We study lepton flavour violation via flavour changing Rutherford scat
tering, i.e. the conversion of relativistic electrons into muons by sc
attering in the external field of a massive nucleus. We show that for
a class of models with heavy neutrinos and extended gauge sectors, all
the unknown form-factors associated with purely electromagnetic trans
itions may be absorbed into the predicted value of Gamma(mu-->e gamma)
, leading to a compact analytical expression for the cross-section. Th
e experimental realisation via a beam-dump experiment at LEP is discus
sed.