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Energy--angle differential and total probabilities of positron creation in slow supercritical collisions of two identical heavy nuclei are calculated beyond the monopole approximation. The time-dependent Dirac equation (TDDE) for positrons is solved using the generalized pseudospectral method in modified prolate spheroidal coordinates, which are well-suited for description of close collisions in two-center quantum systems. In the frame of reference where the quasimolecular axis is fixed, the rotational coupling term is added to the Hamiltonian. Unlike our previous calculations, we do not discard this term and retain it when solving the TDDE. Both three-dimensional angle-resolved and angle-integrated energy distributions of outgoing positrons are obtained. Three-dimensional angle-resolved distributions exhibit a high degree of isotropy. For the collision energies in the interval 6 to 8 MeV/u, the influence of the rotational coupling on the distributions and total positron creation probabilities is quite small.

We present a theoretical and computational study of positron supercritical resonances in systems consisting of two highly-charged bare nuclei. The resonance positions and widths depending on the internuclear separation are calculated with the help of the complex-scaling generalized pseudospectral method in modified prolate spheroidal coordinates. The results are applied to estimate the probability of spontaneous positron creation in slow U$^{92+}$--U$^{92+}$ and Cm$^{96+}$--Cm$^{96+}$ collisions.

Positron creation probabilities as well as energy and angular distributions of outgoing positrons in slow collisions of two identical heavy nuclei are obtained within the two-center approach beyond the monopole approximation. The time-dependent Dirac equation for positron wave functions is solved with the help of the generalized pseudospectral method in modified prolate spheroidal coordinates adapted for variable internuclear separation. Depending on the nuclear charge, the results are obtained for both subcritical and supercritical regimes of the positron creation. The signatures of transition to the supercritical regime in the total positron creation probabilities and energy spectra are discussed. The angular distributions of emitted positrons demonstrate a high degree of isotropy.

The relativistic energies and widths of hydrogen-like ions exposed to the uniform electric field are calculated. The calculations are performed for the ground and lowest excited states using the complex scaling technique in combination with a finite-basis method. The obtained results are compared with the non-relativistic values. The role of relativistic effects is investigated., Comment: 21 pages, 5 figures

In slow collisions of two bare nuclei with the total charge number larger than the critical value, $Z_{\rm cr} \approx 173$, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. Detection of the spontaneous emission of positrons would be the direct evidence of this fundamental phenomenon. However, the spontaneous emission is generally masked by the dynamical positron emission, which is induced by a strong time-dependent electric field created by the colliding nuclei. In our recent paper [I.A. Maltsev et al., Phys. Rev. Lett. 123, 113401 (2019)] it has been shown that the spontaneous pair production can be observed via measurements of the pair-production probabilities for a given set of nuclear trajectories. In the present paper, we have significantly advanced this study by exploring additional aspects of the process we are interested in. We calculate the positron energy spectra and find that these spectra can give a clear signature of the transition from the subcritical to the supercritical regime. It is found that focusing on a part of the positron spectrum, which accounts for the energy region where the spontaneously created positrons can contribute, allows to get a much stronger evidence of the transition to the supercritical mode, making it very well pronounced in collisions, for example, of two uranium nuclei. The possibility of extending this study to collisions of bare nuclei with neutral atoms is also considered. The probability of a vacancy in the lowest-energy state of a quasimolecule which is formed in collisions of a bare U nucleus with neutral U and Cm atoms has been calculated. The relatively large values of this probability make such collisions suitable for observing the vacuum decay., Comment: 18 pages, 22 figures, 1 table Minor corrections, results unchanged

The current status of tests of quantum electrodynamics with heavy ions is reviewed. The theoretical predictions for the Lamb shift and the hyperfine splitting in heavy ions are compared with available experimental data. Recent achievements and future prospects in studies of the $g$ factor with highly charged ions are also reported. These studies can provide precise determination of the fundamental constants and tests of QED within and beyond the Furry picture at the strong-coupling regime. Theoretical calculations of the electron-positron pair creation probabilities in low-energy heavy-ion collisions are also considered. Special attention is paid to tests of QED in supercritical-field regime, which can be accessed in slow collisions of two bare nuclei with the total charge number larger than the critical value, $Z_{\rm crit} \approx 173$. In the supercritical field, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. It is demonstrated that this fundamental phenomenon can be observed via impact-sensitive measurements of the pair-production probabilities., Comment: Presented at International Conference on Precision Physics and Fundamental Physical Constants - FFK2019, 9-14 June, 2019, Tihany, Hungary

In slow collisions of two bare nuclei with the total charge larger than the critical value $Z_{\rm cr} \approx 173$, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. Detection of the spontaneous emission of positrons would be the 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. Possibility of such observation is demonstrated using numerical calculations of pair production in low-energy collisions of heavy nuclei.

The present status of tests of QED with highly charged ions is reviewed. The theoretical predictions for the Lamb shift and the transition energies are compared with available experimental data. Recent achievements in studies of the hyperfine splitting and the $g$-factor isotope shift with highly charged ions are reported. Special attention is paid to tests of QED within and beyond the Furry picture at strong-coupling regime. Prospects for tests of QED at supercritical fields that can be created in low-energy heavy-ion collisions are discussed as well., Comment: 8 pages, 1 figure, 3 tables

Electron-positron pair production in low-energy collisions of heavy nuclei is considered beyond the monopole approximation. The calculation method is based on the numerical solving of the time-dependent Dirac equation with the full two-center potential. Bound-free and free-free pair-production probabilities as well as the energy spectra of the emitted positrons are calculated for the collisions of bare uranium nuclei. The calculations are performed for collision energy near the Coulomb barrier for different values of the impact parameter. The obtained results are compared with the corresponding values calculated in the monopole approximation.

The probabilities of bound-free electron-positron pair creation are calculated for head-on collisions of bare uranium nuclei beyond the monopole approximation. The calculations are based on the numerical solving of the time-dependent Dirac equation in the target reference frame with multipole expansion of the projectile potential. In addition, the energy dependence of the pair-creation cross section is studied in the monopole approximation., Comment: 11 pages

The most precise to-date evaluation of the nuclear recoil effect on the $n=1$ and $n=2$ energy levels of He-like ions is presented in the range $Z=12-100$. The one-electron recoil contribution is calculated within the framework of the rigorous QED approach to first order in the electron-to-nucleus mass ratio $m/M$ and to all orders in the parameter $\alpha Z$. The two-electron $m/M$ recoil term is calculated employing the $1/Z$ perturbation theory. The recoil contribution of the zeroth order in $1/Z$ is evaluated to all orders in $\alpha Z$, while the $1/Z$ term is calculated using the Breit approximation. The recoil corrections of the second and higher orders in $1/Z$ are taken into account within the nonrelativistic approach. The obtained results are compared with the previous evaluation of this effect [A. N. Artemyev et al., Phys. Rev. A 71, 062104 (2005)]., Comment: 25 pages, 3 figures, 5 tables