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.     

Energies, Auger and radiative probabilities of the doubly-excited 1s23l3l′ states for Be-like neon

Energy levels, Auger decay and radiative transition rates of the doubly-excited 1s ²3l3l′ states for Be-like neon are calculated using relativistic Multiconfiguration Dirac-Fock (MCDF) method. Electron correlation and relaxation effects are taken into account. The magnitude of Auger rates for the 35 doubly-excited states and their decay channels are discussed. Present calculated values are in agreement with the latest experimental electron spectra as well as other theoretical results.     

Isotope shifts and energies of the 1s 2p states in helium

The specific mass shift (SMS) and energies of the (1s2p)^{1, 3} P states in helium are evaluated using wave functions expressed in terms of radial “pair functions” which are obtained by numerical solution of inhomogeneous two-particle differential equations. The results obtained when including successively higher angular symmetries in the wave function indicate that the SMS converges asl _max ^?3 for the singlet state and betweenl _max ^?5 andl _max ^?6 for the triplet state. These convergence rates are considerably slower than thel _max ^?5 andl _max ^?7 behaviours found for the singlet and triplet energies. The total energies,E(2¹ P)=?2.123835 a.u. andE(2³ P)=?2.133155 a.u., are about 0.00001 a.u. above the “exact” non-relativistic results obtained with perimetric coordinates and also the SMS between³He and⁴He, SMS(2¹ P)=0.4533 cm^?1 and SMS(2³ P)=?0.6356 cm^?1, are very close to the “exact” results.     

A dispersion analysis of pion photoproduction from nucleons. II

The paper gives an account of numerical results forl=0 andl=1 multipole amplitudes of pion photoproduction. They have been obtained by solving integral equations which originate from fixed angle dispersion relations that have been deduced in an earlier paper. In this Part II presented are solutions of truncated integral equations for photoproduction amplitudes, which take into account coupling with the most important transitionsM ₁₊ ⁽³⁾ (in the isovector case) andE ₀₊ ⁽⁰⁾ (in the isoscalar case). Discussed are implications of such an approach and a comparison of results obtained by a different method is being made.     

Optical second harmonic generation in asymmetric double triangular quantum wells

The second harmonic generation (SHG) in the asymmetric double triangular quantum wells (DTQWs) is investigated theoretically. The dependence of the SHG coefficient on the right-well width of the DTQWs is studied, and the influence of the applied electric field on SHG coefficient is also taken into account. The analytical expression of the SHG coefficient is analyzed by using the compact density-matrix approach and the iterative method. Finally, the numerical calculations are presented for the typical GaAs/Al_xGa_1−xAs asymmetric DTQWs. The results show that the calculated SHG coefficient in this coupled system can reach the magnitude of 10⁻⁵ m/V, 1–2 orders of magnitude higher than that in step quantum well, and that in double square quantum wells. Moreover, the SHG coefficient is not a monotonic function of the right-well width, but has complex relationship with it. The calculated results also reveal that an applied electric field has a great influence on the SHG coefficient. Applying an appropriate electric field to a DTQW with a wider right well can induce a sharper peak of the SHG coefficient due to the double-resonant enhancement.     

The nonparaxial propagation of the TEM0l doughnut beam with the orbital angular momentum in the far field

The analytical expression for nonparaxial electric field amplitude of the TEM_0l^? doughnut beam with the orbital angular momentum quantum number l is derived in the far field by means of the angular spectrum representation and the stationary phase method. It is shown that the divergent angle of the far field of TEM_0l^? doughnut beam will be smaller with the decreasing of the orbital angular momentum quantum number l or the increasing of the beam waist width w of the initial beam. And the maximal radial intensity of the beam is decreased with its propagation at different rates for different l and w.     

Energy levels and level ordering in the WKB approximation

Energy levels and level orderings for a particle in a non-relativistic potential are examined in the WKB approximation. In particular, power-law potentials (V(r) = ar^γ, ?2 < γ < ∞) are discussed in some detail. The energy levels are shown to be determined in terms of a single function G(η, γ) of a variable η. Expansions of this function, valid for small (large) angular momentum quantum numbers (l) and large (small) radial quantum numbers (n), approximate the energy levels well. The ordering of the levels follows from the monotonic behavior of (?/?η)G(η, γ). The values γ = 2 (harmonic oscillator potential) and γ = ?1 (Coulomb potential) for which the WKB approximation gives the exact (i.e. Schrödinger) results lead to degenerate levels. It is about these values of γ that the monotonic behavior of (?/?η)G(η, γ) changes sign (as a function of γ). We also find an ordering theorem for arbitrary central potentials which is valid for large l and small n and is possibly correct for smaller l. The ordering depends on various sums of derivatives of the potential. Similar theorems, which follow from the Schrödinger equation, have been obtained recently for low-lying levels and are compared to our results.     

The strictly attractive 1/l interaction between steps of crystal surfaces

Using SSH model for the step structure of crystal surfaces, a strictly attractive 1/l² energy, which originates from the quantum effect of surface atoms’ collective relaxation, was obtained for the first time and shown to generally exist between steps. The repulsive 1/l step interaction was confirmed to come from the surface electrons’ interaction. These results are crucial for understanding the dynamics of steps and for reconciling the dilemma associated with the equilibrium crystal shape of gold crystallites.     

Optical properties of a suspension of hard spheres

The optical properties of suspensions are studied in a wide range of concentrations. An expression for the polarization operator is obtained taking into account the contributions of two-and three-particle correlations. The extinction length l and the transport length l* are calculated in terms of a model of hard spheres. A detailed comparison of the results of calculations with experimental data is performed. In calculations, the structure factor is determined in the Percus-Yevick approximation, while the form factor is taken into account in the Rayleigh-Gans approximation and in terms of the Mie theory. It is shown that taking into account the contribution of three-particle correlations improves the agreement of the theory with experiment. It is found that, in the range of high suspension concentrations, the optical parameters are more sensitive to the choice of the model for the structure factor than for the form factor.     

Spectral properties of quantum dots influenced by a confining potential model

We obtain the exact energy spectra and corresponding wave functions of the spherical quantum dots for any (n,l) state in the presence of a combination of pseudo-harmonic, Coulomb and linear confining potential terms within the exact analytical iteration method (EAIM). The interaction potential model under consideration is labeled as the Cornell modified-plus-harmonic (CMpH) type which is a correction form to the harmonic, Coulomb and linear confining potential terms.     

Quantum efficiency and radiative lifetime in degenerate n-type GaAs

The hole lifetime, the radiative lifetime, the non-radiative lifetime, and the internal quantum efficiency in degenerate n-type GaAs crystals have been investigated with a simplified model of degenerate semiconductors, in which the recombination constant B is approximately proportional to the$\text{?13}\text{8}$ power of the electron density.In n-type GaAs at 77 K, the radiative lifetime reaches a minimum equal to 4 × 10^?9 sec. at 6 × 10¹⁷ cm^?3, and the internal quantum efficiency exhibits a maximum equal to 50% at 8 × 10¹⁷cm^?3, in good agreement with the theoretical prediction of Dumke and the experiments of Cusano. At high impurity concentrations, the polytropy effect is taken into account in the case of GaAs crystals doped with tellurium and selenium. Finally, it is suggested that, for a given high concentration, the internal quantum efficiency increases with increasing temperature, in accordance with the observed results.     

L X-ray-gamma angular correlations following the decay of139Ce

A reinvestigation of theL X-ray-gamma angular correlations following the decay of¹³⁹Ce is made by using a Si(Li) semiconductor detector asL X-ray detector. Coincidence measurements at five different angles were made between the 166-keV gamma ray and theL X-ray spectrum. The data were handled in two different ways: (i) the counts under theL _l +L _α+L _β+L _γ peaks were taken; (ii) the counts under theL _l +L _α+L _β peaks were only considered. Chance coincidences as well as coincidences background were taken into account. The results indicate that no anisotropy is to be found within a margin of error of 6×10^?3.     

Theoretical Study of the 4He(γ, p)3H and 4He(γ, n)3He Reactions

Ab initio calculation of the total cross section for the reactions ⁴He(γ, p)³H and ⁴He(γ, n)³He is presented, using state-of-the-art nuclear forces. The Lorentz integral transform (LIT) method is applied, which allows exact treatment of the final state interaction (FSI). The dynamic equations are solved using the effective interaction hyperspherical harmonics method. In this calculation of the cross sections the three-nucleon force is fully taken into account, except in the source term of the LIT equation for the FSI transition matrix element.     

Excitation of high-spin particle-hole states in A = 28 nuclei by 27Al(α, t) and (α, 3He) reactions

The ²⁷Al(α, t) and (α, ³He) reactions have been measured at E_α = 64.5 MeV. The experimental angular distributions were analyzed by the exact finite-range DWBA calculations assuming a nucleon stripping mechanism. The distributions of spectroscopic strengths for the single-particle transitions with transferred angular momenta l = 0, 1, 2, 3 and 4 have been obtained. The strengths for the transitions to the stretched 6^? states in ²⁸Si and ²⁸Al are compared to those obtained from inelastic scattering on ²⁸Si. The present results show no distinctive differences in the structures for 6^?T = 0 and 1 states in ²⁸Si such as are observed in proton and pion inelastic scattering on ²⁸Si.     

Higher overtones of the bending vibrations of the ground states of 12CS2 and 13CS2

Large numbers of ‘hot’ bands in the first electronic absorption systems of ¹²CS₂ and ¹³CS₂ have been analyzed from plates taken at high dispersion, and accurate rotational constants have been obtained for the overtones of the ground state bending vibration up to v₂ = 6 and l = 3 for ¹²CS₂ and v₂ = 4, l = 2 for ¹³CS₂. The energy differences between the various levels with the same l value have been determined to an accuracy of about ±0.006 cm^?1, but (because of the parallel polarization of the electronic transition) the absolute energies of levels with l > 0 cannot be obtained.     

Electron impact excitation rate coefficients for Ni-like gadolinium

A detailed and large-scaled calculation is performed on the total electron impact excitation rate coefficients from the ground state to the 106 fine-structure levels in 3l^-14l^′ of Ni-like Gd³⁶⁺ employing the relativistic configuration-interaction distorted-wave approximation. The resonance contributions from 3l¹⁷4l^′n^′′l^′′ and 3l¹⁷5l^′n^′′l^′′ doubly-excited states of Cu-like Gd³⁵⁺ are taken into account using the isolated process and isolated resonances approximation. The effects of the radiative decays from the resonances are investigated carefully and are found to be significant. The present rate coefficients, as well as the collision strength, are compared extensively with the previously published results. We believe our results should be more accurate and reliable.     

Formation of black holes in quantum cosmology

The formation of black holes in the quantum cosmology scheme has been discussed by means of calculating the wave function of the universe with a black hole, which is described by a Schwarzschild-de Sitter metric. The average radius of the Schwarzschild black holes formed in the process of the birth of the universe is shown to be about l_p⁶H²/a³, where l_p is the Planck length; ∧=3H² is the cosmological constant; a is the radius of the universe when it enters into the classical era.     

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The total Born cross sections summed over the orbital quantum numbers, as well as the corresponding excitation rates for transitions between highly excited states induced by electron impact, are calculated. The calculations were made for the following principal quantum numbers: 10≤n≤100, Δn/n≤0·3 (Δn=n|n?n′|). The results are presented in a form convenient for interpolations (see Tables 1 and 2).The calculations were performed by using an asymptotic expansion in powers of 1/n and 1/n′, for the exact analytical expression of the total generalized oscillator strength. Comparison of the exact results with the asymptotic ones shows that an accuracy of about 10 percent is achieved for n?2 (see Figs. 1 and 2).For high electron energies, analytical expressions are obtained for the cross sections and the excitation rates. The approximation used is analogous to that of Kramers for the oscillator strenght, the errors do not exceed ～30 percent.     

Optical properties and site distribution of Cr ions in alkali-disilicate glasses

The optical properties of the low-field sites of Cr³⁺-doped alkali (Li, Na, K) disilicate glasses have been investigated using the single configurational coordinate model. The assumption of a Gaussian site distribution for the Cr³⁺ ions taking as parameter the zero-phonon energy has been considered. For alkali disilicate glasses the inhomogeneous contribution to the broadening of the bands, associated to the site distribution, is lower than the homogeneous one. The electron-lattice coupling S and the mean phonon energy ?ω₀ have been obtained with results around 4 and 500 cm⁻¹, respectively, similar to those obtained by other authors in oxide glasses. The site-resolved study of the emission and excitation spectra and the luminescence decay curves have been carried out as a function of temperature. On the one hand, there is evidence of a non-radiative de-excitation process that becomes important over 140 K. On the other hand, and related to the site dependence of the radiative and non-radiative probabilities, different results involving low values for the quantum efficiencies and blue shifts of the emission bands as temperature increases have been explained. Besides, the non-exponential luminescence decay curves have been fitted to an expression proposed by the authors, which takes into account non-coupled distributions for the radiative and non-radiative de-excitation probabilities for the range of temperature covering from 13 to 300 K. From the fits, the temperature dependence of the non-radiative de-excitation probability is obtained for each disilicate glass, the results are in good agreement with the expression obtained assuming the harmonic approximation in the single configurational coordinate model.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.