We present a microscopic simulation of convoy electron emission in gla
ncing-angle ion-surface scattering which accounts for both dynamic ima
ge interactions and multiple scattering. We find that the position and
shape of the convoy peak are determined by rainbow scattering of elec
trons in the dynamically screened field of the ion. The nonclassical c
ontribution to rainbow scattering is estimated using a uniform semicla
ssical approach. Core polarization is shown to contribute significantl
y to dynamical screening. Good agreement with experiment is found for
Li+-SnTe(001) collisions.