LPM effect in cosmic-ray electron observations with emulsion chambers

We have performed a series of cosmic-ray electron + positron observations using balloon-borne emulsion chambers since 1968, together with electron beam tests at CERN-SPS. In emulsion chamber experiments, we can measure the location of shower tracks in each emulsion plate with a precision of 1 μm. Because of the high position resolution, we can identify the first electron-positron pairs of electron-induced showers. The LPM effect predicts a reduction of amplitude for bremsstrahlung photon emission by a high-energy electron. It causes the optical depth of the first electron-positron pair to increase. From the measurements of the first pair depths with 200 GeV and 250 GeV beam electrons at CERN, and cosmic ray electrons + positrons from 400 GeV to 3 TeV (on average at 900 GeV), we found direct evidence of suppression of the bremsstrahlung cross section due to the LPM effect. In this work, we present the experimental results compared to analytic approximations and Monte-Carlo simulations.