Isotope shifts in dielectronic recombination spectra were studied for Li-like ${}^A\mathrm{Nd}^{57+}$ ions with $A=142$ and $A=150$. From the displacement of resonance positions energy shifts $\delta E^{142\hspace{0.17em}150}(2s-2p_{1/2})=40.2(3)(6)\mathrm{meV}$ [(stat)(sys)] and $\delta E^{142\hspace{0.17em}150}(2s-2p_{3/2})=42.3(12)(20)\mathrm{meV}$ 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 ${}^{142\hspace{0.17em}150}\delta ⟨r^2⟩=-1.36(1)(3){\mathrm{fm}}^2$. The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.

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 reanalyze experimental data on the nuclear-charge-distribution parameters in ${}^{238}\text{U}$ and to revise the nuclear-size corrections to the binding energies in H- and Li-like ${}^{238}\text{U}$. As a result, the theoretical uncertainties for the ground-state Lamb shift in ${{}^{238}\text{U}}^{91+}$ and for the $2p_{1/2}-2s$ transition energy in ${{}^{238}\text{U}}^{89+}$ are significantly reduced. The isotope shift of the $2p_j-2s$ transition energies for ${{}^{142}\text{N}\text{d}}^{57+}$ and ${{}^{150}\text{N}\text{d}}^{57+}$ is also evaluated including nuclear size and nuclear recoil effects within a full QED treatment.

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 configuration-interaction 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.

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 ${\mathrm{U}}^{91+}$($1s$)-U${}^{92+}$ (at energies from 6 to 10 MeV/u) are calculated for both relativistic and nonrelativistic cases.

In slow collisions of two bare nuclei with the total charge larger than the critical value $Z_{\mathrm{cr}}\approx 173$, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. The detection of the spontaneous emission of positrons would be direct evidence of this fundamental phenomenon. However, the spontaneously produced particles are indistinguishable from the dynamical background in the positron spectra. We show that the vacuum decay can nevertheless be observed via impact-sensitive measurements of pair-production probabilities. The possibility of such an observation is demonstrated using numerical calculations of pair production in low-energy collisions of heavy nuclei.