^?3, which may correspond to either a degenerate or a Boltzmann plasma characterized by a strong Coulomb Γ _D =1–10) and a strong interatomic Γ _a =r _a n _a ^1/3 ～1) interaction. A sharp increase (by three to five orders of magnitude) in the electrical conductivity of a strongly nonideal plasma due to pressure-produced ionization was recorded, and theoretical models were invoked to describe this increase. Experimental data available in this region and theoretical models proposed by various authors are analyzed. The possibility of a first-order “phase transition” in a strongly nonideal plasma is indicated.     

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

In the framework of Bohmian quantum mechanics, the Klein–Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave ?(x) in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein–Gordon equation? We examine this approach for ?⁴(x) and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.     

Coulomb deexcitation of muonic hydrogen within the quantum close-coupling method

The Coulomb deexcitation of muonic hydrogen in collisions with the hydrogen atom has been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The calculations of the l-averaged cross sections of the Coulomb deexcitation are performed for (μp)_n and (μd)_n atoms in the initial states with the principal quantum number n = 3–9 and at relative energies E = 0.1–100 eV. The obtained results for the n and E dependences of the Coulomb deexcitation cross sections drastically differ from the semiclassical results. An important contribution of the transitions with Δn > 1 to the total Coulomb deexcitation cross sections (up to ～37%) is predicted.     

A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

Ab Initio Calculation of the Lowest Singlet and Triplet Excited States of the N<Subscript>2</Subscript> Molecule

Ab initio calculations of the adiabatic potential curves and matrix elements of radial nonadiabatic coupling of the N₂ molecule for the states related to dissociation limits I–V were performed. The most important spectral characteristics of the adiabatic states agreed well with the available experimental and theoretical data. The diabatic states were constructed. The diabatic quantum defects and radial matrix elements of the configuration interaction of the dissociative and Rydberg configurations whose states converge to the ground state \(X^{2}\Sigma{_g^+}\) and the first electronically excited state A²Π_u of the \(\rm{N_2^+}\) ion were calculated. The possibility of using the results for calculating the cross sections and rate constants of dissociative recombination and associative ionization within the framework of the multichannel quantum defect theory was discussed.     

Structure of three-loop contributions to the β-function of <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric QED with <Emphasis Type="Italic">N</Emphasis><Subscript>f</Subscript> flavors regularized by the dimensional reduction

In the case of using the higher derivative regularization for N = 1 supersymmetric quantum electrodynamics (SQED) with N _f flavors, the loop integrals giving the β-function are integrals of double total derivatives in themomentum space. This feature allows reducing one of the loop integrals to an integral of the δ-function and deriving the Novikov–Shifman–Vainshtein–Zakharov relation for the renormalization group functions defined in terms of the bare coupling constant. We consider N = 1 SQED with N _f flavors regularized by the dimensional reduction in the \(\overline {DR} \)-scheme. Evaluating the scheme-dependent three-loop contribution to the β-function proportional to (N _f)² we find the structures analogous to integrals of the δ-singularities. After adding the schemeindependent terms proportional to (N _f)¹, we obtain the known result for the three-loop β-function.     

Distribution function and electron state density in nonequilibrium plasma created by dye laser

Ultracold nonequilibrium plasma created by a dye laser has been studied by the molecular dynamics method. Electrons and protons in this model of nonequilibrium plasma interacted according to the Coulomb law. In the case of electron-proton interaction and a distance between particles r < a ₀ (Bohr radius), the interaction energy is constant, e ²/a ₀ (e is the charge of electron). An initial proton kinetic energy is set randomly so that the average kinetic energy is 0.01–1 K. Initial full electron energy is also set randomly, but at the same time it is positive; i.e., all the electrons according to our task are located in the continuous spectrum. Average kinetic electron energy per one particle varies from 1 to 50 K. The motion equations in periodical boundary condition for this system have been solved by molecular dynamics method. We have calculated the distribution function in the region near the ionization threshold. The distribution function is being described using electron state density in the nearest neighbor approximation with activity correction.     

Forbidden 2<Emphasis Type="Italic">P</Emphasis>–<Emphasis Type="Italic">nP</Emphasis> and 2<Emphasis Type="Italic">P</Emphasis>–<Emphasis Type="Italic">nF</Emphasis> transitions in the energy spectrum of ultracold Rydberg lithium-7 atoms

Forbidden 2P–nP and 2P–nF transitions in the ranges of the principal quantum number n = 42–114 and n = 38–48 have been detected in the optical spectra of ultracold highly excited lithium-7 atoms. The presence of forbidden transitions is due to induced external electric fields. The quantum defects and ionization energy obtained in various experiments and predicted theoretically have been discussed.     

The probabilities of radiative transitions and lifetimes of levels in the spectra of Cu XX,La IV

The probabilities of radiative electric dipole transitions 2p ⁵3p, 2p ⁶–2p ⁵3s, and 2p ⁵3d in the spectrum of neon-like copper Cu XX and 5p ⁵6p, 5p ⁶–5p ⁵6s, 5p ⁵7s, and 5p ⁵5d in the spectrum of xenon-like lanthanum La IV are calculated. The wave functions of the intermediate coupling were found from the wellknown experimental energy levels by the least-squares method (LSM). To transfer to an absolute scale the radial integrals for the transitions calculated in the form of a length on the Hartree–Fock functions have been used. By summing the calculated probabilities of the transitions, the lifetimes of the levels of configurations 2p ⁵3s, 2p ⁵3p, and 2p ⁵3d in the spectrum of Cu XX and levels of configurations 5p ⁵6s, 5p ⁵6p, and 5p ⁵7s in the spectrum of La IV have been obtained.     

Radiative Lifetimes of the Energy Levels of Palladium-like Ions Pr XIV and Nd XV

Radiative lifetimes for the 4d⁹4f, 4d⁹5p, 4d⁹5d, and 4d⁹6s levels in the spectra of palladium-like ions Pr XIV and Nd XV are calculated in the electric-dipole approximation by the intermediate coupling semiempirical method with the use of experimental energy levels available in the literature. The radial integrals of transitions necessary for calculating absolute values of transition probabilities are obtained in the length form with Hartree–Fock functions.     

Ionic composition of a humid air plasma under ionizing radiation

A kinetic model is proposed for ion–molecular processes involving charged particles of a humid air plasma produced by a fast electron beam. The model includes more than 600 processes involving electrons and 41 positive and 14 negative ions, including hydrated ions H₃O⁺ (H₂O) _n and O ₂ ^? (H₂O) _n with n = 1, 2, …, 12. The energy costs of production of electron–ion pairs and electronic and vibrational (for water molecules, also rotational) excitation of molecules are calculated in nitrogen, oxygen, water vapor, air, and humid air. A method is proposed for calculating the energy costs in mixtures by the calculation data in pure gases. The evolution of the plasma composition is studied by the numerical solution of a system of 56 time-dependent balance equations for the number of charged particles of plasma by the fourth-order Runge–Kutta method. The steady-state composition of plasma is determined by solving nonlinear steady-state balance equations for the ionization rates of humid air from 10 to 10¹⁶ cm^–3/s and the fraction of water molecules from 10^–3% to 1.5%. It is established that, for water vapor content (the ratio of the number density of water molecules to the total number density of air molecules) of 0.015–1.5% in air at atmospheric pressure and room temperature, the main ion species are two types of positive ions H₃O⁺ (H₂O) _n with the number of water molecules n = 5, 6 and three species of negative ions O ₂ ^? (H₂O) _n with n = 5, 8, 9.     

Visualization of a Berezinskii–Kosterlitz–Thouless Topological Phase Transition in a Josephson Medium: Detection of an Anomalous Temperature Dependence of the Magnetoresistance of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7–δ</Subscript> Granular High-Temperature Superconductors

The density of states of the valence band of a p-GaAs layer formed on an n-GaAs surface owing to the bombardment by 2500-eV Ar⁺ ions has been studied by photoelectron spectroscopy. A number of peaks have been detected in the spectrum of the edge of the valence band in the binding energy range E_V < 1.2eV. Their number and energy positions correspond to the quantum confinement levels calculated for a hole quantum well on the surface with the width about the ion penetration depth R_p = 3.6nm. Electronic transitions from these levels to the bottom of the conduction band have been revealed in the spectrum of characteristic energy losses of electrons reflected from the surface. Thus, it has been shown that the action of the argon ion beam on n-GaAs results in the formation of a quantum well on the surface.     

Streuung von 25 keV-Elektronen an Gasen

The angular distribution of 25 kev electrons scattered elastically and inelastically by molecular hydrogen has been measured in the angular range 7·10^?4≦?≦4,3·10^?2. By the separation of the inelastically scattered electrons observation of deviations from the Debye Ehrenfest theory of the electron diffraction by molecules at small angles is possible. These deviations are due to the alteration of the electron density distribution of the hydrogen atoms induced by the bonding. The energy loss spectra at different scattering angles (energy resolution ≈1 ev) shows a strong peak atΔE=12,6 ev. At larger angles forΔE>15 ev a continuum appears. That part of the inelastic processes which leads to ionization of the molecule is raising with increasing scattering angle. Normalization of the experimental values to the theoretical elastic differential cross section enables comparison of the angular distribution of the 12,6 ev energy loss with the distribution calculated byRoscoe. The shape of the experimental curve is in fairly good agreement with the calculated one but the experimental values at small angles are 20–30% higher. For zero angle the energy loss spectrum is taken with better resolution (≈0,04 ev). It shows vibrational states of the Lyman and Werner band and higher terms. The probability of the excitation of some vibrational states of the Werner band (square of the overlapp integral) calculated here is inspite of the required approximations in excellent agreement with the measurement, while Hutchisson's result fails for the Lyman band.