Electron-positron pair creation in low-energy collisions of heavy bare nuclei

A new 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.

Relativistic calculations of the isotope shifts in highly charged Li-like ions

Relativistic calculations of the isotope shifts of energy levels in highly charged Li-like ions are performed. The nuclear recoil (mass shift) contributions are calculated by merging the perturbative and large-scale configuration-interaction Dirac-Fock-Sturm (CI-DFS) methods. The nuclear size (field shift) contributions are evaluated by the CI-DFS method including the electron-correlation, Breit, and QED corrections. The nuclear deformation and nuclear polarization corrections to the isotope shifts in Li-like neodymium, thorium, and uranium are also considered. The results of the calculations are compared with the theoretical values obtained with other methods.

Relativistic calculations of the x-ray emission following the Xe-Bi$^{83+}$ collision

We study the x-ray emission following the collision of a Bi$^{83+}$ ion with a neutral Xe atom at the projectile energy 70 MeV/u. The collisional and post-collisional processes are treated separately. The probabilities of various many-electron processes at the collision are calculated within a relativistic independent electron model using the coupled-channel approach with atomic-like Dirac-Fock-Sturm orbitals. The analysis of the post-collisional processes resulting in the x-ray emission is based on the fluorescence yields, the radiation and Auger decay rates, and allows to derive intensities of the x-ray emission and compare them with experimental data. A reasonable agreement between the theoretical results and the recent experimental data is observed. The role of the relativistic effects is investigated.

Relativistic calculations of the K-K charge transfer and K-vacancy production probabilities in low-energy ion-atom collisions

The previously developed technique for evaluation of charge-transfer and electron-excitation processes in low-energy heavy-ion collisions [I.I. 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 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 ions (atoms), 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 keV/u 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.

Relativistic calculations of the charge-transfer probabilities and cross sections for low-energy collisions of H-like ions with bare nuclei

A new method for solving the time-dependent two-center Dirac equation is developed. The time-dependent Dirac wave function is represented as a sum of atomic-like Dirac-Sturm orbitals, localized at the ions. The atomic orbitals are obtained by solving numerically the finite-difference one-center Dirac and Dirac-Sturm equations with the potential which is the sum of the exact reference-nucleus potential and a monopole-approximation potential from the other nucleus. An original procedure to calculate the two-center integrals with these orbitals is proposed. The approach is tested by calculations of the charge transfer and ionization cross sections for the H(1s)--proton collisions at proton energies from 1 keV to 100 keV. 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 for the Ne^{9+}(1s)--Ne^{10+} (at energies from 0.1 to 10 MeV/u) and U^{91+}(1s)--U^{92+} (at energies from 6 to 10 MeV/u) collisions are calculated in both relativistic and nonrelativistic cases.

Parity nonconservation in radiative recombination of electrons with heavy hydrogenlike ions

The parity nonconservation effect on the radiative recombination of electrons with heavy hydrogenlike ions is studied. Calculations are performed for the recombination into the $2^1S_0$ state of helium-like thorium and gadolinium, where, due to the near-degeneracy of the opposite-parity $2^1S_0$ and $2^3P_0$ states, the effect is strongly enhanced. Two scenarios for possible experiments are studied. In the first scenario, the electron beam is assumed to be fully polarized while the H-like ions are unpolarized and the polarization of the emitted photons is not detected. In the second scenario, the linearly polarized photons are detected in an experiment with unpolarized electrons and ions. Corresponding calculations for the recombination into the $2^3P_0$ state are presented as well.

Nuclear deformation effect on the binding energies in heavy ions

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