From uncertainty as the longitudinal momentum transfer gets small the particles wavelength will increase, if the wavelength becomes longer than the mean free path in the medium (the average distance between scattering sites) then the scatterings can no longer be treated as independent events, this is the LPM effect.
In QED the rescattering of the high energy electron dominates the process, in QCD the emitted gluons carry color charge and interact with the medium also.
Lev Landau and Isaak Pomeranchuk showed that the formulas for bremsstrahlung and pair creation in matter which had been formulated by Hans Bethe and Walter Heitler (the Bethe–Heitler formula) were inapplicable at high energy or high matter density.
The effect of multiple Coulomb scattering by neighboring atoms reduces the cross sections for pair production and bremsstrahlung.
In 1994 a team of physicists at SLAC National Accelerator Laboratory experimentally confirmed the Landau–Pomeranchuk–Migdal effect.