Energy-loss measurements in transmission experiments on carbon and gold foils with ∼ 100-keV/nucleon ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{+}$ beams reveal that protons moving in spatially correlated clusters have effective charge numbers significantly larger than unity. The theory traces the origin of this effect to the coherent dynamic response of the target electrons due to the vicinage of particles in tight clusters and, in linear response approximation, predicts quantitatively the observed enhanced energy loss of proton clusters.

• Received 19 August 1974

DOI:https://doi.org/10.1103/PhysRevLett.33.1325