Dirac-Fock Wave Functions Research Articles

Excitation energies, oscillator strengths, and lifetimes of levels along the gold isoelectronic sequence

Energies of ns[1/2] (n= 6-9), np[j] (n = 6-8), nd[j] (n= 6-7), and 5f[j] states in neutral Au and Au-like ions with nuclear charges Z = 80 - 83 are calculated using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates and lifetimes are determined for the 30 possible nl[j]-n'l'[j'] electric-dipole transitions. Results for a limited number states ns[1/2], np[j] (n= 6-7) and 6d[j] are obtained in the relativistic single-double (SD) approximation, where single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. Using SD wave functions, accurate values are obtained for energies of the eight lowest states and for the fourteen possible electric-dipole matrix elements between these states. With the aid of the SD wave functions, we also determine transition rates and oscillator strengths for the fourteen transitions together with lifetimes of 6p[j], 7p[j], and 6d[j] levels. We investigate the hyperfine structure in HgII and TlIII. The hyperfine A-values are determined for 6s[1/2] and 6p[j] states in 199Hg+, 201Hg+, and 205Tl++ isotopes. These calculations provide a theoretical benchmark for comparison with experiment and theory.

Net-value of the relativistic crystal field effect

The relativistic crystal field theory in case of the rare earth ion doped materials is presented. In order to calculate the values of crystal field splittings the effectively relativistic crystal field operators are applied. The matrix elements of these operators are evaluated in the non-relativistic LS scheme, whereas the radial integrals include one electron Dirac–Fock wavefunctions. The numerical results of the relativistic crystal field effects are presented for Ce3+ or Yb3+ ions in LuPO4, and they are compared with those obtained from the non-relativistic approach.

Excitation of fine-structure states of krypton and xenon by positron impact

Experimental measurements of the excitation of ns J=1 fine-structure levels for some noble gases by positron impact have recently been performed. We present here calculations of the cross-sections for excitation of such levels in krypton and xenon. We used a relativistic distorted wave method with multi-configuration Dirac–Fock wave functions for atomic states. The results obtained showed good agreement with the experimental results for excitation to the [3/2] level in xenon near threshold.

A relativistic version of the generalized non-perturbative polarized-orbital method

We have previously published a non-relativistic generalization of the non-perturbative polarized-orbital method which can be used to calculate long range polarization potentials for electron and positron scattering from atomic systems. Here we present a relativistic version of this method which is designed for heavy atomic systems with large polarizabilities such as caesium or the excited states of xenon. The detailed formulae are based upon the representation of atomic states by Dirac–Fock wavefunctions.

Spectral Study on Lightning Return Stroke in Plateau Area

AbstractUsing a slit‐less spectrograph, the spectra in the range of 400~ 700nm for first return strokes of CG lightning flashes have been obtained in the Qinghai plateau, and the 604.6nm, 619.4nm new lines have been recorded. Applying the large‐scale multi‐configuration Dirac‐Fock wave functions, parameters such as wavelength, oscillator strengths and excited energies have been calculated for the transitions related to lightning spectra. Compared the calculated results with experimental spectra, it shows that Document Metadatathe spectra in plateau area have a distinctive characteristic. Beside the lines of lower excited state with n = 3 in NII ions, transitions of NI and OI are increased, their excited energies are around 13 ~ 14eV, and there are rarely lines from OII ion in the spectra of this region.

Relativistic configuration-interaction oscillator strength calculations with ab initiomodel potential wavefunctions

The relativistic configuration-interaction (CI) method with numerical Dirac–Fockwavefunctions generated using an ab initio model potential with non-integeroutermost core shell occupation number to improve the efficiency of the CIrepresentation of core–valence electron correlation, is used to calculateoscillator strengths for the lowest spin-allowed and spin-forbidden ns2 1S0–nsnp 1P1, 3P1transitions in some systems with two valence electrons. The present results arecompared with our earlier data obtained with core–valence correlation representedin the semiclassical core polarization picture.

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 X α 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.

Complete description of the excitation of the 63P1 and61P1states of mercury by spin-polarized electrons

We have carried out relativistic distorted wave calculations for the excitation of the 63P1 and61P1states of mercury from the ground 1S0state by spin-polarized electrons. The ground and excited states are representedby multiconfiguration Dirac–Fock wavefunctions. We have corrected previouslypublished expressions for the generalized Stokes parameters (GSP) andthe complete set of independent scattering parameters. Results for GSP,generalized STU parameters and the complete set of independent scatteringparameters for incident electrons with an energy of 8 eV are obtained andcompared with the available experimental data and theoretical semirelativisticR-matrixand distorted wave Born approximation calculations.

Black-body radiation effects and light shifts in atomic frequency standards

A general method is presented for calculating the higher-order terms of series in powers of the black-body radiation field for the Stark-state wavefunctions, dipole transition matrix elements and corresponding frequency shifts of hyperfine splitting in the ground states for Cs and Rb atoms. A numerical method for calculating the light shifts in Sr atoms is described. It is based on the Green function method for summation over all intermediate states and exact Dirac–Fock wavefunctions for the resonant transitions to the first excited s-, p- and d-states. By comparing the calculated Stark shift with results of measurements employing atomic frequency standards, the black-body radiation effects on the ground state are analysed.

Theoretical transition probabilities and lifetimes in nickel-like Se $ \mathsf {^{6+}}$ , Y $ \mathsf {^{11+}}$ and Sn $ \mathsf {^{22+}}$ ions

The 17 levels of the 3 d 10 , 3 d 9 4 s and 3 d 9 4 p configurations, and the electric-dipole transitions among these levels are calculated for the three nickel-like ions Se6+, Y11+ and Sn22+ by using large-scale multiconfiguration Dirac-Fock wavefunctions. From these computations, the excitation energies and transition probabilities as well as the lifetimes of 3 d 9 4 p levels are derived, including all dominant effects of relativity, correlation and of the rearrangement of the electron density within the same framework. Comparison is made with the scarce number of experimental data and previous semi-empirical computations.

Fully relativistic calculation of nuclear magnetic shieldings and indirect nuclear spin-spin couplings in group-15 and -16 hydrides

Fully relativistic calculations of the isotropic and anisotropic parts of both indirect nuclear spin–spin couplings J1(X-H) and J2(H-H) and nuclear magnetic shieldings σ(X) and σ(H) for the group-15 and -16 hydrides are presented. Relativistic calculations were performed with Dirac–Fock wave functions and the random phase approximation method. Results are compared to its nonrelativistic counterpart. Paramagnetic and diamagnetic contributions to the nuclear magnetic shielding constants are also reported. We found very large relativistic corrections to both properties in the sixth-row hydrides (BiH3 and PoH2). Our calculations of the relativistic corrections to the isotropic part of σ at the heavy nucleus X show that it is roughly proportional to Z3.2 in both series of molecules. Paramagnetic term σp is more sensitive to the effects of relativity than the diamagnetic one σd, even though both have a behavior proportional to third power of the nuclear charge Z.

Ab initio all-electron fully relativistic Dirac–Fock self-consistent field calculations for molecules of superheavy elements: Seaborgium hexabromide

Gargantuan ab initio all-electron fully relativistic Dirac–Fock (DF) and nonrelativistic (NR) Hartree–Fock (HF) limit self-consistent field (SCF) molecular calculations are reported for SgBr6 at various Sg–Br bond distances assuming an octahedral geometry. Our fully relativistic Dirac–Fock and nonrelativistic HF calculations predict for SgBr6 bond distance of 2.52 and 2.59 Å, respectively. Both our DF and NR HF SCF calculations predict the ground state of SgBr6 to be bound, with the predicted atomization energy of 18.75 and 11.53 eV, respectively. A relativistic Dirac–Fock wave function predicts for SgBr6∼63% larger atomization energy than the corresponding NR HF calculation. The vertical ionization potential of SgBr6 calculated with our DF and HF wave functions is almost the same, viz., 10.60 and 10.78 eV, respectively. This is due to the fact that the HOMO consists entirely of the combination of the 4p AOs of the six Br ligands, for which relativistic effects are nominal. However, the vertical electron affinity calculated with our HF and DF wave function for SgBr6 is 5.35 and 3.80 eV, respectively. The calculated HF HOMO–LUMO gap of 7.74 eV is in fairly close agreement with that of 8.91 eV obtained from the corresponding DF relativistic MOs for SgBr6. These results can be understood in terms of the nature of the HOMOs and LUMOs calculated in our HF and DF calculations for SgBr6. Mulliken population analysis of our relativistic DF and HF wave functions yields a charge of 1.26 and 0.70, respectively on Sg in SgBr6; our DF wave function predicts SgBr6 to be more ionic (and less volatile) than that by the corresponding HF wave function. Our prediction of the bond dissociation energy of 44 and 72 kcal mol−1 with our NR HF and relativistic DF wave functions, respectively for SgBr6 is a first for a species of a superheavy transactinide element, as is our prediction of a positive electron affinity for SgBr6 with both our HF and DF wave functions.

Excitation of the4s1P1and3P1states of argon by positron impact

Recent experimental measurements of the excitation of the 4s J= I fine-structure levels of argon by positron impact have prompted us to carry out calculations for this process. We have used the relativistic distorted-wavemethod with multiconfiguration Dirac-Fock wave functions for atomic states. Distortion potentials with and without a polarization potential were used. Results obtained for distortion potentials without polarization gave good agreement with the experimental measurements for positron impact energies between 20 and 30 eV.

Ionization of boron, aluminum, gallium, and indium by electron impact

Measurements of electron impact ionization of neutral Al, Ga, and In show large cross sections compared to other elements in the same rows of the periodic table. Semiempirical and classical calculations of direct ionization cross sections are all substantially smaller. Calculations by McGuire [Phys. Rev. A 26, 125 (1982)] for aluminum that include excitations to autoionizing ${3s3p}^{2}$ doublet levels are 2.5 times higher than experiment at the peak. We report the direct ionization cross sections based on the binary-encounter-Bethe model of Kim and Rudd [Phys. Rev. A 50, 3954 (1994)], which is an ab initio theory. We add the autoionization contribution using scaled plane-wave Born cross sections as recently developed by Kim [Phys. Rev. A 64, 032713 (2001)] for excitations to the first set of autoionizing levels. Dirac-Fock wave functions are used for the atomic structure. Our results are in excellent agreement with experimental values and support substantial contributions from excitation-autoionization to the total ionization cross sections for these elements. We also compare the total ionization cross section of boron to available theories, though no experimental data are available.

Theoretical investigations on the 3d94p−3d10 spectrum of CuII

Abstract The low-lying level structure and the 3 d 9 4 p −3 d 10 resonance and intercombination transitions of the spectrum CuII have been studied by using large-scale multiconfiguration Dirac–Fock wavefunctions. Excitation energies and transition probabilities are calculated by including all dominant effects of relativity, correlation, and of the rearrangement of the electron density within the same framework. Comparison with experiment and previous computations is made which shows a remarkable improvement in the accuracy of the theoretical results.

Theoretical Level Structure and Decay Dynamics of Nickel-like Ions: Search for Laser Lines in the Soft X-ray Domain

Multiconfiguration Dirac–Fock wave functions have been applied to study the level structure and transition probabilities of high-Z nickel-like ions in the range 74 ≤ Z ≤ 84. Several level crossings are found which strongly influence the decay dynamics of the excited ions and explain why some of these lines cannot (so easily) be observed for all elements along the isoelectronic sequence. For two selected ions, the role of configuration interactions and relaxation is explored by large-scale expansions.

Relativistic pseudopotentional incorporating core/valence polarization and nonlocal effects.

A relativistic pseudopotentional (RPP) for use in ab initio molecular electronic structure calculations is derived in the context of the relativistic effective core potential (REP) method of Lee et al. The resulting atom-specific RPP has salient features of the REP imbedded within it while retaining the form of a functional that is dynamically defined at runtime when used in calculations on molecules. The RPP is determined from Dirac-Fock wave functions for the isolated atom. Outer core two-electron interactions are incorporated into the RPP by means of variable coefficients that are defined in the context of the final molecular wave function. This form permits polarization of the outer core shells analogous to that occurring in all-electron molecular Hartree-Fock calculations while retaining these shells as part of the atomic pseudopotentional. Use of the RPP in post-Hartree-Fock molecular calculations permits the incorporation of core/valence correlation effects.

Energy levels, lifetimes and branch fractions for Fe XI

We present transition energies, probabilities and branching ratios for the electric dipole allowed (E1) and forbidden (M1, E2, M2) lines of the 3s23p4, 3s3p5 and 3s23p33d configurations of Fe xi. Large-scale multiconfiguration Dirac–Fock wavefunctions are applied to include the effects of relativity, correlation and rearrangement of the electron density consistently within the same (computational) model. From the transition probabilities, lifetimes of the 46 lowest-lying excited levels are derived, and the prospects for experimental verification are discussed. An M2 transition is identified in the solar extreme ultraviolet spectrum.

Energy levels, lifetimes and branch fractions for Fe xi

We present transition energies, probabilities and branching ratios for the electric dipole allowed (E1) and forbidden (M1, E2, M2) lines of the 3s23p4, 3s3p5 and 3s23p33d configurations of Fe xi. Large-scale multiconfiguration Dirac-Fock wavefunctions are applied to include the effects of relativity, correlation and rearrangement of the electron density consistently within the same (computational) model. From the transition probabilities, lifetimes of the 46 lowest-lying excited levels are derived, and the prospects for experimental verification are discussed. An M2 transition is identified in the solar extreme ultraviolet spectrum.

Relativistic configuration-interaction study of transition probabilities in mercury withab initiomodel potential wave functions

The relativistic configuration-interaction method based on numerical Dirac-Fock wave functions (CIDF) is employed to determine $6s6p{}^{3}{P}_{0,1,2},$ ${}^{1}{P}_{1}--6s7s{}^{3}{S}_{1}{,}^{1}{S}_{0}$ transition energies and probabilities in mercury. The influence of electron correlation on both transition energies and probabilities is investigated. An alternative approach to the generation of spin orbitals used to construct configuration interaction wave functions is proposed. This is a configuration interaction method with relativistic wave functions generated using an ab initio model potential [CIDF(MP)]. The CIDF(MP) method is tested for resonance spin-forbidden and spin-allowed ${6s}^{2}{}^{1}{S}_{0}--6s6p$ transitions in mercury and later successfully used for $6s6p--6s7s$ transition array.