Low-energy proton-hydrogenlike-ion scattering in the Coulomb-Born approximation

Excitation probabilities for the 1s-2s transition of hydrogenlike ions by low-energy (4-100)Eₜₕ protons are calculated in the Coulomb-Born approximation and compared to the corresponding calculations in the semiclassical approximation with hyperbolic trajectories. Through the use of a Fourier-Bessel transform, an effective energy is derived for the semiclassical approximation, which brings the total cross section into agreement with the Coulomb-Born results.