Intermediate Coupling Scheme Research Articles

Relativistic calculations for total energies, ionization energies, and one-electron binding energies for Neodymium ions Nd I to Nd[formula omitted]

We present the results of calculations for the total energies, ionization energies, and one-electron binding energies for ground-state configurations of neodymium ions Nd I to Nd59+. These calculations are based on the Dirac–Fock approximation taking the Breit and quantum electrodynamics corrections into account. The configuration interaction method, taking into account all relativistic configurations corresponding to the non-relativistic one, is used to obtain total energies and wave functions in the intermediate coupling scheme. Comparison is given with other available data.

Site‐dependent correlation strength and occupation number of 5f electrons in alpha phase plutonium metal

AbstractIn order to quantify the site‐dependent correlation strengths in terms of the quasi‐particle weights and the occupation numbers of 5f electrons in alpha phase plutonium metal with eight crystallographically nonequivalent atomic sites Pun (n = 1–8), we perform a first principles calculation by using a many‐body method merging density functional theory with dynamical mean‐field theory plus the relativistic and correlation effects. The quasi‐particle weight, the electronic spectrum function, the hybridization function, as well as the occupation number of Pu 5f electrons all suggest that Pu1 and Pu8 atoms have the most itinerant and the most localized 5f electrons, respectively, while the other atoms Pun (n = 2–7) exhibit an intermediate correlation strength. The quasi‐particle weights demonstrate that only the jj or intermediate coupling scheme is more appropriate for Pu 5f electrons in comparison with the Russel–Saunders (LS) scheme. The electronic spectrum function and the occupation analysis establish that Pu 5f electrons simultaneously have dual itinerant and localized regimes with average 5f occupation numbers of n5f between 4.8994 and 4.9628, which are mainly composed of 5f4, 5f5, and 5f6 configurations, irrespective of different atomic sites. Finally, we also estimate the so‐called quasi‐particle band structure to directly compare with angle‐resolved photoemission spectrum.

Hard x-ray photoemission spectroscopy of the ferrimagnetic series Gd6(Mn1−xFex)23

We study the evolution of the electronic structure of the intermetallic series ${\mathrm{Gd}}_{6}{({\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x})}_{23}, x=0.0--0.75$, which shows nonmonotonic ferrimagnetic ordering temperatures ${T}_{C}$ but with a systematic reduction of the total bulk magnetization upon increasing Fe content, $x$. We have carried out hard x-ray photoemission spectroscopy to elucidate the relation between electronic structure and properties of the series. The Gd $3d$ and Gd $4d$ core-level spectra indicate trivalent ${\mathrm{Gd}}^{3+}$ multiplets in the intermediate-coupling scheme with features due to $L\text{\ensuremath{-}}S$ and $j\text{\ensuremath{-}}J$ coupling. The Fe $2p$ core levels show asymmetric single peak metal-like spectra, while the Mn $2p$ core levels show asymmetric doublet peaks. The relative intensities of the Mn $2p$ doublets as a function of $x$ indicate occupancy changes of distinct crystallographic sites associated with Mn up-spin and down-spin states. The valence band spectra identify the Gd $4f$ states at high binding energies ($\ensuremath{\sim}7.4$ eV). The Mn $3d$ states occur at the Fermi level and as a broad feature between 2 and 5 eV binding energy in ${\mathrm{Gd}}_{6}{\mathrm{Mn}}_{23}$. Upon substitution, the Fe $3d$ states show up as small shifts to higher binding energies compared to Mn $3d$ states. The Fe $3s$ and Mn $3s$ spectra show exchange split peaks, allowing an estimate of the Mn and Fe magnetic moments using a Van Vleck analysis, which also provides a quantification of occupancy changes with $x$. The overall results are consistent with the bulk net magnetization, indicating that Mn up-spin sites become Fe down-spin sites on substitution, while the nonmonotonic ${T}_{C}$ originates in a change from Mn sublattice to Fe sublattice derived ordering.

Assessing the correlated electronic structure of lanthanum nickelates

The series of nickel-oxide compounds LaNiO3 (formal Ni(d 7)), La2NiO4 (formal Ni(d 8)) and LaNiO2 (formal Ni(d 9)) is investigated by first-principles many-body theory, using a combination of density functional theory, self-interaction correction and dynamical mean-field theory. The characteristics of these different nickelates, in good agreement with available experimental data, is revealed by employing a compound-independent choice for the local Coulomb interactions. The dichotomy within the low-energy dominant Ni-e g sector of kind is rising with growing Ni(3d) filling across the series. An intermediate-coupling scheme for spin-polarized calculations is introduced, which leads to very weak Ni ordered moments for the infinite-layer compound LaNiO2 in contrast to the robust-moment system La2NiO4.

Hard x-ray photoemission spectroscopy of GdNi and HoNi

We study the electronic structure of GdNi and HoNi, which are magnetic materials with a Curie temperature ${T}_{c}=69$ and ${T}_{c}=36\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, respectively. These materials are useful for magnetic refrigerator applications at low temperature as they exhibit a large magnetocaloric effect near ${T}_{c}$. We have used hard x-ray photoemission spectroscopy (HAXPES) to investigate the core-level and valence-band electronic states of GdNi and HoNi. HAXPES measurements of the Gd and Ho $3d, 4d, 4p, 5p$, and $4s$ core-level spectra have been compared with atomic multiplet calculations of ${\mathrm{Gd}}^{3+}$ and ${\mathrm{Ho}}^{3+}$ ionic configurations. The good match between the experimental and calculated spectra clarify the important role of spin-orbit coupling, as well as Coulomb and exchange interactions in the intermediate-coupling scheme. The core-level spectra also show plasmons in addition to the atomic multiplets. The Gd and Ho $4s$ spectra show clear evidence of exchange splitting. The Ni $2p$ and $3s$ spectra of GdNi and HoNi show a correlation satellite at a binding energy of 7 eV above their main peaks. The Ni $2p$ and Ni $3s$ spectra could be reproduced using charge transfer multiplet calculations. Valence-band HAXPES of GdNi and HoNi shows that the Gd $4f$ and Ho $4f$ features are also consistent with atomic multiplets and occur at high binding energies away from the Fermi level. The Ni $3d$ density of states are spread from the Fermi level to about 3 eV binding energy. The results indicate a partially filled Ni $3d$ band and show that the charge transfer model is not valid for describing the electronic structure of GdNi and HoNi.

Measurements of experimental transition probabilities of 3p54p → 3p54s arrays in neutral argon.

We have determined the absolute transition probabilities of 27 emission lines of neutral argon originating from the 3p54p→3p54s transition array in the wavelength region from 650 to 1100 nm using an argon-filled hollow cathode discharge lamp. The absolute transition probabilities have been deduced using the lifetimes of the upper levels and the measured branching fractions. Atomic oscillator strengths and relative line strengths for all the transitions have been computed using calculated transition probabilities. The experimentally determined transition probabilities are found to be in good agreement with that calculated in the intermediate coupling (IC) scheme. The comparison of experimentally determined transition probabilities with reported theoretical transition probabilities confirms that the IC scheme for the lower as well as for the upper levels seems to be a useful scheme for the level designation for the 3p54p to 3p54s configuration-based levels in argon. Furthermore, the measured relative line strengths are used to validate the J-file sum rule for the 3p54p→3p54s transition array of argon. The reported transition probabilities, oscillator strengths, and relative line strengths are compared with the published data, showing good agreement.

Measurements of branching fractions, absolute transition probabilities and J-file sum rule for the 4p55p→4p55s transitions array in neutral krypton

We present new results of transition rates for twenty two electric dipole transitions of neutral krypton associated with the 4p55p→4p55 s configurations-based levels covering the wavelength region from 500 to 1000 nm using a krypton filled hollow cathode discharge lamp coupled with a set of four miniature spectrometers. The branching fractions of various dipole allowed transitions were extracted using the observed line intensity ratios, whereas, the absolute values of the transition probabilities were deduced from the measured branching fractions in combination with the known lifetimes of the upper levels. The experimental data are in good agreement with that calculated in the intermediate angular momentum coupling scheme. In addition, line strengths for all the transitions have been extracted using the measured transition probabilities. The J-file sum rule was also tested for each level attached to the 4p55p→4p55 s configurations based on the recently measured and calculated normalized multiplet strengths.

Радиационные константы в спектре иона W VII

Radiative transition probabilities 4f135p66p + 4f145p56p - 4f136s, 4f137s, and 4f137s levels lifetimes for erbium-like W VII were calculated smiempirically in intermediate coupling scheme using experimental energy levels. Radial transition integrals were derived in length form with Hartree-Fock functions.

Probabilities of Radiative Transitions in the Spectra of Nickel-like Ions Cd XXI, In XXII, and Sn XXIII

Probabilities of electric-dipole 3d94p → 3d10, 3d94s transitions in the spectra of nickel-like ions Cd XXI, In XXII, and Sn XXIII are calculated semiempirically in the intermediate coupling scheme. The radial integrals necessary for obtaining absolute values of the probabilities are calculated in the length form with Hartree–Fock functions.

Pressure-driven 5f localized-itinerant transition and valence fluctuation in cubic phase californium

A combination of the density functional theory and the single-site dynamical mean-field theory is employed to study the pressure dependence of electronic structure for cubic phase californium. We predict that its 5$f$ electrons could undergo an orbital-selective localized-itinerant transition under moderate pressure. The volume contraction causes remarkable charge redistribution and valence fluctuation behaviors, which are the driving forces of the divalent-trivalent transition. Additionally, we find that the angular momentum coupling mechanism is hardly affected by pressure. The 5$f$ orbital occupancy is well described by the intermediate coupling scheme.

Вероятности радиационных переходов в спектрах никелеподобных ионов Cd XXI, In XXII, Sn XXIII

AbstractProbabilities of electric-dipole 3 d ^94 p → 3 d ^10, 3 d ^94 s transitions in the spectra of nickel-like ions Cd XXI, In XXII, and Sn XXIII are calculated semiempirically in the intermediate coupling scheme. The radial integrals necessary for obtaining absolute values of the probabilities are calculated in the length form with Hartree–Fock functions.

The KLM + KLN Auger electron spectrum of rubidium in different matrices

The KLM + KLN Auger electron spectrum of rubidium (Z = 37) emitted in the electron capture decay of radioactive 83Sr in a polycrystalline platinum matrix and also 85Sr in polycrystalline platinum and carbon matrices as well as in an evaporated layer onto a carbon backing were experimentally studied in detail for the first time using a combined electrostatic electron spectrometer. Energies, relative intensities, and natural widths of fifteen basic spectrum components were determined and compared with both theoretical predictions and experimental data for krypton (Z = 36). Relative spectrum line energies obtained from the semi-empirical calculations in intermediate coupling scheme were found to agree within 3σ with the measured values while disagreement with experiment exceeding 3σ was often observed for values obtained from our multiconfiguration Dirac–Hartree–Fock calculations. The absolute energy of the dominant spectrum component given by the semi-empirical approach agrees within 1σ with the measured value. Shifts of +(0.2 ± 0.2) and −(1.9 ± 0.2) eV were measured for the dominant KLM spectrum components between the 85Sr sources prepared by vacuum evaporation on and implanted into the carbon foil, respectively, relative to 85Sr implanted into the platinum foil. A value of (713 ± 2) eV was determined for the energy difference of the dominant components of the KLM + KLN Auger electron spectra of rubidium and krypton generated in the polycrystalline platinum matrix. From the detailed analysis of the measured data and available theoretical results, the general conclusion can be drawn that the proper description of the KLM + KLN Auger electron spectrum for Z around 37 should still be based on the intermediate coupling of angular momenta taking into account relativistic effects.

Parameterization of the spectra of configurations 3p4f and 3p5f of a phosphorus ion P II. Gyromagnetic ratios

In the one-configuration approximation, in the formalism of irreducible tensor operators, and in the intermediate (real) coupling scheme, numerical values of the fine-structure parameters are determined for the 3p4f and 3p5f highly excited configurations of the P II phosphorus ion with the energy-operator matrix in the LK-coupling approximation. With these values of the fine-structure parameters, the energy-operator matrix is numerically diagonalized in the LS-coupling approximation. The gyromagnetic ratios calculated in both basis sets in the absence of a field are compared with one another, as well as with their vector counterparts and the experimental g-factors available for the 3p4f configuration. The experimental and theoretical g-factors calculated with the LS basis set are in good agreement with the sole exception of the 3 F 2 level. Note that the calculation of g-factors from the Zeeman splitting in the linear region totally confirmed their agreement with the values calculated in the LS basis set (g LS ) in the absence of a field. The gyromagnetic ratios are the main objectives of this and previous papers, especially for configurations for which experimental data are absent. Apart from the g-factors, the specific features of Zeeman splitting (the crossings and anticrossings of magnetic components) in the 3p5f configurations were determined. These data are to be compared with results of future experiments. Comparison of gyromagnetic ratios calculated in the intermediate coupling scheme with their vector counterparts showed that most levels of the configurations studied are closer than in the LK-coupling scheme.

Energy levels, oscillator strengths, and transition probabilities for sulfur-like scandium, Sc VI

Energy levels, Oscillator strengths, and transition probabilities for sulfur-like scandium are calculated using CIV3 code. The calculations have been executed in an intermediate coupling scheme using Breit–Pauli Hamiltonian. The present calculations have been compared with the experimental data and other theoretical calculations. LANL code has been used to confirm the accuracy of the present calculations, where the calculations using CIV3 code agree well with the corresponding values by LANL code. The calculated energy levels and oscillator strengths are in reasonable agreement with the published experimental data and theoretical values. We have calculated lifetimes of some excited levels, as well.

A semiempirical calculation of the fine and Zeeman structure of 4p4f and 4p5f configurations of Ge I. Gyromagnetic ratios

The gyromagnetic ratios (g-factors) belong to the most important characteristics of atoms. For the 4p4f configuration of a germanium atom experimental values of g-factors are available only for four levels, while similar experimental data on the 4p5f configuration of Ge I are absent. Therefore, a theoretical study of the fine and Zeeman structures is topical for determining the gyromagnetic ratios. All the calculations are performed in the one-configuration approximation with the energy-operator matrix containing a maximum possible number of interactions, including magnetic: spin-orbit (own and other), spin-spin, and also orbitorbit interaction. The fine structure has been examined in three (LS, LK, and jK) approximations in order to establish the nature of coupling in the systems studied and the reliability of g-factors. Apart from the g-factors, in studying the Zeeman splitting, its specific features—the crossing and anticrossing fields of magnetic components— have been determined. A comparative analysis of g-factors was performed that showed that our results are in agreement with the available, albeit few in number, experimental data. At all stages, the corresponding energy-operator matrices were numerically diagonalized, i.e., all the results presented in the paper were obtained in the intermediate coupling scheme.

Time integrated optical emission studies of the laser produced germanium plasma

We present new time integrated data on the optical emission spectra of laser produced germanium plasma using a Q-switched Nd:YAG laser (1064 nm), power density up to about 5 × 109 W cm−2 in conjunction with a set of five spectrometers covering a spectral range from 200 nm to 720 nm. Well resolved structure due to the 4p5s → 4p2 transition array of neutral germanium and a few multiplets of singly ionized germanium have been observed. Plasma temperature has been determined in the range (9000–11 000) K using four different techniques; two line ratio method, Boltzmann plot, Saha–Boltzmann plot and Marotta’s technique whereas electron density has been deduced from the Stark broadened line profiles in the range (0.5–5.0) × 1017 cm−3, depending on the laser pulse energy to produce the germanium plasma. Full width at half maximum (FWHM) of a number of neutral and singly ionized germanium lines have been extracted by the Lorentzian fit to the experimentally observed line profiles. In addition, we have compared the experimentally measured relative line strengths for the 4p5s 3P0,1,2 → 4p2 3P0,1,2 multiplet with that calculated in the LS-coupling scheme revealing that the intermediate coupling scheme is more appropriate for the level designations in germanium.

Configuration interaction calculations and excitation rates of X-ray and EUV transitions in sulfurlike manganese

Fine-structure calculations of energies and transition parameters have been performed using the configuration interaction technique (CI) as implemented in CIV3 code for sulfurlike manganese, Mn X. The calculations are executed in an intermediate coupling scheme using the Breit-Pauli Hamiltonian. As well as, energy levels and oscillator strengths are calculated using LANL code, where the calculations by LANL have been used to estimate the accuracy of the present CI calculations. The calculated energy levels, oscillator strengths, and lifetimes are in reasonable agreement with the published experimental and theoretical values. Electron impact excitation rates of the transitions emit soft X-ray and extreme ultraviolet (EUV) wavelengths have been evaluated. The level population densities are calculated using the collisional radiative model (CRM), as well. The collisional excitation rates and collision strengths have been calculated in the electron temperature range ≤ the ionization potential, ∼1–250eV.

K-shell photoabsorption and photoionisation of trace elements

Context. With the recent launching of the Hitomi X-ray space observatory, K lines and edges of chemical elements with low cosmic abundances, namely F, Na, P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu and Zn, can be resolved and used to determine important properties of supernova remnants, galaxy clusters and accreting black holes and neutron stars.Aims. The second stage of the present ongoing project involves the computation of the accurate photoabsorption and photoionisation cross sections required to interpret the X-ray spectra of such trace elements.Methods. Depending on target complexity and computer tractability, ground-state cross sections are computed either with the close-coupling Breit-Pauli R-matrix method or with the autostructure atomic structure code in the isolated-resonance approximation. The intermediate-coupling scheme is used whenever possible. In order to determine a realistic K-edge behaviour for each species, both radiative and Auger dampings are taken into account, the latter being included in the R-matrix formalism by means of an optical potential.Results. Photoabsorption and total and partial photoionisation cross sections are reported for isoelectronic sequences with electron numbers 3 11 as they contribute significantly to the monotonic background of the cross section between the L and K edges. Configurations with 3d orbitals are important in rendering an accurate L edge, but they can be practically neglected in the K-edge region.

Construction of the energy matrix for complex atoms

The continuation of series of papers concerning the construction of the energy matrix for complex atoms is presented. The second-order perturbation theory contributions originating from core polarization effects in the hyperfine structure are considered. Fifteen new formulae for angular coefficients of core polarization parameters are given. The complete set of corrections up to the second-order perturbation theory was taken into account and the accuracy of the wave functions in the intermediate coupling scheme, on the example of the lanthanum atom, was checked.

Zeeman splitting, its specific features, and gyromagnetic ratios for configurations 1snf (n = 4–10) of the helium atom

The fine structure parameters of configurations 1snf (n = 4–10) with new refined energy values are calculated by the semiempirical method. The emphasis is on the study of the Zeeman structure in order to determine the gyromagnetic ratios of all four the levels of the configuration from the splitting. For this purpose, the matrices of an energy operator with allowance for the interaction between the atom and a magnetic field were diagonalized for all possible values of quantum number M. For each configuration, 17 values of crossing fields of the Zeeman sublevels with ΔМ = ±1, ±2 and the regions of anticrossings with ΔМ = 0 were determined. It is remarkable that, because the levels are closely spaced, anticrossings are observed for each pair of levels in these systems. The regions of linearity of a magnetic field, which are different for different configurations, and the levels in them are established. The g-factors are calculated from the coefficients of an intermediate coupling scheme in a magnetic field that is guaranteed to be linear. They are compared with the analogous values in the absence of a field.