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Relativistic many-body perturbation theory and a qualitative estimation of non-perturbative effects are used to calculate low energy scattering and annihilation of a positron with noble gas atoms. The existence of a virtual level (resonance) and an annihilation enhancement factor that is produced by the strong e+ e− correlation, is demonstrated for heavy atoms (e.g. Xe and Rn). For molecules, (e+ Xen, e+ Rnn, n ≥ 2) the virtual level can transform into a real bound level for the positron. These results can explain the very high annihilation rate and non-linear dependence on atomic density observed in measurements of positron decay rates in dense xenon gas. The absence of such effects in a e+ -Ne system completes the picture.

Corrections to the g-factors of the Cs, Fr, Au and Hg+ atoms as well as the amplitude of the 6S-7S strongly forbidden M1 transition in Cs have been calculated. For this purpose, the relativistic Hartree-Fock equations involving the interaction between electrons and an external magnetic field are used. With such a method, the effect of polarization of the closed shells is taken into account exactly. The following values of the correction to the g-factor for Cs, Fr and Au have been obtained: δgCs = 2.54 × 10-4; δgFr = 33.3 × 10-4 and δgAu = 11.9 × 10-4 (the experiment gives, correspondingly: 2.23 (1) × 10-4; 26.5 (8) × 10-4; 9.87 (2) × 10-4), and δgHg+ = 10.2 × 10-4 for the Hg+ (refined value 8.5 × 10-4). The amplitude of the 6S-7S transition of Cs is equal to -0.56 × 10-4|μB| (and -0.413 (18) × 10-4 in the experiment).

The energy levels, fine-and hyperfine-structure intervals in the Ra+ ion have been calculated using the relativistic Hartree–Fock method with the core polarization and correlation corrections taken into account. The accuracy of calculation is ~ 1%. The calculation enables us to improve the accuracy of determination of the radium isotopes (A = 211-229) magnetic moments from the data on hyperfine structure (Ref. [1]).

Parity non-conserving (PNC) El-amplitudes for 205Tl are calculated: 7p1/2|Dz|6p1/2 = ?7.9(1 ? 0.06), 6p3/2|Dz|6p1/2 = ?27.0(1 ? 0.03) (in units of 10-11i|e|aB(?Qw/N)), Qw is the weak charge of the nucleus, N = 124 is the number of the neutrons). Using the developed technique we recalculate the PNC El-amplitude for 133Cs with high accuracy: 7s|Dz|6s = 0.90(1 ? 0.02). The method of calculation is the time-dependent Hartree-Fock (TDHF) plus correlation corrections of second order in residual interaction.