High Order Corrections in the Relativistic Perturbation Theory with the Model Zeroth Approximation, Mg-Like and Ne-Like Ions

Abstract

used during the construction of the model potential (MP) and one-quasi-particle wave functions of the zeroth approximation, for the calculation of one-quasi-particle diagram contributions, and also for the effective Calculation Of some second order two-The relativistic perturbation theory is applied to the solution of the manyelectron Dirac equation. The theoretical consideration is accomplished for Some Mg-like ions: s v, Ca IX, ~i XI and F~ xv; the energies of all the states l?2s22p631, j l , 3 1 j 2 are calculated. The Ne-like spectra are calculated for the ions with Z = 16-26; all the states of configurations ls22s22ps3s, 3p, 3d and ls22s2p63s, 3p, 3d are considered.The Dirac equation with the central one-particle model potential VJr) is accepted as a zeroth approximation; the model potential imitates the core potential of the closed shells. The empirical information about the energy structures of one electron above the core or one vacancy inside the core is used here to construct the zeroth approximation.The perturbation theory first order correction is calculated exactly, the high order contributions are accounted for effectively. Two main types of high order corrections are investigated: "polarization" interaction of two "above core" particles and effect of the mutual screening of these particles.quasi-particle diagram contributions. Calculations previously made for the ions of the Mg-like series and the Fe-l&e series (two vacancies above the core 3p63d1') showed that already an elementary calculation within the first order of the PT yields cated multi-configurational Hartree-Fock-Pauli method.In the present paper a regular method for the effective inclusion of high order corrections is described. F~~ ions of the Mg I-like and Ne I-like series the allowance for these corrections appreciably improves the results for the transition energies.Of the Same quality as the more sophisti-

Theoretical Spectroscopy of Rare-Earth Elements: Spectra and Autoionization Resonances

“…[71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88], it has been developed a new formalism of the relativistic many-body PT with using the optimized one-quasiparticle (QP) representation and effective account of the exchange-correlation corrections of the PT second order and higher orders (polarization interaction, quasiparticles screening, etc.). The method of the relativistic many-body PT is constructed on the basis of the same ideas as the well-known PT with the model potential zeroth approximation by Ivanov et al [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64]. However, there are two key differences: namely, the PT zeroth approximation [81,82,85,86] is in fact the Dirac-Kohn-Sham one.…”

Sensing the Hyperfine Structure and Nuclear Quadrupole Moment for Radium

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). It is provided by necessity of further developing the modern as atomic and as nuclear theories.…”

“…Here we carry out sensing and estimating the hyperfine structure parameters and nuclear quadrupole moment of the radium on the basis of gauge-invariant QED PT with an account of relativistic, correlation, nuclear finite size and radiative effects. Let us describe in brief the important moments of the calculation procedure.. Full details of the whole method and corresponding numerical procedure of calculation of the different characteristics, including the hyperfine structure constants and nuclear quadrupole moment, can be found in [5][6][7][8][9][10][11][12][13][14].…”

“…All correlation corrections of the second and high orders of perturbation theory (electrons screening, particle-hole interaction etc.) are accounted for [6,7]. We set the charge distribution in the nucleus by the Gaussian function: Such definition of an effective nuclear radius is to be suitable at least as some zeroth approximation.…”

“…The main exchange effect will be taken into account if in the equation for the nlj orbital we assume V(r)=V(r|1s)+V(r|nlj) and in the equation for the nlj orbital V(r)=V(r|core). The rest of the exchange-correlation effects are accounted for in the first two PT orders by the total inter-electron interaction [6,7]. The core electron density is defined by iteration algorithm within gauge invariant QED procedure [10].…”