Multiconfiguration Dirac-Fock Calculations Research Articles

Theory of conjugate shake-up resonances adjacent to the sub-valence 2p photoionization of sodium atoms

Photoelectron spectra of sub-valence 2p resonance ionization in sodium atoms have been studied employing the multi-configuration Dirac–Fock (MCDF) method. Special interest has been focused on the satellite lines arising from the 3s→3p conjugate shake-up transitions. It has been found that the agreement between our theoretical results and the measured spectra is good if the rearrangement of the residual bound-state electron density is taken into account. By means of large-scale MCDF calculations, the competing spin–orbit and Coulomb interactions have been evaluated satisfactorily to reproduce the experimental shake-up satellite spectra.

Dependence of the probabilities of the electric-multipole electron transitions inW24+on multipolarity

Usually it is accepted that the probabilities of the electric-multipole electron transitions are rapidly decreasing functions of their multipolarity. Therefore while calculating the probabilities of electronic transitions between the configurations of certain chosen parities, it seems sufficient to take into account the first nonzero term, i.e., to consider the electron transitions of lowest multipolarity permitted by the exact selection rules. This paper aims at verifying this assumption on the example of electric-octupole transitions in ${\mathrm{W}}^{24+}$ ion. For this purpose the large-scale multiconfiguration Hartree-Fock and Dirac-Fock calculations have been performed for the configurations [Kr]$4{d}^{10}4{f}^{4}$ and [Kr]$4{d}^{10}4{f}^{3}5s$ energy levels of ${\mathrm{W}}^{24+}$ ion. The relativistic corrections were taken into account in the quasirelativistic Breit-Pauli and fully relativistic Breit (taking into account QED effects) approximations. The role of correlation, relativistic, and QED corrections is discussed. Line strengths, oscillator strengths, and transition probabilities in Coulomb and Babushkin gauges are presented for $E1$ and $E3$ transitions among these levels.

Photoabsorption Spectra of Double- and Triple-Excitations above the Calcium 3pThreshold

Calcium triple photoexcitations leading to 3 p satellites have been observed by photoion spectroscopy measurements in the photoion energy region 35 to 42 eV. Monochromatized synchrotron radiation has been used for light source. The photoions are counted by discriminating the resultant calcium ionic charge states. Many photoion spectral peaks are found above the calcium 3 p double excitation region. Two series of triple excitation have been found; one starts at 37.1 eV and the other starts at 40.6 eV in photon energies. To gain a deep insight of the triple-electron excitations, multi-configuration Dirac–Fock calculations have been carried out. The photo-excited 3 p -vacancy states are found to be a strong mixture of 3 d , 4 s , and 4 p orbitals. A compact 3 d -orbital describes well the lower energy satellite resonances, whereas a diffuse 3 d -orbital describes well the higher energy satellite resonances.

Photoionization study of Kr+ and Xe+ ions with the combined use of a merged-beam set-up and an ion trap

Photoionization cross sections of halogen-like Kr+ and Xe+ ions have been measured in the photon energy range extending up to 15 eV above the threshold. Two different devices were used, a merged-beam set-up and an ion trap. Combination of the two techniques allows for the extraction of the pure ground state ionization cross section on an absolute scale. Multiconfiguration Dirac–Fock calculations reproduce the magnitude of the direct photoionization cross sections well.

Nuclear charge radii and electromagnetic moments of radioactive scandium isotopes and isomers

Collinear laser spectroscopy experiments with the Sc+ transition 3d4s 3D2 → 3d4p 3F3 at λ = 363.1 nm were performed on the 42–46Sc isotopic chain using an ion guide isotope separator with a cooler-buncher. Nuclear magnetic dipole and electric quadrupole moments as well as isotope shifts were determined from the hyperfine structure for five ground states and two isomers. Extensive multi-configurational Dirac–Fock calculations were performed in order to evaluate the specific mass-shift, MSMS, and field-shift, F, parameters which allowed evaluation of the charge radii trend of the Sc isotopic sequence. The charge radii obtained show systematics more like the Ti radii, which increase towards the neutron shell closure N = 20, than the symmetric parabolic curve for Ca. The changes in mean-square charge radii of the isomeric states relative to the ground states for 44Sc and 45Sc were also extracted. The charge radii difference between the ground and isomeric states of 45Sc is in agreement with the deformation effect estimated from the B(E2) measurements but is smaller than the deformation extracted from the spectroscopic quadrupole moments.

RelativeKx-ray intensity studies on valence-electron structure of Ti and Co in TixCo1−xalloys

$K\ensuremath{\alpha}$-to-$K\ensuremath{\beta}$ x-ray intensity ratios of Ti and Co in pure metals and in alloys of Ti${}_{x}$Co${}_{1\ensuremath{-}x}$ ($x=0.7$, 0.6, 0.5, 0.4, and 0.3) have been measured for understanding the charge-transfer and delocalization phenomena in the Ti${}_{x}$Co${}_{1\ensuremath{-}x}$ alloys using the energy-dispersive x-ray fluorescence technique. The valence-electron structure of Ti and Co in the samples have been evaluated by the comparison of the measured $K\ensuremath{\alpha}$-to-$K\ensuremath{\beta}$ x-ray intensity ratios with the results of multiconfiguration Dirac-Fock calculations for various electron structures of these metals. Significant changes in the 3$d$ electron population (with respect to the pure metal) are observed for Ti and Co in different alloy compositions. Our analysis indicates that these changes can be explained by assuming the transfer of 3$d$ electrons from one element to the other element (charge transfer) and/or the rearrangement of electrons between 3$d$ and 4$s$,4$p$ states (delocalization) of the individual metal atoms.

EquilibriumK-,L-, andM-shell ionizations and charge-state distribution of sulfur projectiles passing through solid targets

In the present work, an alternative approach for the evaluation of the equilibrium K-, L-, and M-shell ionizations and the mean charge state q for projectiles passing through various targets has been proposed. The approach is based on measured K x-ray energy shifts and line intensity ratios and utilizes the theoretical analysis of projectile spectra using multiconfiguration Dirac-Fock calculations. It was applied for the satellite and hypersatellite K lines in the x-ray spectra emitted by sulfur projectiles passing with energies of 9.6-122 MeV through carbon, aluminium, titanium, and iron targets, recorded by a Si(Li) detector. It was found that only in the high projectile energy region there was significant dependence of mean equilibrium K-shell ionization on the target atomic number. The equilibrium L-shell ionization rises with the increase of sulfur energy until 32 MeV, but for higher energies the changes are very weak. The equilibrium M-shell ionization changes very weakly for low projectile energy while for higher energies this ionization is practically constant. For each target, the estimated value of q rises with the increase of the sulfur energy value. The dependence of the sulfur charge state on the target atomic number was discussed by taking into account the crossmore » sections for ionization, decay, and electron capture processes. The data were compared with the experimental data measured by other authors and with the predictions of Shima's and Schiwietz and Grande's semiempirical formulas. The presented good agreement points out that this alternative approach delivers quantitative results.« less

Interpretation of the SiKαx-ray spectra accompanying the stopping of swift Ca ions in low-density SiO2aerogel

This article presents a detailed analysis of the $K\ensuremath{\alpha}$ x-ray spectra of Si induced by $11.4$ MeV/u Ca projectiles penetrating a low-density SiO${}_{2}$ aerogel target measured with high spectral and spatial resolution at the UNILAC accelerator at GSI-Darmstadt. The low-density material used in the experiment was crucial for the space-resolved studies of the Si x-ray radiation (for different energies of stopping Ca ions). The stopping length of the $11$ MeV/u Ca ions reaches up to $10$ mm in the low-density SiO${}_{2}$ aerogel, whereas in regular quartz solid targets it is about $100$ times shorter. The analysis of the x-ray spectra emitted by the stopping medium has shown a high level of the $L$-shell ionization, especially in the later considered phase (${E}_{p}~5$ MeV/u) of the stopping process. It has been further demonstrated that the population of the highly ionized states produced in the ion-atom collisions can be substantially reduced in the time between the collision and the x-ray emission due to the very intense rearrangement processes occurring in Si situated in the chemical environment of oxygen atoms. Moreover, comparison of the experimental values of the $K\ensuremath{\alpha}$ $L$-shell satellite energy shifts with the results of the multiconfiguration Dirac-Fock calculations allows us to find that Si valence electron configuration is enriched due to electron transfer from valence-electron-rich oxygen atoms into highly ionized silicon atoms. Our results indicate that the Coulomb explosion in a highly ionized track core is prevented by rapid neutralization in the femtosecond time scale.

Observation of internal structure of theL-shell x-ray hypersatellites for palladium atoms multiply ionized by fast oxygen ions

An observation of the internal structure of the L-shell hypersatellite x rays resulting from the one-photon decay of L{sup -2} double-vacancy states in palladium multiply ionized by oxygen ions is reported. The Pd L{sub 3}{yields}M{sub 4,5} x-ray spectrum was measured with a von Hamos high-resolution crystal spectrometer. The complex shape of the observed spectrum could be interpreted in detail using relativistic multiconfiguration Dirac-Fock calculations. The relative intensities of the measured x rays were found to be in good agreement with semiclassical approximation calculations using relativistic Dirac-Hartree-Fock wave functions.

Atomic Structures and Radiative Properties of He-like Ions in Debye Plasmas

A detailed investigation of plasma screening effects on atomic structure and transition properties are presented for He-like ions embedded in dense plasma environment. Multi-configuration Dirac-Fock calculations were carried out for these ions by considering a Debye-Hückel potential. A large-scale relativistic configuration-interaction method is adopted to calculate transition energies and transition probabilities and to allow for a systematic improvement of the calculations. Comparison of the presently calculated results with others, when available, is made.

Multiconfiguration Dirac–Fock calculations of angle- and spin-resolved Auger spectra

The energies, line intensities as well as angular anisotropy and spin polarization parameters have been calculated for the L 2,3M 1M 4,5 Auger spectra of Zn, Kr, Sr, Pd, Cd, Xe, Ba, Yb, Hg, Rn, Ra and No, the M 2,3N 1N 4,5 Auger spectra of Pd, Cd, Xe, Ba, Yb, Hg, Rn, Ra and No, the N 2,3O 1O 4,5 Auger spectra of Hg, Rn, Ra and No, the M 4,5N 1N 2,3 Auger spectra of Kr, Sr, Pd, Cd, Xe, Ba, Yb, Hg, Rn, Ra and No, and the N 4,5O 1O 2,3 Auger spectra of Xe, Ba, Yb, Hg, Rn, Ra and No. The calculations have been performed describing the Auger emission process in the context of scattering theory (relativistic distorted wave approximation) where the Auger transition amplitudes and scattering phases have been evaluated applying a relaxed orbital method within a multiconfiguration Dirac–Fock approach. Comparisons with other theoretical and experimental data are made wherever possible.

4d−1photoelectron spectra and subsequentN4,5OOAuger electron spectra of atomic Sb

$4{d}^{\ensuremath{-}1}$ photoelectron and subsequent ${N}_{4,5}\mathit{OO}$ Auger electron spectra of Sb have been measured using synchrotron radiation. Features created by an open shell electronic structure of atomic Sb in the spectra have been interpreted using multiconfigurational Dirac-Fock calculations. The results are compared with the molecular Sb${}_{4}$ and the comparison shows that the relaxation pathways of the hole states in atomic and molecular Sb are very different, so that different groups of states are populated in the corresponding Auger spectra.

Correlation, relativistic, and quantum electrodynamics effects on the atomic structure of eka-thorium

Large-scale multiconfiguration Dirac-Fock calculations have been performed for the superheavy element eka-thorium, $Z=122$. The resulting atomic structure is compared with that obtained by various computational approaches involving different degrees of approximation in order to elucidate the role that correlation, relativistic, Breit, and quantum electrodynamics corrections play in determining the low-energy atomic spectrum. The accuracy of the calculations is assessed by comparing theoretical results obtained for thorium with available experimental data.

First Optical Hyperfine Structure Measurement in an Atomic Anion

We have investigated the hyperfine structure of the transition between the 5d{7}6s{2} {4}F{9/2}{e} ground state and the 5d{6}6s{2}6p {6}D{J}{o} excited state in the negative osmium ion by high-resolution collinear laser spectroscopy. This transition is unique because it is the only known electric-dipole transition in atomic anions and might be amenable to laser cooling. From the observed hyperfine structure in 187Os- and 189Os- the yet unknown total angular momentum of the bound excited state was found to be J=9/2. The hyperfine structure constants of the {4}F{9/2}{e} ground state and the {6}D{9/2}{o} excited state were determined experimentally and compared to multiconfiguration Dirac-Fock calculations. Using the knowledge of the ground and excited state angular momenta, the full energy level diagram of 192Os- in an external magnetic field was calculated, revealing possible laser cooling transitions.

High-resolution X-ray study of the multiple ionization of Pd atoms by fast oxygen ions

The multiple ionization of the L- and M-shells of Pd by fast oxygen ions has been studied by measuring with high-resolution the satellite structures of the Lα1,2 X-ray transitions. Relativistic multi-configuration Dirac-Fock (MCDF) calculations were used to interpret the complex X-ray spectrum, allowing to derive the number of L- and M-shell spectator vacancies at the moment of the X-ray emission. After correcting these numbers for the atomic vacancy rearrangement processes that take place prior to the X-ray emission, the ionization probabilities corresponding to the collision time were obtained. The latter were compared to predictions of the semiclassical approximation (SCA) and the geometrical model. The SCA calculations were performed using relativistic hydrogenic and self-consistent Dirac-Hartree-Fock (DHF) electronic wave functions. It was found that the use of the more realistic DHF wave functions in the SCA calculations leads to a much better description of the measured ionization probabilities for both the L- and M-shells.

Valence-electron configuration of Ti and Ni in TixNi1−x alloys from Kβ-to-Kα X-ray intensity ratio studies

Kbeta-to-Kalpha X-ray intensity ratios of Ti and Ni have been measured in pure metals and in alloys of Ti(x)Ni(1-x) (x=0.7, 0.6, 0.5, 0.4 and 0.3) following excitation by 22.69 keV X-rays from a 10 mCi (109)Cd radioactive point source. The valence-electron configurations of these metals were determined by corporation of measured Kbeta-to-Kalpha X-ray intensity ratios with the results of multiconfiguration Dirac-Fock calculation for various valence-electron configurations. Valence-electron configurations of 3d-transition metals in alloys indicate significant differences with respect to the pure metals. Our analysis indicates that these differences arise from delocalization and/or charge transfer phenomena in alloys. Namely, the observed change of the valence-electron configurations of metals in alloys can be explained with the transfer of 3d electrons from one element to the other element and/or the rearrangement of electrons between 3d and 4s, 4p states of individual metal atoms.

Photoelectron angular distribution and linear magnetic dichroism in the4pphotoemission from Rb atoms

The angular distribution of photoelectrons and linear magnetic dichroism in the angular distribution for the $4p$ photoemission from Rb atoms in the ground state, oriented by laser pumping, were measured in the photon energy range from $50$ to $100$ eV. The experimental results are compared with the multiconfiguration Dirac-Fock (MCDF) calculations. We show that the zero-crossing of the dichroism as a function of energy is connected with the Cooper minimum in the cross section. This fact can be used for an accurate determination of the position of the Cooper minimum.

Atomic structure calculations and beam-foil observations of La IV

Relativistic Hartree–Fock and multiconfigurational Dirac–Fock calculations of atomic structure and transition rates have been carried out in trebly ionized lanthanum (La3+, Z = 57). The calculations have to cope with configuration interaction effects but also with the very complex situation of the collapse of the 4f wave function. The calculations are compared to experimental data obtained with beam-foil spectroscopy in the extreme ultraviolet, at ion energies that favour the production of the spectrum La IV. Besides lines known from sliding spark discharges, many more lines are observed that have not yet been identified. Time-resolved measurements yield three level lifetimes in La IV that agree roughly with the results of our own calculations.

Fast decay of 4p and 4s core holes in Sb4 clusters

The 4s and 4p photoelectron spectra of a vapour phase Sb4 antimony cluster have been recorded using synchrotron radiation excitation. Relativistic multiconfiguration Dirac–Fock calculations have been used to predict the spectral features. The strongly different lifetime widths of the two energetically close-lying orbitals have been observed and the existing fast Auger channels are modelled.

Valence-electron configuration of Fe, Cr, and Ni in binary and ternary alloys fromKβ-to-Kαx-ray intensity ratios

$K\ensuremath{\beta}$-to-$K\ensuremath{\alpha}$ x-ray intensity ratios of Fe, Cr, and Ni have been measured in pure metals and in alloys of ${\text{Fe}}_{x}{\text{Ni}}_{1\ensuremath{-}x}$ ($x=0.8$, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2), ${\text{Ni}}_{x}{\text{Cr}}_{1\ensuremath{-}x}$ ($x=0.8$, 0.6, 0.5, 0.4, and 0.2), ${\text{Fe}}_{x}{\text{Cr}}_{1\ensuremath{-}x}$ ($x=0.9$, 0.7, and 0.5), and ${\text{Fe}}_{x}{\text{Cr}}_{y}{\text{Ni}}_{1\ensuremath{-}(x+y)}$ ($x=0.7\ensuremath{-}y=0.1$, $x=0.5\ensuremath{-}y=0.2$, $x=0.4\ensuremath{-}y=0.3$, $x=0.3\ensuremath{-}y=0.3$, $x=0.2\ensuremath{-}y=0.2$, and $x=0.1\ensuremath{-}y=0.2$) following excitation by 22.69 keV x rays from a 10 mCi $^{109}\text{C}\text{d}$ radioactive point source. The valence-electron configurations of these metals were determined by corporation of measured $K\ensuremath{\beta}$-to-$K\ensuremath{\alpha}$ x-ray intensity ratios with the results of multiconfiguration Dirac-Fock calculation for various valence-electron configurations. Valence-electron configurations of $3d$ transition metals in alloys indicate significant differences with respect to the pure metals. Our analysis indicates that these differences arise from delocalization and/or charge transfer phenomena in alloys. Namely, the observed change of the valence-electron configurations of metals in alloys can be explained with the transfer of $3d$ electrons from one element to the other element and/or the rearrangement of electrons between $3d$ and $4s,4p$ states of individual metal atoms.