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

TL;DR

This paper introduces a novel method for solving the time-dependent Dirac equation to accurately compute charge transfer probabilities in low-energy ion collisions, incorporating relativistic effects for high-Z ions.

Contribution

A new approach using atomic-like Dirac-Sturm orbitals for solving the two-center Dirac equation in collision problems, including a method for calculating two-center integrals.

Findings

Accurate charge transfer cross sections for H(1s)--proton collisions from 1 keV to 100 keV.

Relativistic effects significantly influence charge transfer cross sections for high-Z ions.

Comparison with experimental and other theoretical data validates the method's accuracy.

Abstract

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.