On the influence of elastic scattering on asymmetric xp-signal distribution

In the standard equation for the strength of photoelectron signals the angular dependence of emitted photoelectrons is represented by the asymmetry parameter. As the geometry has a number of characteristic angles, γ, for example due to a finite solid angle of electron detection, one expects an effective asymmetry parameter β* instead of the theoretical β. But elastic electron scattering causes much more of a spread from the characteristic angle γ to a spectrum of possible γ-values. This paper aims to obtain quantitative results allowing a quantification of the influence of elastic scattering on the theoretical asymmetry parameter β. For photoelectrons with kinetic energies within 1–1.5 keV and elements up to Z = 46 the result is β* = (1.0688 ?0.0235Z+0.000188Z²)β     

The influence of relaxation and nondipole effects on the intensity of X-ray photoelectron spectra

The photoionization cross sections; dipole and nondipole parameters of the angular distribution of photoelectrons; and the spectroscopic factors for the main X-ray photoelectron lines, which are used in quantitative analysis of the surface and most of atoms, have been calculated. It is shown that consideration of nondipole effects leads to a significant (up to 10%) change in the photoelectron angular distribution. Therefore, neglect of nondipole transitions may lead to an error above 10% when MgK _α and AlK _α X-ray lines are used for surface analysis. Consideration of the spectroscopic factors leads to a decrease in the absolute line intensity by about 20%. Calculations showed that this value weakly depends on the atomic number and quantum shell numbers.     

Many-electron effects in atomic processes

The major role of the collectivization of electrons in atoms and quasiatomic formations is demonstrated. The random-phase approximation with exchange, which permits allowance for these effects, is discussed in detail. The need to extend the scope of this approximation when some processes are considered, which is achieved by combining it with perturbation theory, is noted. The role of the collective effects is illustrated by the results of recently performed calculations of the photoionization cross sections of atomic iodine and its positive and negative ions, the single-electron ionization of Xe⁺, resonance-enhanced photon emission in collisions of electrons with atoms and quasiatomic formations, the nondipole corrections to the angular distribution of photoelectrons, and the probabilities of two-electron transitions in which all the energy is released in the form of a single photon. Zh. Tekh. Fiz. 69, 31–35 (September 1999)     

Surface spiral waves in a filamentary vortex

Second-order [ O(k(2)), k = omega/c] nondipole effects in soft-x-ray photoemission are demonstrated via an experimental and a theoretical study of angular distributions of neon valence photoelectrons in the 100-1200 eV photon-energy range. A newly derived theoretical expression for nondipolar angular distributions characterizes the second-order effects using four new parameters with primary contributions from pure-quadrupole and octupole-dipole interference terms. Independent-particle calculations of these parameters account for a significant portion of the existing discrepancy between experiment and theory for Ne 2p first-order nondipole parameters.     

Experimental verification of quadrupole-dipole interference in spin-resolved photoionization

We have measured the spin polarization of Xe (4p)(-1) photoelectrons after ionization with circularly polarized light at photon energies close to the ionization threshold where a resonant enhancement of quadrupole transitions has recently been predicted. At a reaction angle of 90 degrees a nonvanishing longitudinal spin polarization component of about 4% clearly indicates a quadrupole contribution to the photoexcitation. This is the first experimental evidence for the influence of nondipole transitions on the photoionization process at excitation energies much below 1 keV in an observable other than the intensity angular distribution.     

Angle- and spin-resolved photoelectron spectroscopy of the Hg 5d 10 subshell

Parameters describing electron spin polarization in Hg 5d ¹⁰ subshell photoionization have been measured at rare-gas resonance wavelengths between 73.59 nm and 30.38 nm. The spin parameters as well as asymmetry parameters β of a recent measurement are discussed in comparison with both nonrelativistic and relativistic ab initio calculations of several authors. The importance of many-electron correlations and spin-orbit coupling effects is considered.     

Influence of nondipolar effects on the photoelectron angular distribution upon photoionization of 2p and 3d atomic shells

Relativistic calculations of the angular distribution of photoelectrons upon photoionization of 2p and 3d shells in the range of photoelectron energies from 1 to 10 keV are carried out for unpolarized and linearly polarized radiation. An exact expression for the angular distribution of photoelectrons that takes into account nondipolar terms of the order of O[(kr)²] (k is the photon energy and r is the radius of the ionized shell) is obtained in the case of unpolarized radiation. It is shown that the contribution of the O[(kr)²] terms to the differential cross section can be considerable, reaching 24% at the maximum energy considered. Accounting for such terms in the calculation of the ratio of differential cross sections, which is experimentally measured at a certain geometry of angles in the case of linearly polarized radiation, can change this ratio twofold. The parameters of the angular distribution, which are necessary for the conduction of a quantitative x-ray photoelectron analysis, are given for the 2p _1/2 and 2p _3/2 shells of elements with 11≤Z≤29 and for the 3d _3/2 and 3d _5/2 shells of elements with 30≤Z≤54.     

Low-energy nondipole effects in molecular nitrogen valence-shell photoionization

Observations are reported for the first time of significant nondipole effects in the photoionization of the outer-valence orbitals of diatomic molecules. Measured nondipole angular-distribution parameters for the 3sigma(g), 1pi(u), and 2sigma(u) shells of N2 exhibit spectral variations with incident photon energies from thresholds to approximately 200 eV which are attributed via concomitant calculations to particular final-state symmetry waves arising from (E1)multiply sign in circle(M1,E2) radiation-matter interactions first-order in photon momentum. Comparisons with previously reported K-edge studies in N2 verify linear scaling with photon momentum, accounting in part for the significantly enhanced nondipole behavior observed in inner-shell ionization at correspondingly higher momentum values in this molecule.     

Autoionization resonances in the photoabsorption spectra of Fe<Superscript><Emphasis Type="Italic">n</Emphasis>+</Superscript> iron ions

The photoabsorption cross sections of a neutral iron atom, as well as positive Fe⁺ and Fe²⁺ ions, are calculated in the relativistic random-phase approximation with exchange in the energy range 20–160 eV. The wavefunctions of the ground and excited states are calculated in the single-configuration Hartree–Fock–Dirac approximation. The resultant photoabsorption spectra are compared with experimental data and with the results of calculations based on the nonrelativistic spin-polarized version of the random-phase approximation with exchange. Series of autoionization resonance peaks, as well as giant autoionization resonance lines corresponding to discrete transitions 3p → 3d, are clearly observed in the photoabsorption cross sections. The conformity of the positions of calculated peaks of giant autoionization resonances with experimental data is substantially improved by taking into account additionally the correlation electron–electron interaction based on the model of the dynamic polarization potential.     

Synchrotron radiation induced X‐ray production cross sections of 66Dy at energies across its Li (i = 1–3) subshell absorption edges

The X‐ray production (XRP) cross sections for the ₆₆Dy L_k (k = l, α, η, β_2,6,7,15, β_1,6, β_1,3,4,6, β_2,7,15, γ_1,5, γ₂,₃) emission lines have been measured by tuning the incident synchrotron radiation at energies over the range 7.8–9.2 keV and ~10–370 eV above the respective L_i (i = 1–3) absorption edges. These measurements aim to check the reliability of the independent particle approximation models used to generate the theoretical data sets of different physical parameters required to calculate the XRP cross sections and also investigate the influence of many body effects on the photoionization process. The measured values have been compared with 4 sets of XRP cross sections calculated using the Dirac–Fock model‐based X‐ray emission rates, 2 sets of the L_i (i = 1–3) subshell photoionization cross sections deduced from the self‐consistent Dirac–Hartree–Fock model‐based values and the nonrelativistic Hartree–Fock–Slater model‐based values, and 2 sets of the fluorescence (ω_i) and Coster–Kronig (f_ij) yields. The present measured Lγ_2,3 (originating from decay of the L₁ subshell vacancies) XRP cross sections are found to be significantly higher than different sets of theoretical values, whereas a good agreement is generally observed for the various other XRP cross sections and relative intensities.     

Photoionization of the Bound Systems at High Energies

We consider photoionization of a system bound by the central potential V(r). We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann–Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential V(r). We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model-dependent. We demonstrate that if the fullerene field V(r) is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which are so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster decrease of the cross sections becomes important in these cases.     

The total binding energy of the doubly closed shell nuclide 13250Sn82

Using the OSIRIS facility, mass-separated samples containing ¹³²Sb and ¹³²Sn have been prepared, and β-spectra in coincidence with different γ-gates have been recorded. Total decay energies and mass excesses are deduced for these isotopes. The total binding energy of the doubly closed shell nuclide ₅₀¹³²Sn₈₂, is compared to Hartree-Fock calculations using different sets of parameters of the Skyrme effective interaction. The predictions are 2.4 to 3.8 MeV off. This puts doubts on the reliability of calculations of nuclear properties far off the stability valley carried out with these sets of parameters.     

Investigation of the <Emphasis Type="Italic">n-γ</Emphasis> angular correlation in the <Superscript>9</Superscript>Be(α,nγ)<Superscript>12</Superscript>C reaction by analysis of the 4.44-MeV <Emphasis Type="Italic">γ</Emphasis>-line shape

A method for evaluating the angular correlation function (ACF) of neutrons and γ quanta produced in nuclear reactions has been developed based on the analysis of Doppler-broadened γ-line shapes. The lineshape analysis of the 4.44-MeV_γ line from the ⁹Be(α, nγ)¹²C reaction at E _α = 4.03 MeV and θ_γ = 0°, 15°, 30°, ..., 150°, taking into account the angular n and γ angular distributions, made it possible to unambiguously fit the ACF parameters. In view of the importance of this reaction for γ diagnostics of plasma, the γ-line shape has been calculated for the monoenergetic component of isotropic α-particle distribution, characteristic of d-t experiments.     

Interference effects in alignment and orientation processes of atoms excited by polarized radiation

The dynamics of the processes of alignment and orientation of atoms subjected to the action of polarized radiation has been studied theoretically in the energy range of excitation of autoionization resonances. The alignment parameters A ₂₀ for the 4p ⁴5p states of Kr II populated through the excitation and autoionization decay of Kr I 3d ⁹ np resonances depend on energy due to the interference between different resonance channels and the channel of direct photoionization. It is predicted that the orientation parameter O ₁₀ of some Kr II 4p ⁴5p states and the parameter of the angular distribution of photoelectrons β_e1 strongly depend on energy. The absolute photoionization cross sections are calculated for the population of the Kr II 4p ⁴5p states in the case where the energy of excitation photons corresponds to the first four 3d ⁹ np resonances. A good agreement between the calculated and measured photoionization cross sections proves that it is important to take into account the interference between different resonance channels in order to appreciate the dynamics of the Auger decay of Kr I 3d ⁹ np resonances.     

Cascade Mi (i = 1–5) subshell X‐ray emission at incident photon energies across the Lj (j = 1–3) subshell absorption edges of 66Dy

The total M shell and the M_k (k = ξ, αβ, γ, m) X‐ray production cross sections for ₆₆Dy have been measured at incident photon energies across its L_j (j = 1–3) subshell absorption edge energies, ranging 7.8–9.2 keV. This study aims to investigate the evolution of the probability for cascade decay of L_j subshell vacancies as the tunable incident energy ionizes progressively different ₆₆Dy L_j subshells. The experimental X‐ray production cross sections have been compared with theoretical ones calculated using the nonrelativistic Hartree–Fock–Slater (HFS) model‐based photoionization cross sections; three sets of the X‐ray emission rates, fluorescence and Coster–Kronig yield based on the nonrelativistic Hartree–Slater (NRHS) model, Dirac–Hartree–Slater (DHS) model and Dirac–Fock (DF) model; the L_j (j = 1–3) subshell to the M_i (i = 1–5) subshell vacancy transfer probabilities evaluated in the present work. Presently measured total M shell and the M_αβ X‐ray production cross sections are found to be significantly lower than the theoretical ones evaluated using physical parameters based on the relativistic Dirac–Fock/Dirac–Hartree–Slater model calculations, whereas a much better agreement is observed with respect to the NRHS model‐based calculations; however, the measured X‐ray production cross sections are still systematically lower than the NRHS values.     

Analog resonances with J π = 3/2− in the 40Ar(pγ)41 K reaction

γ decay of isobaric analog 2p _3/2 resonances in the ⁴¹K nucleus, observed in the ⁴⁰Ar(pγ)⁴¹K reaction at E _p = 1102, 1839, 1842, 1859, 1875, and 1896 keV, has been experimentally investigated. The decay schemes of these resonances are constructed, the angular distributions of γ rays are measured, and the partial γ widths are determined for the first time. The intensities of single-particle M1 transitions are compared with the results of the calculations within the shell model with surface δ interaction.     

Relativistic calculation of spectra of 2-2 transitions in O- and F-like atomic ions

We have studied theoretically the structure of 1s²2s^n₁2p^n₂ levels in O- and F-like ions with z = 25 ÷ 40. Relativistic perturbation theory is used for the total interelectronic interaction. Allowance is made for Coulomb and relativistic interelectronic interactions. The first order perturbation theory for retardation of the interaction has been calculated fully. The complete calculation has also been made for the nonrelativistic correction in the second order and the Hartree-Fock part of the nonrelativistic correction in the third order. The Hartree-Fock relativistic correction in the second order has been taken into account fully for F-like ions and partially for O-like ions. Corrections to higher orders for z ? 28 have been found empirically and extrapolated to the region z = 29 ÷ 40. For energies of 2-2 transitions, calculation errors for z ? 28 do not exceed 900 cm^-1 and do not increase with z. Typical errors obtained with conventional, more cumbersome calculations are 5000 cm^-1 at z = 30.     

Upper Bounds on the Critical Temperature for Kac Potentials

We consider an Ising system in two dimensions with a two body ferromagnetic interaction J _γ(x, y) that depends on the Kac scaling parameter γ. We prove that the inverse critical temperature β_cr(γ) is strictly above the mean-field value (equal to 1), namely that there exists C>0 so that for any b<C, β_cr(γ)> 1 + bγ²log γ^?1 for all γ sufficiently small. The temperature shift Cγ²log γ^?1 is to leading orders equal to the covariance of the magnetization fluctuations.     

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.