Rihan, TH; Muller, B; Greiner, W, *On the adequacy of first-order perturbation theory for calculations of inner-shell ionisation*,
Journal of the Physics B: Atomic and Molecular Physics, vol. 12 no. 5
(1979),
pp. 761-774 [doi] .
**Abstract:**

*Transition probabilities for inner-shell electrons during the formation of quasi-molecular systems in heavy-ion collisions are considered. The effect of transitions to the continuum on discrete transition probabilities is given via a simple prescription satisfying unitarity. In this way, it is also shown that the direct ionisation probabilities will be modified by virtual transitions to the continuum. Adopting a scaling model and the authors' prescription, the effect of such virtual processes on the ionisation of 1s sigma electrons can be calculated analytically. As an example, the authors calculated it for the Pb-Pb quasi-molecular system. It is found that such virtual processes suppress the direct 1s sigma ionisation probability for large impact parameters and/or small relative ion velocities.*