Calculation of electron capture probability of energetic protons colliding with rare-gas atoms: A comparison study on four methods

We calculate the probability of electron capture of energetic protons colliding with rare-gas atoms, comparing four methods based on time-dependent density-functional theory (TDDFT). By approximating the pair-correlation function of the system with an explicit dependence on the fractional number of bound electrons, a new effective model of pair-correlation function is built up. Benchmark calculations are given over a wide range of impact energy, demonstrating that the new designed read-out functional reproduces quite accurately the single-electron capture cross sections and the double-electron capture features which were not properly described by previous TDDFT calculations.