Sublinear and superlinear dependences of average charge and energy loss per ion on particle number for MeV/atom linear-chained carbon-cluster ions traversing a carbon foil

Abstract

The cluster effect in the average charge and the energy loss of swift carbon-cluster ions with kinetic energy of MeV per atom in a linear-chain structure with equal separation of 0.127 nm, passing through carbon foil, was theoretically investigated on the basis of the dielectric function formalism together with the wave-packet model. We assume that inside a foil the dissipated and the conservative forces due to electron polarization are acting on constituent partially stripped ions as well as the repulsive Coulomb forces. In addition, the reductive effect of the cluster average charge is incorporated in a self-consistent manner. On the other hand, outside a foil, only a repulsive Coulomb interaction is assumed to be working. The equation of motion for constituent ions is numerically solved using the molecular dynamics method under the action of the above forces. The calculated results are presented as a function of the incident orientation angle $\ensuremath{\theta}$. By taking the average over $\ensuremath{\theta}$, the energy loss per ion of the carbon cluster displays a sublinear dependence on the number of atoms at lower energies, while at higher energies it shows a superlinear dependence in spite of including the average charge reduction. These two trends in the energy loss are in good agreement with existing experimental results, in which not only the spatial correlation but also the reduction of cluster average charge is found to play a significant role.