Non-relativistic Configuration Research Articles

Damping of the isovector giant dipole resonance in 40,48Ca

The fine structure of the IsoVector Giant Dipole Resonance (IVGDR) in the doubly-magic nuclei 40,48Ca observed in inelastic proton scattering experiments under 0∘ is used to investigate the role of different mechanisms contributing to the IVGDR decay width. Characteristic energy scales are extracted from the fine structure by means of wavelet analysis. The experimental scales are compared to different theoretical approaches allowing for the inclusion of complex configurations beyond the mean-field level. Calculations are performed in the framework of RPA and beyond-RPA in a relativistic approach based on an effective meson-exchange interaction, with the UCOM effective interaction and, for the first time, with realistic two- plus three-nucleon interactions from chiral effective field theory employing the in-medium similarity renormalization group. All models highlight the role of Landau fragmentation for the damping of the IVGDR, while the differences in the coupling strength between one particle-one hole (1p-1h) and two particle-two hole (2p-2h) correlated (relativistic) and non-correlated (non-relativistic) configurations lead to very different pictures of the importance of the spreading width resulting in wavelet scales being a sensitive measure of their interplay. The relativistic approach with particle-vibration coupling, in particular, shows impressive agreement with the number and absolute values of the scales extracted from the experimental data.

Electron-Impact Excitation of Ge iii and Photoionisation of Ge ii

Abstract Energy levels, Einstein A-values and oscillator strengths are calculated for doubly-ionised germanium (Ge iii). We have undertaken a study of the electron-impact excitation of Ge iii and have also completed a study of the photoionisation of Ge ii. Ge iii target structures were generated using the relativistic GRASP0 package. Several scattering models were investigated to assess the uncertainty quantification of our results. Initially, the lowest lying 64 jj fine-structure levels were included in the close-coupling expansion resulting from 14 non-relativistic configurations. A second larger model was subsequently generated using the GASP package and incorporated the lowest 589 jj fine-structure levels from 17 non-relativistic configurations. Both the DARC and Breit-Pauli parallel suite of R-matrix collision codes were utilised in the scattering calculations to generate the collision strengths for incident electron-energies between 0 and 5 Rydbergs and subsequently the Maxwellian averaged effective collision strengths for temperatures in the range 1000 to 200000 Kelvin. The photoionisation calculations comprised of two studies, a DARC and a Breit-Pauli calculation incorporating the 250 lowest lying levels. Photoionisation cross sections for Ge ii are presented in the range 0-5 Ryds. Due to the lack of data available in the literature, the present radiative data and electron-impact/photoionisation cross sections are compared between the models presented in this paper. To assess their significance for astrophysics, the data are incorporated into the stellar atmosphere package sterne. Test models for the heavy-metal subdwarf LSIV−14○116 are not affected by the new data, but models for cooler stars may be sensitive to them.

Static and collapsing configurations supported by the spinor fluid

We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field. For such a configuration, we find a two-parametric family of static regular solutions describing compact objects whose masses and sizes are determined by the central density of the spinor fluid and the mass of the spinor field. Using the similarity method, we consider a gravitational collapse of an initially uniform system consisting of the spinor fluid. We estimate the general characteristics of the collapse and show that a resulting nonuniform distribution of the fluid occurs that may serve as a core for the creation of equilibrium starlike configurations.

Magic wavelengths for the helium 23S1→21P1 forbidden transition

A series of magic wavelengths for the forbidden transition of $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}$ in helium are determined by performing large-scale full relativistic configuration interaction calculations based on Dirac-Coulomb-Breit Hamiltonian with the mass shift operator included. QED corrections to magic wavelengths are taken into account by using the perturbation theory in nonrelativistic configuration interaction calculations. The 1335.55(2)-nm magic wavelength for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}(M=\ifmmode\pm\else\textpm\fi{}1)\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}(M=0)$ transition is found to be sensitive to the finite nuclear mass, relativistic, and QED effects, and its measurement might provide a test of atomic structure theory.

CI calculations for ground and the lowest core-excited states of Li and Li−

Large scale, accurate non-relativistic configuration interaction (CI) calculations for the ground and core excited states of Li (2S, 4P° and 4P) and Li− (1S, 5P and 5S°) corrected for relativistic and mass polarization effects. Priori selected CI and CI by parts techniques are implemented to approximate both the large scale wavefunction and the solution of large CI eigenvalue problem respectively. Systematic studies of energy and electron affinity convergence with respect to CI excitation level are reported. The calculated value of electron affinity of the ground 1S state is 618.05(5) meV in excellent agreement with experiment. Calculations on excited states reveal more accurate values of the positions of 5P and 5S° states of Li−, lying 505.86(5) meV and 291.20(5) meV below 4P° and 4P states respectively of Li. Transition energies and wavelength of the electric dipole decay 4P → 4P° of Li and 5S° → 5P of Li−, show reasonably good agreement with available theoretical and experimental data.

Relativistic calculations of x-ray transition energies and isotope shifts in heavy atoms

X-Ray transition energies and isotope shifts in heavy atoms are evaluated. The energy levels with vacancies in the inner shells are calculated within the approximation of the average of nonrelativistic configuration employing the Dirac-Fock-Sturm method. The obtained results are compared with other configuration-interaction theoretical calculations and with experimental data.

Neon in ultrashort and intense x-rays from free electron lasers

We theoretically examine neon atoms in ultrashort and intense x-rays from free electron lasers and compare our results with data from experiments conducted at the Linac Coherent Light Source. For this purpose, we treat in detail the electronic structure in all possible nonrelativistic cationic configurations using a relativistic multiconfiguration approach. The interaction with the x-rays is described in rate-equation approximation. To understand the mechanisms of the interaction, a path analysis is devised which allows us to investigate what sequences of photoionization and decay processes lead to a specific configuration and with what probability. Thereby, we uncover a connection to the mathematics of graph theory and formal languages. In detail, we study the ion yields and find that plain rate equations do not provide a satisfactory description. We need to extend the rate equations for neon to incorporate double Auger decay of a K-shell vacancy and photoionization shake off for neutral neon. Shake off is included for valence and core ionization; the former has hitherto been overlooked but has important consequences for the ion yields from an x-ray energy below the core ionization threshold. Furthermore, we predict the photon yields from xuv and x-ray fluorescence; these allow one insights into the configurations populated by the interaction with the x-rays. Finally, we discover that inaccuracies in those Auger decay widths employed in previous studies have only a minor influence on ion and photon yields.

Excited state electron affinity calculations for aluminum

Excited states of negative aluminum ion are reviewed, and calculations of electron affinities of the states $$(3s^23p^2)^1D$$ and $$(3s3p^3){^5}{S}{^\circ }$$ relative to the $$(3s^23p)^2P^\circ$$ and $$(3s3p^2)^4P$$ respectively of the neutral aluminum atom are reported in the framework of nonrelativistic configuration interaction (CI) method. A priori selected CI (SCI) with truncation energy error (Bunge in J Chem Phys 125:014107, 2006) and CI by parts (Bunge and Carbo-Dorca in J Chem Phys 125:014108, 2006) are used to approximate the valence nonrelativistic energy. Systematic studies of convergence of electron affinity with respect to the CI excitation level are reported. The calculated value of the electron affinity for $$^1D$$ state is 78.675(3) meV. Detailed Calculations on the $$^5S^\circ$$ state reveals that is 1216.8166(3) meV below the $$^4P$$ state.

SEMILLAC: A new hybrid atomic model of hot dense plasmas

SEMILLAC is a fast, yet highly accurate method to calculate ionic population distributions in plasmas at a given electron temperature and density. SEMILLAC solves rate equations for non-relativistic configurations population distributions. It considers electron collisional, radiative and autoionizing atomic processes. The code is designed to be highly versatile so it can be used for modeling a wide range of laboratory plasmas. The population distributions can be calculated for steady state or time dependent conditions, with or without the presence of a radiation field. SEMILLAC is designed to be used as a tool for population distributions calculations and spectroscopic modeling of plasmas. Our aim is to get high accuracy while keeping the code fast enough to be used for standard PC calculations. At the heart of our method, average transitions energies and rate coefficients are calculated for a restricted set of simple non-relativistic ionic configurations using the HULLAC code. We then use this basic set to calculate energies and rates coefficients of more complex, multiply excited configurations.

Relativistic energy-consistent pseudopotentials for superheavy elements 119 and 120 including quantum electrodynamic effects

Relativistic energy-consistent pseudopotentials for the superheavy elements with nuclear charges 119 and 120 replacing 92 electrons of a [Xe]4f(14)5d(10)5f(14) core were adjusted to relativistic multi-configuration Dirac-Coulomb-Breit finite nucleus all-electron reference data including lowest-order quantum electrodynamic effects, i.e., vacuum polarization and electron self-energy. The parameters were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total valence energies of 131 to 140 relativistic states arising from 31 to 33 nonrelativistic configurations covering also anionic and highly ionized states, with mean absolute errors for the nonrelativistic configurations below 0.01 eV. Primitive basis sets for one- and two-component calculations with errors below 0.02 and 0.03 eV to the Hartree-Fock limit, respectively, as well as general contractions of these basis sets with double- to quadruple-zeta quality were obtained. Atomic highly correlated test calculations using the Fock-space coupled-cluster method yield for valence excitation energies and ionization potentials mean absolute errors of 26 cm(-1) and 59 cm(-1), respectively. Correlated and uncorrelated molecular test calculations show deficiencies below 0.005 Å for the bond lengths and 3 N m(-1) for the force constants.

Autoionization widths of open-M-shell germanium ions: effects on inner-shell absorptions

Large-scale configuration interaction calculations were carried out to obtain the level-by-level autoionization (AI) rates and resonance widths of the inner-shell excited configurations for the open-M-shell germanium ions. Detailed results are presented for Ge5+ as an example. The dominant ionization channels of the autoionized levels 2p53/23s23p63d10 and 2p51/23s23p63d10 of Ge5+ were determined, and it is shown that the channel from level 3s23p6(3d−13/23d−15/2)4 contributes the largest fraction of AI widths of 0.195 and 0.188 eV to the total width of 0.577 and 0.544 eV, respectively, from all possible channels. For typical experimental plasmas at temperatures of several tens and hundreds of eV, the AI resonance broadening is the dominant mechanism among the Doppler, electron impact and natural lifetime broadenings. Among the physical effects such as relativistic and the interaction between fine-structure levels belonging to the same non-relativistic configuration and different configurations, particular attention is paid to the effect of AI resonance broadening on the L-shell absorption. Different features of the inner-shell absorption due to AI broadening are presented in detail for Ge5+, Ge10+ and Ge17+. The total AI widths of levels from the configuration of one 2p electron being excited to 3d orbital were systematically investigated for Ge6+–Ge21+. Except for Ge20+ and Ge21+, the AI widths of the open-M-shell germanium ions dominate over all other line broadening mechanisms.

Accurate relativistic energy-consistent pseudopotentials for the superheavy elements 111 to 118 including quantum electrodynamic effects

Energy-consistent two-component semi-local pseudopotentials for the superheavy elements with atomic numbers 111-118 have been adjusted to fully relativistic multi-configuration Dirac-Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian, including perturbative corrections for the frequency-dependent Breit interaction in the Coulomb gauge and lowest-order quantum electrodynamic effects. The pseudopotential core includes 92 electrons corresponding to the configuration [Xe]4f(14)5d(10)5f(14). The parameters for the elements 111-118 were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total energies of 267 up to 797 J levels arising from 31 up to 62 nonrelativistic configurations, including also anionic and highly ionized states, with mean absolute errors clearly below 0.02 eV for averages corresponding to nonrelativistic configurations. Primitive basis sets for one- and two-component pseudopotential calculations have been optimized for the ground and excited states and exhibit finite basis set errors with respect to the finite-difference Hartree-Fock limit below 0.01 and 0.02 eV, respectively. General contraction schemes have been applied to obtain valence basis sets of polarized valence double- to quadruple-zeta quality. Results of atomic test calculations in the intermediate coupling scheme at the Fock-space coupled-cluster level are in good agreement with those of corresponding fully relativistic all-electron calculations based on the Dirac-Coulomb-Breit Hamiltonian. The results demonstrate besides the well-known need of a relativistic treatment at the Dirac-Coulomb level also the necessity to include higher-order corrections for the superheavy elements.

Nonrelativistic isothermal fluid in the presence of a chameleon scalar field: Static and collapsing configurations

We consider a gravitating spherically symmetric nonrelativistic configuration consisting of a massless chameleon scalar field nonminimally coupled to a perfect isothermal fluid. The object of this paper is to show the influence of the chameleon scalar field on the structure and evolution of an isothermal sphere. For this system we find static, singular and regular solutions depending on the form of the coupling function. A preliminary stability analysis indicates that both stable and unstable solutions exist. For unstable configurations, by choosing the special form of the coupling function, we consider the problem of the gravitational collapse by applying the similarity method.

Detailed Theoretical Investigations on the L-Shell Absorption of Open-M-Shell Germanium Plasmas:Effect of Autoionization Resonance Broadening

Radiative opacity of open-M-shell germanium plasmas in the L-shell photon energy region were investigated in detail by using a fully relativistic detailed level accounting approach. Among other physical effects such as relativistic and the interaction between fine-structure levels belonging to the same non-relativistic configuration and different configurations, particular attention is paid on the effect of autoionization resonance broadening on the L-shell absorption. The results show that for plasmas at present and past typical experimental conditions, line width due to autoionization resonance broadening dominate among all the physical broadening mechanisms including electron impact and Doppler broadenings. Such an effect is most pronounced for ions with just a few 2p-nd transition lines such as Ge14+, while it is not so pronounced for complex ions such as Ge16+, where there are so many 2p-nd lines that line overlapping partly conceal the effect of autoionization resonance broadening. After taking the effect of autoionization resonance broadening into account, detailed comparisons are made with available experimental spectra at different physical conditions of different plasma temperatures and densities. The L-shell absorption is sensitive to the plasma temperature, especially in the 2p-3d excitation energy region. The potential of utlizing the relative shape and intensity of the 2p-3d spin-orbit splitting as temperature diagnostics is investigated.

Modeling the population kinetics of NLTE plasmas based on approximations of nonrelativistic configurations

For the rapid calculation of population kinetics of high-Z nonlocal thermodynamic equilibrium (NLTE) plasmas, a collisonal–radiative model based on the nonrelativistic configurations approach was developed. The required atomic data about the collisonal and radiative processes such as photoexcitation, electron-impact excitation, photoionization, electron-impact ionization and autoionzation were obtained by using a set of analytical formulae. The population kinetics were determined by solving the rate equation in the steady-state approach. As illustrative results, experimental measurements of the average ionization degree and population distribution of Xe and Au plasmas were reproduced, and overall good agreement was found. The present model provides a useful tool for modeling the population kinetics of NLTE plasmas.

Accurate Relativistic Small-Core Pseudopotentials for Actinides. Energy Adjustment for Uranium and First Applications to Uranium Hydride

The options to adjust accurate relativistic energy-consistent pseudopotentials for actinides are explored using uranium as an example. The choice of the reference data and the core-valence separation is discussed in view of a targeted accuracy of 0.04 eV or better in atomic energy differences such as excitation energies and ionization potentials. A new small-core pseudopotential attributing 60 electrons to the core has been generated by an energy adjustment to state-averaged multiconfiguration Dirac-Hartree-Fock/Dirac-Coulomb-Breit Fermi nucleus reference data of 100 nonrelativistic configurations of U to U(7+) corresponding to 30190 reference J levels. At the finite-difference multiconfiguration Hartree-Fock level the mean absolute errors are 0.002 and 0.024 eV for the configurations and J levels, respectively. A first molecular application to uranium monohydride UH yields very satisfactory agreement with results from all-electron calculations based on the Douglas-Kroll-Hess Hamiltonian.

Absorption spectroscopy of mid and neighboring Z plasmas: Iron, nickel,copper and germanium

Opacities of four medium Z element plasmas (iron, nickel, copper and germanium) have been measured at the LULI-2000 facility in similar conditions: temperatures between 15 and 25 eV and densities between 2 and 10 mg/cm 3, in a wavelength range (8–18 Å) including the strong 2p–3d structures. Two laser beams from the LULI facility were used in the nanosecond-picosecond configuration. The NANO-2000 beam (at λ = 0.53 μm) heated a gold hohlraum with an energy between 30 and 150 J with a duration of 0.6 ns. Samples covering half a hohlraum hole were thus radiatively heated. The picosecond pulse PICO-2000 beam (at λ = 1.053 μm) has been used to produce a short (about 10 ps) X-ray backlighter in order to reduce time variations of temperatures and densities during the measurement. A crystal high-resolution spectrometer was used as the main diagnostic to record at the same time the non-absorbed and the absorbed backlighter spectra. Radiation temperatures were measured using a broadband spectrometer. 1D and 2D simulations have been performed in order to estimate hydrodynamic plasmas parameters. The measured spectra have been compared with theoretical ones obtained using either the superconfiguration code SCO or the detailed term accounting code HULLAC. These comparisons allow us to check the modeling of the statistical broadening and of the spin-orbit splitting of the 2p–3d transitions and related effects such as the interaction between relativistic subconfigurations belonging to the same non-relativistic configuration.

Relativistic stars inf(R)gravity, and absence thereof

Several $f(R)$ modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such $f(R)$ theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of $f(R)$ models.

Detailed-level-accounting approach calculation of radiative properties of aluminium plasmas in a wide range of density and temperature

In this work it is accomplished a study of radiative properties of aluminium plasmas. It is analyzed the calculation of spectrally resolved and mean opacities both under NLTE and LTE approaches. Furthermore, the effect of the re-absorption of the radiation in these magnitudes is also examined. The calculations were performed into the detailed-level-accounting approach including configuration interaction among the levels belonging to the same non-relativistic configuration.

Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y–Pd

Scalar-relativistic pseudopotentials and corresponding spin-orbit potentials of the energy-consistent variety have been adjusted for the simulation of the [Ar]3d(10) cores of the 4d transition metal elements Y-Pd. These potentials have been determined in a one-step procedure using numerical two-component calculations so as to reproduce atomic valence spectra from four-component all-electron calculations. The latter have been performed at the multi-configuration Dirac-Hartree-Fock level, using the Dirac-Coulomb Hamiltonian and perturbatively including the Breit interaction. The derived pseudopotentials reproduce the all-electron reference data with an average accuracy of 0.03 eV for configurational averages over nonrelativistic orbital configurations and 0.1 eV for individual relativistic states. Basis sets following a correlation consistent prescription have also been developed to accompany the new pseudopotentials. These range in size from cc-pVDZ-PP to cc-pV5Z-PP and also include sets for 4s4p correlation (cc-pwCVDZ-PP through cc-pwCV5Z-PP), as well as those with extra diffuse functions (aug-cc-pVDZ-PP, etc.). In order to accurately assess the impact of the pseudopotential approximation, all-electron basis sets of triple-zeta quality have also been developed using the Douglas-Kroll-Hess Hamiltonian (cc-pVTZ-DK, cc-pwCVTZ-DK, and aug-cc-pVTZ-DK). Benchmark calculations of atomic ionization potentials and 4d(m-2)5s(2)-->4d(m-1)5s(1) electronic excitation energies are reported at the coupled cluster level of theory with extrapolations to the complete basis set limit.