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

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 Ne⁹⁺($1s$)-Ne¹⁰⁺ (at energies from $0.1$ to $10$ MeV/u) and U⁹¹⁺($1s$)-U⁹²⁺ (at energies from 6 to 10 MeV/u) are calculated for both relativistic and nonrelativistic cases.