First experimental investigation of the KLL Auger spectrum of Ge (Z=32)

The KLL Auger spectrum of ⁷³Ge from the electron capture decay of ⁷³As was measured with 7 eV instrumental resolution using a combined electrostatic spectrometer and a source prepared by a gas-chemical method. The energies and relative intensities of all the nine resolved KLL lines were precisely determined. A rather poor agreement was found between the measured KLL transition energies and predictions of the widely used semiempirical calculations. Our relative KLL transition intensities agree only with results of the relativistic calculations in intermediate coupling with configuration interaction. The predicted influence of the relativistic effects on the KL₁L₂(³P₀) transition rate was also proven.     

Precise measurement of the KLL and KLX Auger spectra of cadmium from the EC-decay of 111In

The KLL and KLX Auger spectra of Cd from the EC-decay of ¹¹¹In have been analyzed with the 7 eV instrumental resolution using a combined electrostatic spectrometer and a source prepared by a modified Langmuir–Blodgett method. Energies and relative intensities of all the nine well resolved KLL lines have been precisely determined. While the latter quantities were found to be in very good agreement with the relativistic intermediate coupling calculations, the former ones deviate from results of the widely used semi-empirical calculations especially in the case of the absolute energies. The predicted strong influence of the relativistic effects on the KL₁L₂(³P₀) transition intensity has been proved. Most of the main KLX Auger lines have been well separated and their complex structures have been observed. Accurate energies and intensities obtained for these lines have been compared with results of calculations. The intermediate coupling splitting of the KL₂L₂ and KL₃L₃ lines have been revealed. The KLX/KLL, KLN(O)/KLM, and KXY/KLL group intensity ratios have also been determined. A conclusion is made that further finer theoretical investigation on the complex interaction mechanism for two inner-shell vacancies is still very much needed.     

The enhancement effect in K-shell radiative recombination of \mbox{\sffamily\bfseries U}^{\hbox{\sffamily\bfseries\fontsize{10}{12}\selectfont 92+}} ions with cooling electrons

We report the results of the x-ray radiative recombination (RR) experiment at the electron cooler of the ESR storage ring performed, for the first time, for detuned (off-cooling) electron energies. In this experiment the recombination of stored, decelerated bare uranium ions with electrons in the energy range 0–1000 meV was studied by observing K-RR x-ray photons emitted from direct radiative recombination to the lowest n=1 state. In this way the RR process was studied in a state selective manner for several off-cooling electron energies. The measured dependency of the recombination rate on the relative electron energies for K-shell RR x-ray photons are compared with the predictions of both nonrelativistic and fully relativistic calculations for the radiative recombination. A role of the relativistic effects, which contribute substantially for higher relative electron energies, are discussed. Strong enhancement of the recombination rate is observed for the the zero relative electron energy (cooling condition) for the K-shell.     

Study of parameters of the angular distribution of photoelectrons in the relativistic quadrupole approximation

Relativistic calculations of differential cross sections for photoionization are performed and the behavior of parameters β, γ, and δ describing the angular distribution of photoelectrons in the quadrupole approximation is studied. The calculations were carried out for a number of atoms for kinetic energies of photoelectrons E _k ≈50 000 eV. The electronic wave functions of the initial and final states are calculated by the Dirac-Fock method taking into account the exchange interaction and a hole produced in the atomic shell upon photoionization. The dependence of parameters β, γ, and δ on the physical assumptions used in the calculations is studied. Comparison with nonrelativistic calculations shows that relativistic values of the nondipole parameters γ and δ can be substantially different even at low energies of photoelectrons. Our calculations of nondipole parameters γ and δ for the 2p-shell of the Kr atom better agree with the recent experimental data than nonrelativistic calculations performed earlier taking approximately into account the exchange interaction and neglecting a hole.     

Low-field mobilities of rare-earth metals

The KLL Auger spectrum of Ni generated in the electron capture decay of radioactive ⁶⁴Cu in a solid state matrix was measured for the first time using a combined electrostatic electron spectrometer adjusted to a 7 eV instrumental resolution. Energies and relative intensities of the all nine basic spectrum components were determined and compared with data obtained from X-ray induced spectra of metallic Ni and with theoretical results as well. Absolute energy of 6562.5 ± 1.3 eV (related to the Fermi level) measured for the dominant KL₂L₃(¹D₂) than a value obtained from the X-ray induced spectra which is probably caused by the effects of chemical bonding and physico-chemical environment. Moreover, it is higher by 20.4 eV (16??) than a prediction of the semi-empirical calculations by Larkins which indicates an influence of the ??atomic structure effect?? on absolute energies of the Auger transitions following the electron capture decay and, possibly, some imperfections in the calculations. Good agreement of the measured and predicted KL₁L₂(³P₀/¹P₁) transition intensity ratios indicates perceptible influence of the relativistic effects on the KLL Auger spectrum even at Z = 28.     

L-subshell ionization cross sections for Au,Pb, and Bi by 60–600 keV electron impact

TheL ₁-,L ₂- andL ₃-subshell ionization cross sections of Au, Pb and Bi by 60–600 keV electron impact have been determined from the measured x-ray production cross sections. The experimental results have been compared with the relativistic PWBA, the Binary Encounter Approximation (BEA) and the Kolbenstvedt Approximation (KA) calculations. These calculations, especially the relativistic PWBA, give good agreement with the experimental data for theL ₃-subshell. For theL ₁- andL ₂-subshells there are some deviations and these can explain the disagreement observed for theL _α/L _χ- andL _γ/L _χ intensity ratios.     

Electroweak radiative corrections toe + e −→γγ

The explicit analytic expressions for the electroweak radiative corrections to the differential cross sectione ⁺ e ^?→γγ are calculated to one-loop in the framework of the Glashow-Salam-Weinberg model for relativistic energies. Special attention is given to the influence of the parametersM _Z ,M _W on these corrections.     

Das KLL-Auger-Spektrum für 10≦Z≦36

The configuration interaction, applied very recently byAsaad to the calculations ofKLL-Auger spectra, could remove the large discrepancies which existed for lowZ between experimental and theoretical relative group intensities I(KL₁L_2,3)/I(KL₁L₁) and I(KL_2,3L_2,3)/I(KL₁L₁).Asaad's calculations, however, were based on binding energies E(L₁) and energies of the Coulomb and spin-orbit interaction, which were not very accurate. In the present calculations use has been made of more accurate binding energies E(L₁) and Coulomb and spin-orbit interaction energies. It is shown that the absolute error in the results of the new calculations is less than 10%. From this it follows that the remaining discrepancies between theoretical and experimental values of the group intensities for 10≦Z<25 may be solely attributed to the inadequacy of the calculated transition probabilities. This calls for calculations of transition amplitudes of the KLL-process with more accurate wave functions for Z<25, in particular for Z=10.     

Electric dipole transitions for highly excited states in helium-like sulphur

We have calculated relativistic energies, weighted oscillator strengths and transition probabilities for electric dipole (E1) transitions among the terms belonging to 1snl (n?9, l?3) configurations in helium-like sulphur. The calculations are based upon the multiconfiguration Hartree-Fock method within the framework of Breit-Pauli relativistic corrections. Our calculated values are also compared with other experimental and theoretical results.     

Relativistic calculations of ground states of single-electron diatomic molecular ions

We have performed relativistic calculations of ground-state energies for a series of single-electron homonuclear dimers A ₂ ^(2Z?1)+ with nucleus charge Z = 1, 2, 10, 20, 30, 40, 50, 60, 70, 80, 90, 92, and 100 and internuclear distances R = 2/Z. The work involves the Born-Oppenheimer approximation and the single-electron two-center Dirac Hamiltonian, which describes the interaction between an electron and two immovable point charges. Analysis of the convergence process and comparison with data presented in other works for H ₂ ⁺ and Th ₂ ¹⁷⁹⁺ dimers shows that the relative error of the obtained results is on the order of 10^?11–10^?12. High-accuracy values of ground-state energies for some dimers other than Z = 1 and 90 have been obtained in this work for the first time.     

Spin-polarized relativistic calculations on highly ionized molybdenum

The energies of K_α X-ray satellite lines of molybdenum ionized to different degrees in the L shell with closed and open outer shells (n=3,4 and 5) are reported in this work. The calculations have been carried out using Xα method with spin-polarized single configuration relativistic Dirac-Fock wavefunctions. Calculations have also been carried out with un-polarized relativistic wavefunctions. The effect of relativistic spin exchange potential on the total energies of the various states ionized to different degrees in the inner and outer shells are analyzed. As the transition assignments in the spin-polarized treatment of atomic orbitals take into account the spin orientations of the electrons in the initial and final states, the present calculations elucidate the significance of this technique in giving unique spin-dependent transition assignments to experimental energies.     

Vapour phase M4,5N4,5N4,5 Auger electron spectra of antimony and tellurium

High resolution M_4,5N_4,5N_4,5 Auger electron spectra from Sb₄ and Te₂ vapours have been measured using electron impact excitation. The spectra have been decomposed into line components and relative intensities and energies of the components are compared with calculated intensities and energies. The calculations have been done for these molecular samples using the free-atom calculation model involving initially filled shells. The calculations have been treated in the mixed coupling scheme using jj coupling for initial state and intermediate coupling for the final state. The experimental results agree well with the calculated values, indicating that the molecular effects on the relative intensities and energies are very small for these core level transitions. The clear molecular effects are found in the broadening of lines and in the kinetic energy shifts due to extra-atomic relaxation effects.     

Magnetic moments of negative parity baryons from the effective Hamiltonian approach to QCD

The magnetic moments of the S ₁₁(1535) and S ₁₁(1650) baryons are studied in the framework of the relativistic three-quark Hamiltonian derived in the Field Correlation Method. The baryon magnetic moments are expressed via the average current quark energies which are defined by the fundamental QCD parameters: the string tension σ, the quark masses, and the strong coupling constant α _s . The resulting magnetic moments for the J ^P = 1/2^? nucleons are compared both to model calculations and to those from lattice QCD.     

Semiclassical treatment of light-ion induced alignment of theL 3-subshell in heavy atoms

Light ion induced alignment measurements ofL ₃-subshell in heavy atoms are analyzed within the framework of the semiclassical theory of inner shell ionization. Coulomb deflection effects are exactly taken into account by hyperbolic classical orbits while the electron in the initial and final states is approximated by screened relativistic hydrogenic wave functions. Satisfactory agreement between experiments and theory is obtained for proton- and α-particle induced reactions within the whole region of bombarding energies.     

Transition energies, wavelengths, oscillator strengths and transition probabilities between 1s, 1sns and 1snp (2?n?9) states for He-like Silicon

Multiconfiguration Hartree-Fock calculations with Breit-Pauli relativistic corrections are reported for electric dipole transition (E1) energies, wavelengths, weighted oscillator strengths and transition probabilities between all of the 1s², 1sns and 1snp (2?n?9) states for He-like silicon. The results are found to compare very well with available other results except Δn=0 due to differences in the calculated excitation energies.     

A combined experimental and theoretical approach to determine X‐ray atomic fundamental quantities of tin

The knowledge of atomic fundamental parameters, such as the mass attenuation coefficients or fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X‐ray fluorescence analysis techniques. For example, several databases giving the mass attenuation coefficients are accessible and frequently used within a large community of users. These compilations are most often in good agreement for photon energies in the hard X‐ray ranges. However, they significantly differ for low photon energies and around the absorption edges of the elements. In the case of the fluorescence yields, some authors made a review of measured values found in the literature. However, reliable measurements are not so many illustrating the inherent difficulties. Mass attenuation coefficients of tin were determined experimentally in the photon energy range from 100 eV to 35 keV by using monochromatized synchrotron radiation at SOLEIL (France). The fluorescence yields of the 3 L‐subshells of tin were also determined using a reflection geometry setup and the X‐ray fluorescence setup of Physikalisch‐Technische Bundesanstalt. The Coster–Kronig factors for the tin L‐shells were also experimentally determined. The application of high‐accuracy experimental techniques resulted in low uncertainty mass attenuation coefficients and L‐subshell fluorescence yields that are directly compared with existing databases and with updated relativistic configuration mixing Dirac–Fock calculations including Quantum electrodynamics (QED) corrections.     

One-electron spectrum of Yb+: Relativistic energies,transition probabilities and dipole polarizability

Calculations are reported of relativistic ionization energies and transition probabilities in the one-electron spectrum of singly-ionized ytterbium. The relativistic model potential approach used takes into account both valence-core electron exchange and correlation. The influence of polarization of the core by valence electrons on ionization energies and transition probabilities has been studied. Strong cancellation effects have been found for higher transitions of the principal series; these affect both transition probabilities and relative line strengths. The energies are predicted for some states which have not yet been experimentally localized. The static dipole polarizability for Yb⁺ is estimated to be 48.18 g₀³ from computed oscillator strengths; this estimate is compared with lower bounds determined from experimental data.     

Photoelectron spectra of Ga20, In20 and Tl20

The HeI photoelectron spectra of Ga₂O, In₂O, and Tl₂O, as well as atomic In, have been obtained. Some spectral features of the recently published photoelectron spectrum of Al₂O differ noticeably from the heavier suboxides. The assignment of spectral features is supported by fully relativistic DVM SSC X_α calculations, which have been extended to include Al₂O. Best agreement is obtained between calculation and experiment for linear Al₂O, but for bent heavier metal suboxides. In general, the spectral features are indicative of ionic bonding, analogous to the behavior of group IIIB monohalides. Along the sequence Al₂O:Ga₂O:In₂O:Tl₂O, the highest occupied orbital becomes less and less localized on the metal atoms, with a rather dramatic decrease in metal character occurring at Tl₂O. The latter effect is attributable to a change in relative energies of the charge-adjusted metal and oxygen atomic orbitais and relativistic effects., A decrease in the relative ionization cross-section for molecular orbitais which have a large metal ns contribution is correlated with a similar behavior of the relative (ns)⁻¹cross-section for the corresponding atoms.     

Relativistic effects in heavy-ion collisions at SIS energies

The covariant and non-covariant Quantum Molecular Dynamics models are applied to investigate possible relativistic effects in heavy ion collisions at SIS energies. These relativistic effects which arise due to the full covariant treatment of the dynamics are studied at bombarding energiesE _lab=50, 250, 500, 750, 1000, 1250, 1500, 1750 and 2000 MeV/nucl. A wide range of the impact parameter fromb=0 fm tob=10 fm is also considsered. In the present study, five systems¹²C-¹²C,¹⁶O-¹⁶O,²⁰Ne-²⁰Ne,²⁸Si-²⁸Si and⁴⁰Ca-⁴⁰Ca are investigated. The full covariant treatment at low energies shows quite good agreement with the corresponding non-covariant whereas at higher energies it shows less stopping and hence less thermal equilibrium as compared to the non-covariant approach. The collisions dynamics is less affected. The density using RQMD rises and drops faster than with QMD. The relativistic effects show some influence on the resonance matter production. Overall, the relativistic effects at SIS energies (≦2000 MeV/nucl.) are less significant.