On the nonperturbative contributions to the stopping of H- and He-like heavy ions

The nonperturbative contributions to the electronic stopping of hydrogen- and heliumlike heavy ions penetrating matter in frozen charge states at energies of 10–1000 MeV/u are calculated numerically in a previously developed quantum mechanical approach. The aim is to determine whether it is possible to create a simple model based on the nonrelativistic bare-ion Bloch correction, or, more generally, its relativistic counterpart, by means of which the nonperturbative contributions for dressed ions may be estimated reasonably accurately. A significant dependence on the sign of the interaction is detected at all energies in the exact results for the correction for internal ion structure. This moderates prospects for a general model. Yet it is possible to devise a couple of simple constructions, one analytical, for approximate inclusion of all dressed-ion corrections which deliver the stopping number to within ±0.01 for the parameter range considered here, that is, roughly Zα/β⩾12γ and kinetic energy of at least 10 MeV/u (whereby the speed βc of the ion is at least 0.15c and its atomic number Z   at least 10; γ≡1/1-β2 denotes the ion’s total relativistic energy in units of its energy at rest).