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A new method for solving the time-dependent two-center Dirac equation is developed. The approach is based on the using of the finite basis of cubic Hermite splines on a three-dimensional lattice in the coordinate space. The relativistic calculations of the excitation and charge-transfer probabilities in the low-energy U 91 +(1 s)–U 92+ collisions in two and three dimensional approaches are performed. The obtained results are compared with our previous calculations employing the Dirac-Sturm basis sets [I.I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)]. The role of the negative-energy Dirac spectrum is investigated within the monopole approximation. [ABSTRACT FROM AUTHOR]

Recent progress in quantum electrodynamics (QED) calculations of highly charged ions is reviewed. The theoretical predictions for the binding energies, the hyperfine splittings, and the g factors are presented and compared with available experimental data. Special attention is paid to tests of bound-state QED at strong field regime. Future prospects for tests of QED at the strongest electric and magnetic fields as well as for determination of the fine structure constant and the nuclear magnetic moments with heavy ions are discussed. [ABSTRACT FROM AUTHOR]

Abstract: A review of the current status of the theoretical study of spectral line profile for systems with few electrons is given in this paper. The hydrogen atom and highly charged ions are presented in this work. In particular, the line profiles for cascade processes, the asymmetry of the line profile beyond the resonance approximation and the overlap of the resonances are investigated. The line profile approach is introduced for the investigation of the energy levels and the transition probabilities for bound electrons within the framework of quantum electrodynamics. The energies and transition probabilities for few-electron systems are evaluated. The line profile approach is also applied to the case of the quasidegenerate levels in highly charged ions. [Copyright &y& Elsevier]

Abstract: We present an accurate QED calculation of the interelectron interaction corrections to the energy of the (1s2p)1 P 1 and (1s2p)3 P 1 two-electron configurations for ions with nuclear charge 10⩽ Z ⩽92. When the fully relativistic treatment based on j–j coupling scheme is employed, the corresponding energy levels become quasidegenerate in the region Z ⩽40. To evaluate the energies of these configurations within the framework of QED we utilize the line profile approach. The numerical results we have obtained are compared with available experimental data and with different calculations. [Copyright &y& Elsevier]

This review surveys the quantum theory of electromagnetic radiation for atomic systems. In particular, a review of current theoretical studies of multiphoton processes in one and two-electron atoms and highly charged ions is provided. Grounded on the quantum electrodynamics description the multiphoton transitions in presence of cascades, spin–statistic behaviour of equivalent photons and influence of external electric fields on multiphoton in atoms and anti-atoms are discussed. Finally, the nonresonant corrections which define the validity of the concept of the excited state energy levels are introduced. [ABSTRACT FROM AUTHOR]