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 U 91+ (1s)-U 92+ (at energies from 6 to 10 MeV/u) are calculated for both relativistic and nonrelativistic cases.
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.
A new method for solving the time-dependent two-center Dirac equation is developed. The approach is based on the using of the finite basis of cubic Hermite splines on a three-dimensional lattice in the coordinate space. The role of the negative-energy Dirac spectrum is investigated within the monopole approximation.
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