Theory of average charge and energy loss of cluster ions in foils

We study the average charge and the electronic energy loss of the swift (but not relativistic) clusters in a solid. A self-consistent average-charge theory for clusters in foils is presented on the basis of the fluid-mechanical model. Here the electron stripping rate is evaluated not only for an isolated ion, but also for cluster ions under the same background by taking into account the binding effect of the surrounding ions. This theory can elucidate very well not only the reduction of the cluster average charge per ion, but also its cluster-size and foil-thickness dependences of the recent data for the MeV/atom carbon clusters (Cn) in carbon foils. The structure dependence is also proposed theoretically. In spite of the average-charge reduction, we can reconcile the enhancement of the energy losses of the corresponding clusters. The cluster energy losses with the inclusion of the Coulomb explosion by the wave-packet model is in much better agreement with the data at energies of 1-5.65 MeV/atom. Consistent agreement both in the diminution of average charge and in the enhancement of energy loss supports that the charge-state bulk effect is dominant in the cluster average charge