The generalized relativistic energy approach with using the Debye shielding model is used for studying spectral parameters of ions in plasma and determination of the oscillator strengths for the Be-like ions. An electronic Hamiltonian for N-electron ion in a plasma is added by the Yukawa-type electron-electron and nuclear interaction potential. Oscillator strengths gf for 2s 2-[2s 1/2 2p 3/2 ] 1 transition in Be-like Fe are computed for different values of the electron density and temperature (n e =10 22-10 24 cm-3 , T=0.5-2 keV) of plasmas are presented and compared with available alternative spectroscopic data.

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The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order Dirac-Kohn-Sham one-particle approximation are used for preliminary estimating the energies and oscillator strengths of radiative transitions from the ground state to the low-excited and Rydberg states, in particular, 6s2 -6snp (n =7-30) transitions, of the barium atom. The comparison of the calculated oscillator strengths with available theoretical and experimental (compillated) data is performed. The important point is linked with non-accounting for the polarization effect contribution into the oscillator strength value that has led to ~40% difference between the empirical (compillated) and theoretical data.

The hyperfine structure and electric quadrupole moment of the mercury isotope 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 interelectron correlation effects, nuclear (due to the finite size of a nucleus), relativistic and radiative corrections. The key difference between the results of the RHF, RMPT methods calculations is explained by using the different schemes of taking into account the inter-electron correlations. 2. Relativistic method to computing hyperfine structure parameters of atoms and ions Let us describe the key moments of the approach (more details can be found in refs. [3,4,10-20]). The electron wave functions (the PT zeroth basis) are found from solution of the relativistic Dirac equation with potential, which includes ab initio mean-field potential, electric, polarization potentials of a nucleus. The charge distribution in the Li-like ion is modelled within the Gauss model. The nuclear model used for the Cs isotope is the independent particle model with the Woods-Saxon and spin-orbit potentials (see refa. [3,4]). Let us consider in details more simple case of the Li-like ion. We set the charge distribution in the Li-like ion nucleus ρ(r) by the Gaussian function:

The hyperfine structure parameters and electric quadrupole moment of the 201 Hg 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 manybody 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.