Reciprocity in the electronic stopping of slow ions in matter

The principle of reciprocity, i.e., the invariance of the inelastic excitation in ion-atom collisions against interchange of projectile and target, has been applied to the electronic stopping cross section of low-velocity ions and tested empirically on ion-target combinations supported by a more or less adequate amount of experimental data. Reciprocity is well obeyed (within ~10%) for many systems studied, and deviations exceeding ~20% are exceptional. Systematic deviations such as gas-solid or metal-insulator differences have been looked for but not identified on the present basis. A direct consequence of reciprocity is the equivalence of Z₁ with Z₂ structure for random slowing down. This feature is reasonably well supported empirically for ion-target combinations involving carbon, nitrogen, aluminium and argon. Reciprocity may be utilized as a criterion to reject questionable experimental data. In cases where a certain stopping cross section has not been or cannot be measured, the stopping cross section for the inverted system may be available and serve as a first estimate. It is suggested to build in reciprocity as a fundamental requirement into empirical interpolation schemes directed at the stopping of low-velocity ions. Examination of the SRIM and MSTAR codes reveals cases where reciprocity is obeyed accurately, but deviations of up to a factor of two are common. In case of heavy ions such as gold, electronic stopping cross sections predicted by SRIM are asserted to be almost an order of magnitude too high.