A method for calculations of electron-positron pair-creation probabilities in low-energy heavy-ion collisions is developed. The approach is based on the propagation of all one-electron states via the numerical solving of the time-dependent Dirac equation in the monopole approximation. The electron wave functions are represented as finite sums of basis functions constructed from B-splines using the dual-kinetic-balance technique. The calculations of the created particle numbers and the positron energy spectra are performed for the collisions of bare nuclei at the energies near the Coulomb barrier with the Rutherford trajectory and for different values of the nuclear charge and the impact parameter. To examine the role of the spontaneous pair creation, the collisions with a modified velocity and with a time delay are also considered. The obtained results are compared with the previous calculations and the possibility of observation of the spontaneous pair creation is discussed.

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 previously developed technique for evaluation of charge transfer and electron-excitation processes in low-energy heavy-ion collisions [Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)] is extended to collisions of ions with neutral atoms. The method employs the active-electron approximation, in which only the active-electron participates in the charge transfer and excitation processes while the passive electrons provide the screening density-functional theory (DFT) potential. The time-dependent Dirac wave function of the active electron is represented as a linear combination of atomic-like Dirac-Fock-Sturm orbitals, localized at the ions (atoms). The screening DFT potential is calculated using the overlapping densities of each ion (atom), derived from the atomic orbitals of the passive electrons. The atomic orbitals are generated by solving numerically the one-center Dirac-Fock and Dirac-Fock-Sturm equations by means of a finite-difference approach with the potential taken as the sum of the exact reference ion (atom) Dirac-Fock potential and of the Coulomb potential from the other ion within the monopole approximation. The method developed is used to calculate the K-K charge transfer and K-vacancy production probabilties for the Ne(1s 2 2s 2 2p 6 )-F 8+ (1s) collisions at the F 8+ (1s) projectile energies 130 and 230 keV/u. The obtained results are compared with experimental data and other theoretical calculations. The K-K charge transfer and K-vacancy production probabilities are also calculated for the Xe-Xe 53+ (1s) collision.

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.