The LPM effect for EeV hadronic showers in ice: implications for radio detection of neutrinos

We study the longitudinal development of hadronic showers in ice for energies up to 100 EeV and its implications for radio and optical Cherenkov emission. A small fraction of showers induced by primaries of energy above 1 EeV is shown to display the characteristic elongation associated to the Landau Pomeranchuck Migdal (LPM) effect. The rest look like ordinary showers because the highest energy $\pi^0$'s interact instead of decaying in two photons. The LPM effect observed in this fraction of the showers is mainly due to $\eta$ and $\eta '$ production and decay. We give parameterizations for the total and excess charge tracklengths and for the amplitude and angular spread of the electric field spectrum in the Cherenkov direction. Implications for neutrino detection are briefly addressed.