Impact parameter dependence of electronic energy loss: Oscillator model

Abstract

The mean energy loss due to Coulomb excitation by a uniformly moving point charge has been evaluated accurately as a function of impact parameter in the first Born approximation for a spherical harmonic oscillator as a target. The mean energy loss is found to decrease monotonicaUy with increasing impact parameter at all projectile speeds. At small impact parameters, the variation is less pronounced than that of the electron density in the ground state. In the limit of large impact parameters, the energy loss approaches Bohr's classical result. We find that for the system investigated, the local-density picture overestimates the variation of energy loss with impact parameter. The energy loss spectrum at fixed impact parameter is close to a Rutherford spectrum for not too low excitation levels and impact parameters within the radius of the electron distribution. With some caution, the oscillator model of atomic stopping is extended to allow for the variation with impact parameter. Qualitative consideration is given to the enhancement of average electronic energy loss for specific trajectories of charged particles in crystals.