  By a mix of form-factors and analyticity techniques, we determine some
fundamental scattering amplitudes in non-Fermi liquid systems. These include
the reflection and transmission amplitudes for Laughlin quasiparticles at a
point contact between two g=1/2 Luttinger liquids, and the e->e_{edge} at a
point contact between a Fermi liquid and a g=1/3 Luttinger liquid (all liquids
chiral or not). These results are obtained in closed form, and give rise to
rather simple expressions for the probabilities of the most basic processes of
non Fermi liquid physics at these special values of the couplings.
