ABSTRACT
In this chapter, we consider single electron capture in two types of collisions, such as collisions between hydrogen-like projectiles and hydrogen-like targets as well as multi-electron targets
(ZP, e1)i1 + (ZT, e2)i2 −→ (ZP; e1, e2)f + ZT (18.1)
(ZP, e1)i1 + (ZT, e2; {e3, e4, . . . , eN+2})i −→ (ZP; e1, e2)f +(ZT; {e3, e4, . . . , eN+2})f ′ (18.2)
where the set {e3, e4, . . . , eN+2} denotes the N non-captured electrons. In the case of a multi-electron target, we introduce the following assumptions. All the N non-captured electrons are viewed as being passive, such that their interactions with the active electrons e1 and e2 do not contribute to the capture process. We also suppose that the passive electrons occupy the same orbitals before and after the collisions [44]. In such a frozen-core approximation, the final state of the target is ignored. In this model, the passive electrons do not participate individually in capture of the active electron, and this permits the use of an effective local target potential VT.
