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.     

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.     

Precision measurements of optical excitation functions for the cadmium atom

An experimental setup and a technique for the investigation of excitation of atoms by ultramonoenergetic electrons are described. The optical excitation functions are given for 14 spectral lines of the cadmium atom originating from the n ¹ S ₀, 5¹ P ₁, n ³ S ₁, 5³ P ₁, and n ³ D _j levels. More than 150 specific features are found in the energy dependences of the effective excitation cross sections measured from the excitation threshold to 16 eV. The most pronounced of these features are in good agreement with the fine structure observed previously. The main mechanisms of the initial-level population, namely, the direct transition of an electron from the ground atomic state to the initial level of a spectral line, the population of the initial levels due to the decay of short-lived states of a negative ion, and the cascade population, are separated. In the excitation functions of the lines originating from the n ¹ S ₀ levels, in the energy range from 10.9 to 12.4 eV, we observed for the first time an effect of postcollision interactions of emitted and scattered electrons in the vicinity of the thresholds of four autoionization states of the cadmium atom.     

Nonexponential decay in the quantum dynamics of nanosystems

The quantum dynamical problem is solved for a system coupled to an equidistant-spectrum bath with the energy difference Ω between the neighboring levels n and n + 1 and the coupling matrix elements C _n ² = C ²(1 + Δ^?2 n ²)^?1 constraining the energy interval comprising the bath states interacting with the system. The evolution in the strong-coupling limit is determined by two parameters, Γ = πC ²/Ω ? 1 and α = Γ/Δ. If α ≠ 0, then the decrease in the population in the initial cycle with a period of 2π/Ω is not exponential and the effective rate constant increases with time. The results qualitatively explain the appearance of nonexponential relaxation regimes for a dense-spectrum nanosystem and predict the possibility of the multiple recovery of the initial-state population.     

The real solution to scalar field equation in 5D black string space

After the nontrivial quantum parameters Ω _n and quantum potentials V _n obtained in our previous research, the circumstance of a real scalar wave in the bulk is studied with the similar method of Brevik and Simonsen (Gen. Rel. Grav. 33:1839, 2001). The equation of a massless scalar field is solved numerically under the boundary conditions near the inner horizon r _e and the outer horizon r _c . Unlike the usual wave function Ψ_ωl in 4D, quantum number n introduces a new functions Ψ_{ωl n} , whose potentials are higher and wider with bigger n. Using the tangent approximation, a full boundary value problem about the Schrödinger-like equation is solved. With a convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients are obtained. If extra dimension does exist and is visible at the neighborhood of black holes, the unique wave function Ψ_{ωl n} may say something to it.     

Resonance conversion of gamma radiation in the radiative transitions between neutron resonances

The influence of the resonance conversion on the α-particle spectra in the reaction (n, α) in low-energy transitions between neutron resonances is discussed. Unusual α spectra from neutron resonances in the reaction ¹⁴⁷Sm(n, α)¹⁴⁴Nd are considered as an example of such influence. The calculation of resonance conversion coefficients was performed for the transitions from K shell in the free levels of P shell of Sm atom. The large effect of resonance in the radiative transitions for the nuclei and atomic electron shells is observed.     

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.     

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.     

Collective states in highly symmetric atomic configurations and single-photon traps

We study correlated states in circular and linear-chain configurations of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behavior is mediated by exchange of transverse photons between the atoms. For a circular atomic configuration containing N atoms, the collective energy eigenstates can be determined by group-theoretical means making use of the fact that the configuration possesses a cyclic symmetry group Z _N . For these circular configurations, the carrier spaces of the various irreducible representations of the symmetry group are at most two-dimensional, so that the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. As a consequence, the radiationless energy eigenstates carry a Z _N quantum number p = 0, 1, …, N, which is analogous to the angular momentum quantum number l = 0, 1, … carried by particles propagating in a central potential, such as a hydrogen-like system. Just as the hydrogen s states are the only electronic wave functions that can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the circular atomic sample can occupy the central atom only for vanishing Z _N quantum number p. When a central atom is present, the p = 0 state splits into two, showing level crossing at certain radii; in the regions between these radii, damped oscillations between two “ extreme” p = 0 states occur, where the excitation occupies either the outer atoms or the central atom only. For large numbers of atoms in a maximally subradiant state, a critical interatomic distance of λ/2 emerges both in the linear-chain and in the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jumplike “critical” behavior for next-neighbor distances close to a half-wavelength. Furthermore, both the linear-chain and the circular configurations exhibit exponential photon trapping once the next-neighbor distance becomes less than a half-wavelength, with the suppression of spontaneous decay being particularly pronounced in the circular system. In this way, circular configurations containing sufficiently many atoms may be natural candidates for single-photon traps.     

Probabilities of radiative dipole transitions of parahelium in an electric field

Quadratic Stark corrections to the wave functions, matrix elements, and probabilities of transitions between the singlet states ¹ S ₀ and ¹ P ₁ of helium atoms are calculated. The coefficients of the polynomials that depend on the effective principal quantum number of the upper level v _f and that approximate the numerical values of the polarizabilities, the quadratic corrections to the wave functions, and the probabilities of transitions to highly excited Rydberg states with large v _f are determined. The results of calculations testify that the probabilities of all σ transitions n _i ¹ S ₀ → n _f ¹ P ₁ and π transitions to the states with n _f > n _i /2 are decreased with increasing electric field strength, except for the transition 2¹ S ₀ → 2¹ P ₁, whose probability increases both for σ and for π transitions.     

Multiple exchanges in lepton pair production in high-energy heavy ion collisions

As an archetype reaction for pQCD multigluon hard processes in collisions of ultrarelativistic nuclei, we analyze generic features of lepton pair production via multiphoton processes in peripheral heavy ion scattering. We report explicit results for collisions of two photons from one nucleus with two photons from the other nucleus, 2γ + 2γ → l⁺l^?. The results suggest that the familiar eikonalization of Coulomb distortions breaks down for oppositely moving Coulomb centers. The breaking of eikonalization in QED suggests that multigluon pQCD processes cannot be described in terms of collective nuclear gluon distributions. We discuss a logarithmic enhancement of the contribution from the 2γ + 2γ → l⁺l^? process to production of lepton pairs with large transverse momentum; similar enhancement is absent for the nγ + mγ → l⁺l^? processes with m, n > 2. We comment on the general structure of multiphoton collisions and properties of higher-order terms that cannot be eikonalized.     

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.     

Quantum Image Encryption Based on Iterative Framework of Frequency-Spatial Domain Transforms

A novel quantum image encryption and decryption algorithm based on iteration framework of frequency-spatial domain transforms is proposed. In this paper, the images are represented in the flexible representation for quantum images (FRQI). Previous quantum image encryption algorithms are realized by spatial domain transform to scramble the position information of original images and frequency domain transform to encode the color information of images. But there are some problems such as the periodicity of spatial domain transform, which will make it easy to recover the original images. Hence, we present the iterative framework of frequency-spatial domain transforms. Based on the iterative framework, the novel encryption algorithm uses Fibonacci transform and geometric transform for many times to scramble the position information of the original images and double random-phase encoding to encode the color information of the images. The encryption keys include the iterative time t of the Fibonacci transform, the iterative time l of the geometric transform, the geometric transform matrix G i which is n × n matrix, the classical binary sequences K (\(k_{0}k_{1}{\ldots } k_{2^{2n}-1}\)) and \(D(d_{0}d_{1}{\ldots } d_{2^{2n}-1}\)). Here the key space of Fibonacci transform and geometric transform are both estimated to be 2²⁶. The key space of binary sequences is (2 ^n×n ) × (2 ^n×n ). Then the key space of the entire algorithm is about \(2^{2{n^{2}}+52}\). Since all quantum operations are invertible, the quantum image decryption algorithm is the inverse of the encryption algorithm. The results of numerical simulation and analysis indicate that the proposed algorithm has high security and high sensitivity.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique in the case of different quark masses

The Bethe-Salpeter equations for quark-antiquark composite systems with different quark masses, such as \(q\bar s(with q = u,d),q\bar Q\), and \(s\bar Q\) (with Q = c, b), are written in terms of spectral integrals. For mesons characterized by the mass M, spin J, and radial quantum number n, the equations are written for the (n, M²) trajectories with fixed J. The mixing between states with different quark spin S and angular momentum L is also discussed.     

Giant fluctuations of radiation intensity of two-dimensional electrons in double quantum wells

Giant fluctuations of the recombination-radiation intensity of two-dimensional electrons were studied in double quantum wells with different well and barrier widths in the regime of the integer quantum Hall effect. It was found that the giant fluctuations of photoluminescence intensity in double quantum wells with a narrow barrier (l<150 Å) occur in a narrow magnetic-field interval, where the sum of electron concentrations in both wells corresponds to the integer filling factors 4, 8, and 12. It was established that, under these conditions, the coefficient C₁₂ of correlation between the radiation intensities from different wells is close to unity. It is shown that, as the barrier width increases (l>200 Å), the coefficient C₁₂ decreases, changes sign, and goes to zero at l=400 Å.     

Fluctuations and a rigorous uncertainty relation of trigonometric operators of the phase and the number of photons of an electromagnetic field for general quantum superpositions of coherent states

The quantum-statistical properties of states of an electromagnetic field of general superpositions of coherent states of the form of N _α,β(α?+e ^iξ β? are investigated. Formulas for the fluctuations (variances) of Hermitian trigonometric phase field operators ? ≡ côs φ, ? ≡ sîn φ (the so-called “Susskind–Glogower operators”) are found. Expressions for the rigorous uncertainty relations (Cauchy inequalities) for operators of the number of photons and trigonometric phase operators, as well as for operators ? and ?, are found and analyzed. The states of amplitude \({N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i\varphi }}\rangle + {e^{i\xi }}\left| {{{\sqrt {{n_\beta }e} }^{i\varphi }}\rangle } \right.} \right.} \right)\), φ = φ_α = φ_β, and phase \({N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i{\varphi _\alpha }}}\rangle + {e^{i\xi }}\left| {{{\sqrt {ne} }^{i{\varphi _\beta }}}\rangle } \right.} \right.} \right)\), n = n _α = n _β, superpositions of coherent states are considered separately. The types of quantum superpositions of meso- and macroscales (n _α, n _β » 1) are found for which the sines and/or cosines of the phase of the field can be measured accurately, since, under certain conditions, the quantum fluctuations of these quantities are close to zero. A simultaneous accurate measurement of cosφ and sinφ is possible for amplitude superpositions, while an accurate measurement of one of these trigonometric phase functions is possible in the case of certain phase superpositions. Amplitude superpositions of coherent states with a vacuum state are quantum states of the field with a “maximum” level of the quantum uncertainty both in the case of a mesoscopic scale and in the case of a macroscopic scale of the field with an average number of photons n _α/β ≈ 0, n _β/α » 1.     

Mechanisms of low-temperature high-frequency conductivity in systems with a dense array of Ge<Subscript>0.7</Subscript>Si<Subscript>0.3</Subscript> quantum dots in silicon

High-frequency (HF) conductivity in systems with a dense (with a density of n = 3 × 10¹¹ cm^?2) array of self-organized Ge_0.7Si_0.3 quantum dots in silicon with different boron concentrations n_B is determined by acoustic methods. The measurements of the absorption coefficient and the velocity of surface acoustic waves (SAWs) with frequencies of 30–300 MHz that interact with holes localized in quantum dots are carried out in magnetic fields of up to 18 T in the temperature interval from 1 to 20 K. Using one of the samples (n_B = 8.2 × 10¹¹ cm^?2), it is shown that, at temperatures T ≤ 4 K, the HF conductivity is realized by the hopping of holes between the states localized in different quantum dots and can be explained within a two-site model in the case of

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, where ω is the SAW frequency and τ₀ is the relaxation time of the populations of the sites (quantum dots). For T > 7 K, the HF conductivity has an activation character associated with the diffusion over the states at the mobility threshold. In the interval 4 K < T < 7 K, the HF conductivity is determined by a combination of the hopping and activation mechanisms. The contributions of these mechanisms are distinguished; it is found that the temperature dependence of the hopping HF conductivity approaches saturation at T* ≈ 4.5 K, which points to a τ₀ ≤ 1. A value of τ₀(T*) ≈ 5 × 10^?9 s is determined from the condition ωτ₀(T*) ≈ 1.

     

Thermal correction to resistivity in dilute Si-MOSFET two-dimensional systems

Neglecting electron-electron interactions and quantum interference effects, we calculate the classical resistivity of a two-dimensional electron (hole) gas, taking into account the degeneracy and the thermal correction due to the combined Peltier and Seebeck effects. The resistivity is found to be a universal function of the temperature, expressed in units of (h/e²)(k_Fl)^?1. Analysis of the compressibility and thermopower points to the thermodynamic nature of the metal-insulator transition in two-dimensional systems. We reproduce the beating pattern of Shubnikov-de Haas oscillations in both the crossed field configuration and Si-MOSFET valley splitting cases. The consequences of the integer quantum Hall effect in a dilute Si-MOSFET two-dimensional electron gas are discussed. The giant parallel magnetoresistivity is argued to result from the magnetic-field-driven disorder.     

<Emphasis Type="Italic">Ab initio</Emphasis> theory of the electronic structure and spectra of impurity <Emphasis Type="Italic">nl</Emphasis> ions

The fundamentals of the theory of the electronic structure of impurity clusters and the results of numerical calculations for the iron-, lanthanum-, and actinium-group ions in Me⁺ⁿ: [L]_k clusters are presented. The effects of the interionic distance and ligands in the Me⁺ⁿ: [L]_k clusters on the electronic structure of the nl ^N and nl^N?1n′l′ configurations of the 3d, 4f, and 5f ions are considered. The correspondence between the optical and x-ray spectra of different impurity crystals is also analyzed.     

Studying the possibility of deep laser cooling of <Superscript>24</Superscript>Mg atoms in an optical lattice: Two-level quantum model

The possible deep laser cooling of ²⁴Mg atoms in a deep optical lattice in the presence of an additional pumping field resonant to the narrow 3s3s¹S₀ → 3s3p³P₁ (λ = 457 nm) optical transition is studied. Two quantum models of the laser cooling of atoms in the optical trap are compared. One is based on the direct numerical solution to the kinetic quantum equation for an atomic density matrix; it considers both optical pumping and quantum recoil effects during interaction between the atoms and field photons. The second, simplified model is based on decomposing the states of the atoms over the levels of vibration in the optical trap and analyzing the evolution of these states. The comparison allows derivation of optical field parameters (pumping field intensity and detuning) that ensure cooling of the atoms to minimal energies. The conditions for fast laser cooling in an optical trap are found.