Spatial excitation patterns induced by swift ions in condensed matter

Abstract

It is shown that a charged particle moving with velocity $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$ in a medium of resonance frequency ${\ensuremath{\Omega}}_{0}$ may set up two types of electron-density fluctuations. Collective fluctuations trail the particle, composing a conical pattern in a relatively extended periodic wake of wavelength $\ensuremath{\sim}\frac{2\ensuremath{\pi}v}{{\ensuremath{\Omega}}_{0}}$. They constitute a mode of energy transport from the particle track leading eventually to particle-hole excitations. Single-particle interactions give rise to bow waves ahead of the particles of wavelength $\frac{2\ensuremath{\pi}\ensuremath{\hbar}}{\mathrm{mv}}$. The gradient along $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$, at the site of the ion, of the wake potential set up by density fluctuations, multiplied by the ionic charge, yields an expression for the retarding force of the medium on the projectile in exact agreement with the Bethe stopping-power formula appropriate to the medium. The wake of a dicluster causes forces between the constituent ions which account quantitatively for measurements of the breakup behavior of swift molecular ions in thin foils. The increase in the energy straggling of a test charge, when moving in the wake of a leading ion, is shown to be small compared with the straggling induced by its own wake under normal conditions.