The relativistic nuclear recoil, higher-order interelectronic-interaction, and screened QED corrections to the transition energies in Li-like ions are evaluated. The calculation of the relativistic recoil effect is performed to all orders in 1/Z. The interelectronic-interaction correction to the transition energies beyond the two-photon exchange level is evaluated to all orders in 1/Z within the Breit approximation. The evaluation is carried out employing the large-scale configurationinteraction Dirac-Fock-Sturm method. The rigorous calculation of the complete gauge invariant sets of the screened self-energy and vacuum-polarization diagrams is performed utilizing a local screening potential as the zeroth-order approximation. The theoretical predictions for the 2p j − 2s transition energies are compiled and compared with available experimental data in the range of the nuclear charge number Z = 10 − 60.

Nuclear deformation effects on the binding energies in heavy ions are investigated. Approximate formulas for the nuclear-size correction and the isotope shift for deformed nuclei are derived. Combined with direct numerical evaluations, these formulas are employed to reanalyse experimental data on the nuclear-charge-distribution parameters in $^{238}\textrm{U}$ and to revise the nuclear-size corrections to the binding energies in H- and Li-like $^{238}\textrm{U}$. As a result, the theoretical uncertainties for the ground-state Lamb shift in $^{238}\textrm{U}^{91+}$ and for the $2p_{1/2}-2s$ transition energy in $^{238}\textrm{U}^{89+}$ are significantly reduced. The isotope shift of the $2p_{j}-2s$ transition energies for $^{142}\textrm{Nd}^{57+}$ and $^{150}\textrm{Nd}^{57+}$ is also evaluated including nuclear size and nuclear recoil effects within a full QED treatment.Comment: 19 pages, 5 table

Isotope shifts in dielectronic recombination spectra were studied for Li-like A Nd 57+ ions with A=142 and A=150. From the displacement of resonance positions energy shifts δE 142,150 (2s − 2p 1/2 ) = 40.2(3)(6) meV ((stat)(sys)) and δE 142,150 (2s − 2p 3/2 ) = 42.3(12)(20) meV of 2s − 2p j transitions were deduced. An evaluation of these values within a full QED treatment yields a change in the mean-square charge radius of 142,150 δ r 2 = -1.36(1)(3) fm 2 . The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.

A method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomiclike Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are generated by solving numerically the one-center Dirac and Dirac-Sturm equations by means of a finite-difference approach with the Coulomb potential taken as the sum of the exact reference-nucleus potential and of the other nucleus within the monopole approximation. An original procedure for calculating the two-center integrals with these orbitals is proposed. As a first test of the approach developed here, calculations of the charge-transfer and ionization cross sections for the H(1s)-proton collisions at proton energies from 1 to 100 keV are performed. The obtained results are compared with related experimental and other theoretical data. To investigate the role of the relativistic effects, the charge-transfer cross sections in collisions of Ne 9+ (1s)-Ne 10+ (at energies from 0.1 to 10 MeV/u) and U 91+ (1s)-U 92+ (at energies from 6 to 10 MeV/u) are calculated for both relativistic and nonrelativistic cases.

Fully relativistic approach to evaluate the correlation effects in highly charged ions is presented. The interelectronic-interaction contributions of first and second orders in 1/Z are treated rigorously within the framework of bound-state quantum electrodynamics, whereas the calculations of the third-and higherorder contributions are based on the Dirac-Coulomb-Breit Hamiltonian. The developed approach allows one to deal with single as well as degenerate or quasi-degenerate states. We apply this approach to the calculations of the correlation contributions to the n = 1 and n = 2 energy levels in heliumlike ions.The obtained contributions are combined with the one-electron and screened QED corrections, nuclear recoil and nuclear polarization corrections to get the total theoretical predictions for the ionization and transition energies in high-Z heliumlike ions. * Corresponding author: a.v.malyshev@spbu.ru 1