Relativistic Many-body Perturbation Theory Research Articles

CASCADE OF AUGER TRANSITIONS IN SPECTRUM OF XENON: THEORETICAL DATA

The energy parameters of the Auger transitions for the xenon atomic system are calculated within the combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order density functional approximation. The results are compared with reported experimental data as well as with those obtained by semiempirical method. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth order that significantly provides a physically reasonable agreement between theory and experiment.

HYPERFINE STRUCTURE PARAMETERS FOR COMPLEX ATOMS WITHIN RELATIVISTIC MANY-BODY PERTURBATION THEORY

The calculational results for the hyperfine structure (HFS) parameters for the Mn atom (levels of the configuration 3d64s) and the results of advanced calculating the HFS constants and nuclear quadrupole moment for the radium isotope are obtained on the basis of computing within the relativistic many-body perturbation theory formalism with a correct and effective taking into account the exchange-correlation, relativistic, nuclear and radiative corrections. Analysis of the data shows that an account of the interelectron correlation effects is crucial in the calculation of the hyperfine structure parameters. The fundamental reason of physically reasonable agreement between theory and experiment is connected with the correct taking into account the inter-electron correlation effects, nuclear (due to the finite size of a nucleus), relativistic and radiative corrections. The key difference between the results of the relativistic Hartree-Fock Dirac-Fock and many-body perturbation theory methods calculations is explained by using the different schemes of taking into account the inter-electron correlations as well as nuclear and radiative ones.

THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

RELATIVISTIC CALCULATION OF THE RADIATIVE TRANSITION PROBABILITIES AND LIFETIMES OF EXCITED STATES FOR THE RUBIDIUM ATOM IN A BLACK-BODY RADIATION FIELD

We present the results of relativistic calculation of the radiative transition probabilities and excited states lifetimes for a heavy Rydberg atomic systems in a black-body (thermal) radiation field on example of the rubidium. As theoretical approach we apply the combined generalized relativistic energy approach and relativistic many-body perturbation theory with ab initio Dirac zeroth approximation. There are obtained the calculational data for the radiative transition probabilities and excited states lifetimes, in particular, the rubidium atom in the Rydberg states with principal quantum number n=10-100. It is carried out the comparison of obtained theoretical data on the effective lifetime for the group of Rydberg nS states of the rubidium atom at a temperature of T = 300K with experimental data as well as data of alternative theoretical calculation based on the improved quasiclassical model. It is shown that the accuracy of the theoretical data on the radiative transition probabilities and excited states lifetimes is provided by a correctness of the corresponding relativistic wave functions and accounting for the exchange-correlation effects.

NEW RELATIVISTIC APPROACH TO COMPUTING SPECTRAL PARAMETERS OF MULTICHARGED IONS IN PLASMAS

It is presented a new relativistic approach to computing the spectral parameters of multicharged ions in plasmas for different values of the plasmas screening (Debye) parameter (respectively, electron density, temperature). The approach used is based on the generalized relativistic energy approach combined with the optimized relativistic many-body perturbation theory (RMBPT) with the Dirac-Debye shielding model as zeroth approximation, adapted for application to study the spectral parameters of ions in plasmas. An electronic Hamiltonian for N-electron ion in plasmas is added by the Yukawa-type electron-electron and nuclear interaction potential. The special exchange potential as well as the electron density with dependence upon the temperature are used.

THEORETICAL STUDYING SPECTRAL CHARACTERISTICS OF Zn-LIKE IONS ON THE BASIS OF RELATIVISTIC MANY-BODY PERTURBATION THEORY

A theoretical study of the spectroscopic characteristics of Zn-like multiply charged ions is carried out within the framework of the relativistic many-body perturbation theory. The optimized Dirac-Kohn-Shem approximation was chosen as the zero approximation of the relativistic perturbation theory. Optimization has been fulfilled by means of introduction of the parameters to the Kohn-Sham exchange and correlation potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian.

Relativistic Configuration-Interaction and Perturbation Theory Calculations for Heavy Atoms

Heavy atoms present challenges to atomic theory calculations due to the large number of electrons and their complicated interactions. Conventional approaches such as calculations based on Cowan’s code are limited and require a large number of parameters for energy agreement. One promising approach is relativistic configuration-interaction and many-body perturbation theory (CI-MBPT) methods. We present CI-MBPT results for various atomic systems where this approach can lead to reasonable agreement: La I, La II, Th I, Th II, U I, Pu II. Among atomic properties, energies, g-factors, electric dipole moments, lifetimes, hyperfine structure constants, and isotopic shifts are discussed. While in La I and La II accuracy for transitions is better than that obtained with other methods, more work is needed for actinides.

Relativistic Configuration-Interaction and Perturbation Theory Calculations of the Sn XV Emission Spectrum

Recently, there has been increased interest in developing advanced bright sources for lithography. Sn ions are particularly promising due to their bright emission spectrum in the required wavelength range. Cowan’s code has been used to model the emission; however, it has adjustable parameters, which limit its predictive power, and it has limited relativistic treatment. Here, we present calculations based on ab initio relativistic configuration-interaction many-body perturbation theory (CI-MBPT), with relativistic corrections included at the Dirac-Fock level and core-polarization effects with the second-order MBPT. As a proof of principle that the theory is generally applicable to other Sn ions with proper development, we focused on one ion where direct comparison with experimental observations is possible. The theory can also be used for ions of other elements to predict emissions for optimization of plasma-based bright sources.

Two-photon-exchange corrections to the g factor of Li-like ions

We report calculations of QED corrections to the $g$ factor of Li-like ions induced by the exchange of two virtual photons between the electrons. The calculations are performed within QED theory to all orders in the nuclear binding strength parameter $Z\alpha$, where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant. In the region of low nuclear charges we compare results from three different methods: QED, relativistic many-body perturbation theory, and nonrelativistic QED. All three methods are shown to yield consistent results. With our calculations we improve the accuracy of the theoretical predictions of the $g$ factor of the ground state of Li-like carbon and oxygen by about an order of magnitude. Our theoretical results agree with those from previous calculations but differ by 3-4 standard deviations from the experimental results available for silicon and calcium.

Relativistic configuration interaction and many-body perturbation theory of energy levels, wavelengths, oscillator strengths, radiative rates and lifetimes of He-like lithium

Relativistic configuration interaction and many-body perturbation theory of energy levels, wavelengths, oscillator strengths, radiative rates and lifetimes of He-like lithium

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.

THEORETICAL AUGER SPECTROSCOPY OF SOLIDS: CALCULATION OF ENERGY PARAMETERS

The Auger electron spectroscopy is an effective method to study the chemical composition of solid surfaces and near-surface layers. Sensing the Auger spectra in atomic systems and solids gives the important data for the whole number of scientific and technological applications. When considering the method principles, the main attention is given as a rule to the models for drawing chemical information from the Auger spectra and to the surface composition determination methods by the Auger spectrum decoding. It is just the two-step model that is used most widely when calculating the Auger decay characteristics. The relaxation processes due to Coulomb interaction between electrons and resulting in the electron distribution in the vacancy field have no time to be over prior to the transition. In this paper the combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order density functional approximation is applied to determination of the energy and spectral parameters of the Auger decay for the Na, Si, Ge, Ag solids. The results are compared with reported experimental results as well as with those obtained by alternative theoretical schemes. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth approximation, which significantly affects the agreement of theory and experiment.

HYPERFINE STRUCTURE PARAMETERS FOR Li-LIKE MULTICHARGED IONS WITHIN RELATIVISTIC MANY-BODY PERTURBATION THEORY

The relativistic many-body perturbation theory with the optimized Dirac-Kohn-Sham zeroth approximation is applied to calculation of the hyperfine structure parameters for some Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with fulfilment of the gauge invariance principle. The obtained data on the hyperfine structure parameters of the Li-like multicharged ions are analyzed and compared with alternative theoretical and experimental results.

RELATIVISTIC THEORY OF CALCULATION OF E1 TRANSITION AMPLITUDES, AND GAUGE INVARIANCE PRINCIPLE

The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order Dirac-Kohn-Sham one-particle approximation are used for estimating the energies and the E1 radiative transitions amplitudes (oscillator strengths) for the low-excited states of the francium. The comparison with available theoretical and experimental (compilated) data is performed. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth order that significantly provides a physically reasonable agreement between theory and precise experiment.

ELECTRON-COLLISIONAL SPECTROSCOPY OF ATOMS AND IONS: ADVANCED ENERGY APPROACH

An advanced relativistic energy approach combined with a scattering theory is used to calculate the electron-collision excitation cross-sections, collision strengths for a number of multicharged ions. The relativistic many-body perturbation theory is used alongside the gauge-invariant scheme to generate an optimal Dirac-Kohn-Sham- Debye-Huckel one-electron representation. The results of relativistic calculation (taking into account the exchange and correlation corrections) of the electron collision cross-sections (strengths) of excitation of the transition between the fine-structure levels (2P 3/2 - 2P 1/ 2 ) of the ground state of F-like ions with Z = 19-26 and of the [2s 2 1 S-(2s2p 1 Р)] transition in the В-like O 4+ are presented and analysed.

RELATIVISTIC CALCULATION OF THE HYPERFINE STRUCTURE PARAMETERS FOR COMPLEX ATOMS WITHIN MANY-BODY PERTURBATION THEORY

The hyperfine structure parameters and electric quadrupole moment of the 201Hg mercury isotope the Mn atom are estimated within the relativistic many-body perturbation theory formalism with a correct and effective taking into account the exchange-correlation, relativistic, nuclear and radiative corrections. Analysis of the data shows that an account of the interelectron correlation effects is crucial in the calculation of the hyperfine structure parameters. The fundamental reason of physically reasonable agreement between theory and experiment is connected with the correct taking into account the inter-electron correlation effects, nuclear (due to the finite size of a nucleus), relativistic and radiative corrections. The key difference between the results of the relativistic Hartree-Fock Dirac-Fock and many-body perturbation theory methods calculations is explained by using the different schemes of taking into account the inter-electron correlations as well as nuclear and radiative ones.

SPECTROSCOPY OF MULTIELECTRON ATOM IN DC ELECTRIC FIELD: RELATIVISTIC OPERATOR PERTURBATION THEORY

We develop the theoretical basis of a new relativistic operator perturbation theory approach to multielectron atom in a DC electric field combined with a relativistic many-body perturbation theory formalism for a free multielectron atom. As illustration of application of the presented formalism, the results of energy and spectral parameters for a number of atoms are presented. The relativistic OPT method is tested for computing the Stark shifts of Rydberg states for a few the multielectron systems such as the sodium and rubidium. The approach allows an accurate and consistent treatment of a DC strong field Stark effect in multielectron atoms.

Complex scaling in relativistic calculations of cross sections for electron-ion recombination processes

SynopsisWe present an approach to calculate cross sections for electron-ion recombination processes. It is based on the combination of relativistic many-body perturbation theory and complex scaling method. A preliminary comparison between measured and calculated spectra for the electron-ion recombination rate coefficients for Be-like Ca will be given.

RELATIVISTIC APPROACH TO CALCUATION OF IONIZATION CHARACTERISTICS FOR RYDBERG ALKALI ATOM IN A BLACK-BODY RADIATION FIELD

The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth Dirac-Fock-Sham approximation are used for computing the thermal Blackbody radiation ionization characteristics of the alkali Rydberg atoms, in particular, the sodium in Rydberg states with principal quantum number n=10-100. The detailed analysis of the data of computing ionization rates for the Rydberg sodium atom demonstrates physically reasonable agreement between the theoretical and experimental data. The accuracy of the theoretical data is provided by a correctness of the corresponding relativistic wave functions and accounting for the exchange-correlation effects.

DETERMINATION OF RADIATION DECAY PARAMETERS FOR HEAVY COMPLEX ATOMIC SYSTEMS

The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order ab initio model potential optimized one-particle representation are used for precise computing the energy levels and radiative decay probabilities (radiation amplitudes) of heavy alkali elements, in particular, there are listed data for the 7s1/2 – np1/2,3/2, np1/2,3/2-nd3/2,5/2 (n=7-10) transitions in Fr and some E1 and E2 transitions in a single ionized Hg+ atom. The comparison of the calculated values with available theoretical and experimental (compillated) data is performed..