Electronic stopping for swift carbon cluster ions connected with average charge reduction

The cluster effect in the average charge and the electronic energy-loss of swift carbon cluster ions in linear-chained and ring structures with equal separation with kinetic energy ranging from 0.3 to 30 MeV/atom is theoretically investigated on the basis of a recent average charge theory and the dielectric function formalism together with the wave-packet model. The dependence of the cluster average charge on the constituent atoms clearly shows the reductive feature, regardless of the speed, which is more enhanced with increasing the number of constituent atoms. It is proposed that for ring structure, the average charge of constituent ions is determined by an unique self-consistent formula. In the high speed limit it has an asymptotic formula and the reduction effect tends to be vanishing. Regarding the energy loss, the electronic stopping powers of aluminum and silicon targets are calculated for Cn clusters in linear-chain and ring structures with inclusion of the average charge reduction in a bulk. It is found that they show the super-linear cluster effect almost over the range of investigated speed except for large ring clusters at low speed.