In slow collisions of two bare nuclei with the total charge larger than the critical value Z cr ≈ 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. PACS numbers: 34.90.+q, 12.20.Ds Recently the obtained results were confirmed with the monopole approximation [20] as well as beyond

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.

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 αZ. 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 αZ, 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)]. PACS numbers: 31.30.J-, 12.20.Ds

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