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We demonstrate that a recently published quasiclassical M\oller type approach[Geyer and Rost 2002, J. Phys. B 35 1479] can be used to overcome the problemof autoionization, which arises in classical trajectory calculations for manyelectron targets. In this method the target is stabilized dynamically by abackward--forward propagation scheme. We illustrate this refocusing and presenttotal cross sections for single and double ionization of helium by electronimpact.Comment: LaTeX, 6 pages, 2 figures; submitted to J. Phys.

Dynamical stabilization of classical multi-electron targets against autoionization