Relativistic Many-body Perturbation Theory Calculations Research Articles

Electron-impact recombination and excitation rates for charge-state-selected highly charged Si ions

Charge-state selective recombination rate coefficients were measured by time of flight (TOF) analyzed highly charged Si ions extracted from an electron-beam ion trap. Additionally, the combination of simultaneous TOF and x-ray measurements and a separation of the dielectronic recombination contribution in the x-ray spectra is used for extracting electron-impact excitation rate coefficients for several overlaying charge states. Experimentally derived dielectronic recombination spectra for XIII and XIV Si are compared and found in excellent agreement with the results of relativistic many-body perturbation theory calculations.

Forbidden-line spectroscopy of the ground-state configuration of Cd-like W

only using electric-dipole forbidden emission lines, in what we label forbidden-line spectroscopy, we identified several energy levels in cadmium-like tungsten, W26+. The spectrum was recorded at the Shanghai permanentmagnet electron beam ion trap in the visible region. The identifications were supported by large-scale multiconfiguration Dirac-Hartree-Fock calculations which involved careful investigations of core-valence and core-core correlation effects, and by relativistic many-body perturbation theory calculations. With this novel method we identified in all seven lines and measured their wavelengths. From this we can determine the relative position of seven energy levels. Due to the close degeneracy of two levels, we give alternative energies for three of the levels.

All-order relativistic many-body theory of low-energy electron-atom scattering

A generalization of the box-variational method is developed to describe particle scattering with the Dirac equation. The method is applied to extract phase shifts from all-order single + double relativistic many-body perturbation theory calculations of the electron-helium, electron-neon, and electron-krypton systems. Comparisons with experimental elastic and momentum transfer cross sections are made. Agreement at the 1% to 2% level is achieved for helium and neon. The scattering length for krypton is 4% smaller in magnitude than experimental estimates derived from swarm experiments.

Transition energies of theDlines in Na-like ions

The NIST electron beam ion trap (EBIT) was used to measure the ${D}_{1}$(3$s$-3${p}_{1/2}$) and ${D}_{2}$(3$s$-3${p}_{3/2}$) transitions in Na-like ions of xenon, barium, samarium, gadolinium, dysprosium, erbium, tungsten, platinum, and bismuth. The wavelengths are in the range 3--12 nm. Relativistic many-body perturbation theory calculations were carried out for the ${D}_{1}$ and ${D}_{2}$ lines for every element in the isoelectronic sequence from argon ($Z$ $=$ 18) to uranium ($Z$ $=$ 92), taking into account some higher-order terms in the quantum electrodynamics (QED) expansion. Uncertainties in the calculated values were carefully assessed by considering the uncertainties in the various contributions to the total calculated transition energies. We conclude that at the current level of accuracy, the calculated values can be taken to reliably represent the isoelectronic sequence from $Z$ $=$ 18 to 92. The agreement of theory and experiment for the ${D}_{1}$ line of bismuth ($Z$ $=$ 83) provides a test of QED at the level of 0.4$%$. Our results are also sensitive to retardation effects due to the finite speed of light and to variations in the assumed nuclear size.

Relativistic diagrammatic perturbation theory calculations on neon atom

Relativistic many-body perturbation theory calculations have been performed on the ground state of Ne atom. The reference state of the single configuration Dirac–Fock wave function was computed using an expansion of Gaussian basis functions. Second- and third-order correlation corrections were computed by systematically enlarging the basis set. The relativistic and nonrelativistic correlation corrections for Ne are close to one another, indicating relatively small nonadditivity effects in this system.

Calculation of QED corrections in highly charged Zn-like ions

We report calculations of many-electron quantum electrodynamic (QED) effects for the 4s2 1S0–4s4p 1P1 transition in high-Z Zn-like ions with Z = 70, 74, 76, 79, 82, 83, 90, and 92. When combined with earlier relativistic many-body perturbation theory (RMBPT) calculations, good agreement is found with recent measurements, Trabert et al. (Phys. Rev. A, 70, 032506 (2004)) at the level of 1–2 experimental standard deviations. We discuss the additional QED and RMBPT calculations that it would be desirable to perform to confirm this level of agreement.PACS Nos.: 31.30.Jv, 32.30.Rj, 31.25.–v, 31.15.Ar

Nonrelativistic Limit of Dirac-Fock Codes: The Role of Brillouin Configurations

We solve a long standing problem with relativistic calculations done with the widely used multiconfiguration Dirac-Fock method. We show, using relativistic many-body perturbation theory (RMBPT), how, even for relatively high-Z, relaxation or correlation causes the nonrelativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We show that only large scale calculations that include all single excitations, even those obeying Brillouin's theorem, have the correct limit. We reproduce very accurately recent high-precision measurements in F-like Ar, and turn then to a precise test of QED. We obtain the correct nonrelativistic limit not only for fine structure but also for level energies and show that RMBPT calculations are not immune to this problem.

Semiempirical calculation of van der Waals coefficients for alkali-metal and alkaline-earth-metal atoms

The van der Waals coefficients, ${C}_{6},{C}_{8},$ and ${C}_{10}$ for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, ${D}_{8}$ and the three-body coefficient, ${C}_{9}$ are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.

Relativistic many-body perturbation-theory calculations of transition rates for copperlike, silverlike, and goldlike ions

We perform relativistic many-body perturbation theory calculations through third order to study amplitudes of the principal transitions in copperlike, silverlike, and goldlike ions. For low ionicities, semiempirical corrections are given for the omitted fourth- and higher-order terms. Comparisons with experiment are made.

Pseudoconfigurational approach in relativistic many-body perturbation-theory calculations.

The relativistic many-body perturbation theory in a multiconfigurational model space has been extended to include the pseudoconfigurations. Using this approach, we have calculated the beryllium ground-state energy and obtained an accurate theoretical result, -14.669 329 hartrees, which agrees well with the ``experimental energy'' -14.669 332 4 hartrees. \textcopyright{} 1996 The American Physical Society.

Multiconfiguration Hartree-Fock calculations of low-lying excited 2S states in lithium.

The hyperfine interaction constants, specific-mass-shift parameters, and total energies for the 3s${\mathrm{}}^{2}$S and 4s${\mathrm{}}^{2}$S states in lithium were calculated using the multiconfiguration Hartree-Fock method. The configuration expansions were obtained with the active space method, where configuration state functions are generated by excitations from the reference configuration to an active set of orbitals. The active set was increased in a systematic way, allowing the convergence of the studied parameters to be monitored. The obtained nonrelativistic energies are close to the lowest-upper-bound estimates from Hylleraas calculations. Whereas the convergence rate of the hyperfine interaction constants with respect to the increasing basis in the Hylleraas calculations degrades appreciably for higher states in the Rydberg series, no such effect could be seen for the multiconfiguration Hartree-Fock calculations. The uncertainties of the calculated hyperfine interaction constants are estimated to be less than three parts in a thousand for both of the studied states. The value for the 3s${\mathrm{}}^{2}$S state is in excellent agreement with results from relativistic many-body perturbation theory calculations, but is well outside the error bars from a recent precision measurement using Stark spectroscopy.

Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions.

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence.

Relativistic many-body perturbation theory applied to n=2 triplet states of heliumlike ions.

Relativistic many-body perturbation theory calculations of the energies of the 2 3 Po, 2 3 P 2 , and 2 3 Si states of heliumlike ions with nuclear charges Z in the range 10-36 are presented. These calculations include Coulomb correlation corrections through third order, correlation corrections of first order in the Breit interaction and zeroth, first, and second order in the Coulomb interaction, together with second-order Breit-Breit corrections and first-order corrections for retardation of the Breit interaction

Relativistic many-body perturbation theory using discrete basis expansion method: accurate representation of second-order energy of Xe atom with contracted well-tempered Gaussian basis set

Relativistic many-body perturbation theory calculations on Xe have been performed with basis sets of well-tempered Gaussian-type functions of Huzinaga and Klobukowski. The well-tempered Gaussian-type functions were used in both contracted and uncontracted form. The contracted Gaussian basis sets used in the relativistic many-body study are designed to retain flexibility for correlated calculations both in the core and the valence region. They reproduce second-order energy corrections computed with uncontracted Gaussian basis sets to an accuracy of greater than 99%. A compact representation of the relativistic wave functions in terms of contracted well-tempered Gaussian functions used in the present study provides a useful means of curtailing integral storage requirements and the time needed for correlated calculations, while still retaining high accuracy in relativistic electron correlation effects. Keywords: Dirac–Fock, relativistic many-body perturbation theory, well-tempered Gaussian basis, xenon.

Relativistic many-body perturbation-theory calculations on Kr: accurate representation of second- and third-order energies with contracted Gaussian basis set

Relativistic many-body perturbation-theory calculations on Kr have been performed with basis sets of contracted and uncontracted Gaussian-type functions. Second- and third-order Coulomb correlation corrections were computed by systematically enlarging the virtual space. The contracted Gaussian basis sets used in the many-body study are designed to retain flexibility for correlated calculations both in the core and the valence region. They reproduce second- and third-order energy corrections computed with uncontracted Gaussian basis sets to an accuracy of over 99.9%. This type of contraction has the advantage that it reduces integral storage requirements and the time needed for correlated calculations, while retaining high accuracy. Non-additive contributions, due to the interference between relativity and the Coulomb correlation in the second-order correlation energy correction in Kr, is ≈ 0.013 au, an order of magnitude larger than in Ar.

QED contributions to the 3s-3p transitions in highly charged Na-like ions.

The QED contributions to the energy intervals 3${\mathit{s}}_{1/2}$-3${\mathit{p}}_{1/2}$, 3${\mathit{p}}_{1/2}$-3${\mathit{p}}_{3/2}$, and 3${\mathit{s}}_{1/2}$-3${\mathit{p}}_{3/2}$ in highly charged Na-like ions were determined by comparing the transition energies derived from the observations with the relativistic many-body perturbation-theory calculations of Johnson, Blundell, and Sapirstein [Phys. Rev. A 38, 2699 (1988)] that do not include QED effects. The determined QED contributions differ considerably from the one-electron QED contributions and are in better agreement with screened-nucleus QED contributions. Predicted transition energies and wavelengths are presented for the Na-like ions with atomic numbers up to Z=92.