Binary stopping theory for swift heavy ions

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The Bohr theory treats charged-particle stopping as a sequence of interactions with classical target electrons bound harmonically to their equilibrium positions. We demonstrate that equivalent results can be derived on the assumption of free binary collisions governed by a suitable effective potential. This kind of mapping is rigorous in the limits of distant and close collisions and therefore provides a tool to evaluate energy losses via binary-scattering theory. This model was developed with the aim of calculating stopping forces for heavy ions at moderately high velocities, where a classical-orbital calculation is typically superior to the Born approximation. The effective potential employed holds equally well for dressed as for stripped ions. Unlike the Bohr theory, the present evaluation avoids a formal division into regimes of close and distant collisions that do not necessarily join smoothly. Moreover, no perturbation expansion is necessary. For these reasons the overall accuracy as well as the range of validity of the Bohr model are significantly enhanced. Extensive tests have been performed, including comparisons with rigorous evaluations of the Z 1 3 effect, with excellent agreement even where such was not necessarily expected. Moreover, credible results have been obtained under conditions where the perturbation expansion shows poor convergence. A comparison with experimental data on O–Al is encouraging, even though shell corrections and projectile excitation/ionization have not yet been incorporated and input has not yet been optimized.

Received 21 April 2000 and Received in final form 16 June 2000
An erratum to this article is available at