Photoabsorption cross section of the Thomas-Fermi atom

The photoabsorption cross section σ(ω) and the distribution of oscillator strengths df/dω [these values are related as σ=(2π²e²/mc)(df/dω)] were determined for an atom with a large Z value using the semiclassical approach. These values were found for low frequencies with the use of the Vlasov kinetic equations, which were numerically solved by the method of particles. The asymptotic behavior of the distribution of oscillator strengths at high frequencies was determined by semiclassical equations for the photoabsorption cross section of electron shells in a Coulomb potential. The asymptotic equations were used to suggest an interpolation equation for the distribution of oscillator strengths over the whole Thomas-Fermi frequency range 27 eV ? ?ω ? 27Z² eV. This equation was used to calculate the logarithmic mean excitation energy, which appears in problems of ionization loss of charged particles. The distribution of oscillator strengths in a neutral atom allows the radiative properties of dense matter to be determined.     

Photoabsorption cross section of titanium to cobalt

Calculations of the photoabsorption cross section of the elements TiCo are compared with recent measurements. The structure seen near the 3p ionization threshold is explained by the large 3p–3d oscillator strength and the short lifetime of the 3p hole due to a super Coster-Kronig transition.     

Giant dipole resonance in 4d photo absorption of atomic barium

We calculate the photoabsorption cross section for the 4d¹⁰ and 5p⁶ shells of atomic barium using the random phase approximation (RPAE) including relaxation. For both shells the oscillator strength goes mainly into a collective vibration of the entire shell.     

Electron-impact ionization and dissociative ionization of sulfur in the gas phase

We describe the methods and the results of investigation of the yield of positive ions formed as a result of electron-impact ionization of sulfur. The ionization energy for the basic molecule and the energies corresponding to the emergence of fragment ions are obtained from the ionization efficiency curves. The dynamics of formation of molecular sulfur ions in the temperature range 320–700 K is investigated. The energy dependences of efficiency S _n of the ion formation for n = 1–6 are analyzed, and their appearance energies are determined. The total cross section of sulfur ionization by a monochromatic electron beam is also investigated. Using the linear approximation method, we marked out features on the ionization function curve, which correspond to the ionization and excitation energies for multiply charged ions. The total cross section of the formation of negative sulfur ions is measured in the energy range 0–9 eV.     

Measurement of the cross section for the e + e ? → ωπ0 → π0π0γ process in the energy range of 1.1–1.9 GeV

The cross section for the e ⁺ e ^? ?? ???⁰ ?? ??⁰??⁰?? process has been measured in the energy range of 1.1?C1.9 GeV. The measurement has been made with the Spherical Neutral Detector at the VEPP-2000 e ⁺ e ^? collider. The data in the energy range of 1.1?C1.4 GeV are in agreement with the earlier measurements with the SND and CMD-2 detectors. The cross section has also been measured above 1.4 GeV.     

Elastic Scattering of Two Photons by a Multicharged Atomic Ion

The elastic scattering of two X-ray photons by a multicharged atomic ion has been studied theoretically. A pronounced resonance structure and strong angular anisotropy of differential scattering cross section have been predicted in the energy range of a scattered photon from ?ω–I_1s to ?ω+I_1s (where is the energy of the incident photon and is the ionization energy threshold of the shell of the ion). The absolute value of the observed cross section has been quantitatively estimated.     

Anomalous elastic scattering of X-rays by a multiply chargedion

Absolute values and the form of the differential cross section for anomalous elastic scattering of an X-ray photon by a Ne⁶⁺ ion near the ionization threshold of the 1s shell are calculated. The many-particle effect of deep-vacancy stabilization caused by a change from a neutral atom to its multiply charged ion is taken into account. The calculation results are predictable.     

Electron Transitions during the Capture of an Electron by a He<Superscript>2+</Superscript> Ion at the Argon Atom

We have measured the absolute values of the total cross section of the one-electron capture by He²⁺ ions in the kinetic energy range 2–30 keV at the Ar atoms. The absolute values of the differential scattering cross sections of He⁺ ions formed during the one-electron capture and the electron capture with ionization at energies of 2.2, 5.4, and 30 keV have been determined. The electronic states of the formed ions have been determined using collision spectroscopy based on analysis of the change in the kinetic energy of He⁺ after the interaction. We have measured doubly differential (with respect to the kinetic energy and the scattering angle) cross sections of the formation of free electrons. The free electron formation channels (direct ionization and electron capture with ionization) have been analyzed by calculating the electron terms of the (HeAr)²⁺ system. The calculated cross section of capture with ionization is in conformity with the cross section measured using collision spectroscopy.     

Notes on number density fluctuations and the scattering cross section for electromagnetic waves scattered from a thermal nonequilibrium plasma

The scattering cross section and the Doppler spectrum for electromagnetic waves scattered by the electron density fluctuations of a plasma, where the mean kinetic temperature of the electronsT _e may differ from that of the ionsT _i , has been obtained among others byFejer, Buneman, Renau, Camnitz andFlood, andSalpeter. These authors use different methods of approach to calculate the autocovariance of the electron number-density fluctuations (from the mean) and then obtain the scattering cross section. Because of the differing results, the methods, concepts, and derivations of the scattering cross section are carefully examined in this paper. It is shown that the short-time dynamical considerations incorporated in the formulation of the statistical theory of the electron number-density fluctuations of the plasma as used by several authors (for instanceFejer, Buneman, Salpeter,) leads to results of limited validity. In addition, a fundamental error in calculating the electron density fluctuations leads these latter authors to an incorrect scattering cross section. The theory of scattering of electromagnetic waves from a plasma, where the electrons arenot in thermal equilibrium with the ions but statistical equilibrium exists, is developed in a general way. The covariance of the number-density fluctuations from the mean of the charged species of the plasma and the scattering cross sectionσ(q) are obtained. In particular it is shown that for a wavelength λ much greater than the effective Debye lengthd, the backscattering cross section increases and approaches complete incoherent scattering asT _e /T _i increases. This result is explained by noting that in the case of thermal equilibrium, the predicted value of the back-scattering cross section is smaller than that of the backscattering cross section from completely uncorrelated electron density fluctuations because the electrostatic interaction between the charged particles of the plasma, which is a function ofT _e andT _i , introduces a certain amount of organization in otherwise completely uncorrelated electron density fluctuations. When the mean temperature of the electrons increases relative to that of the ions, the organization introduced in the fluctuations diminishes because of the increasing thermal agitation of the electrons relative to that of the ions, and the backscattering process approaches that of incoherent backscattering (Thomson-type scattering). The spectrum function of incoherent scattering of electromagnetic waves from a nonequilibrium plasma is obtained and some cases of current interest are plotted.     

Photoionization cross sections and oscillator strengths of neutral cesium

The absolute photoionization cross sections from the 6p ²P_1/2 excited state of cesium at threshold and above the threshold region have been measured using the saturation absorption technique. The photoionization cross section at the ionization threshold is determined as 22.6±3.6 Mb, whereas in the region above threshold its value ranges from 22 to 20 Mb for photoelectron energies up to 0.1 eV. A comparison of the photoionization cross sections with earlier reported theoretical and experimental data have been presented and are in good agreement within the uncertainty. In addition, the oscillator strengths of the 6p ²P_1/2→n d ²D_3/2 (21≤n≤60) Rydberg transitions of cesium have been calibrated using the threshold value of the photoionization cross section. A complete picture of the oscillator strengths from the present work and previously reported data from n=5–60 is presented.     

Opacities of high temperature uranium plasmas

Cross sections for thermal radiation in a uranium plasma at solid state density and temperatures in the KeV range are presented. The b?-and ??-absorption of ions is described by Kramers-type formulae and scattering on electrons by the Thomson formula. The b?-contributions from different states of ionization and excitation are treated individually, using a Slater model for the mean ionization potential of each electron configuration. It is assumed that all terms of a configuration contribute to one common absorption edge, and that excited configurations give rise to hydrogen-like series. The resulting frequency-dependent cross sections are illustrated. For kT < 10 keV scattering is unimportant. Near the Planck maximum (hν?3kT), the main contributions to the overall absorption arise from the ionization of the ground configurations of the predominant ionization stages.     

Self-avoiding Fractional Brownian Motion��The Edwards Model

In this work we extend Varadhan??s construction of the Edwards polymer model to the case of fractional Brownian motions in ? ^d , for any dimension d??2, with arbitrary Hurst parameters H??1/d.     

Three particle correlation function of metal ions in tetrahedral coordination determined by XANES

The three particle correlation function of local atomic distribution at metal ion sites in solutions has been extracted from XANES (X-ray absorption near edge structure) spectra of [CrO₄]²⁻ and [MnO₄]⁻ ions measured by using synchrotron radiation. The absorption cross section for 1s core level excitation is calculated in the real space multiple scattering approach using the Hedin and Lundqvist energy dependent potential. We show that in these systems the expansion of the total absorption cross section in terms of contributions of higher order scattering processes is possible over a large energy range. This gives a unified theory of XANES and EXAFS and allows the third order correlation function to be extracted from experimental data.     

Distribution of the oscillator strengths in the 2<Emphasis Type="Italic">p</Emphasis> absorption spectra of 3<Emphasis Type="Italic">d</Emphasis> transition metal films

The absorption cross-sections in the region of the resonance structure of the 2p ionization threshold of metal films are originally measured for the total series of 3d metals from Sc to Cu. The partial 2p absorption cross-sections are found, and the integral oscillator strengths are determined. The linear dependence of the sum of oscillator strengths in the range from 0 to 80 eV above the L ₃ absorption edge on the number of unfilled 3d states is established. The dependence breaks down for Cr, Fe, and Ni.     

Excitation of resonance lines of a Zn+ ion by electron impact

Excitation of individual components of the resonance 4p ² P ₁ ^2,3/2/0 doublet of a Zn⁺ ion by electron impact is studied for the first time by the spectroscopic method in crossed beams. A distinct structure (above the ionization potential of an ion as well) found in the energy dependences of the effective excitation cross section is associated mainly with the decay to the resonance levels (direct or cascade) of autoionization states of zinc atoms and ions formed through the excitation of electrons from the subvalence 3d ¹⁰ shell. The results obtained are compared with data of other experiments and theoretical calculations by the method of strong coupling of five and fifteen states, as well as with the semiempirical calculation using the Van Regemorter formula.     

Neutrons scattering as a method for fermi surface investigations

High-T_c A15-compounds are suggested as suitable materials for which Fermi surface investigations by means of thermal neutron scattering might be possible. The structure of the differential neutron—d-electron cross section at small scattering angles is connected in a simple way with parameters defining the Fermi surface of the linear chain model. The magnitude of the cross section is estimated are compared with the phonon background.     

The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the ??extrinsic?? characteristics of the oscillator (amplitudes of ??classical?? oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|_max ?? 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|_max ?? 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|_max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|_max ?? 0. The influence of the CCS formation on the averaged probability ??D?? of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value ??D _r=0?? = 10^?80 to ??D?? ?? 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.     

Streuung von 25 keV-Elektronen an Gasen

The differential cross section of neon, argon, krypton, and xenon for the elastic scattering and for the excitation of optical transitions has been measured. For neon and argon the elastic angular distribution can be described by the cross section calculated according toWentzel andLenz. For krypton and xenon there are considerable deviations from the Wentzel-Lenz cross section. In these cases it is better to calculate the elastic differential cross section from Slater eigenfunctions, from Thomas-Fermi-Dirac or from Hartree-Fock electron density distribution. The differential cross sections for the excitation of optical transitions, so far as measured here, obey for?<? _c the dipol approximation, i.e. for angles not to small the inverse square angular dependence is valid.? _c is higher for the heavier rare gases. The oscillator strengths for some transitions have been determined from the scattering measurements in satisfactory agreement with theoretical values.     

Electron impact ionization rate coefficients and cross sections for highly ionized iron

Electron impact ionization cross sections for the ions Fe(XVII)-(XXVI) have been computed in a distorted wave exchange approximation. Analytic fits are provided for the cross section data, as well as for the rate coefficients assuming a Maxwellian electron velocity distribution. For ejection of a 2p ground state electron, the scaled ionization rate was found to depend linearly on the number of 2p electrons in the ion.