Development of ultrahigh-energy electromagnetic cascades in water and lead including the Landau-Pomeranchuk-Migdal effect

Abstract

Cosmic-ray experiments are approaching energies where electromagnetic-cascade calculations must include the Landau-Pomeranchuk-Migdal (LPM) reduction in bremsstrahlung and pair-production cross sections. The LPM effect is already significant for cascades in Pb at 100 TeV and very important at 1000 TeV; for cascades of incident energy ${E}_{0}$ the LPM effect is significant if ${E}_{0}\ensuremath{\gg}{E}_{\mathrm{LPM}}=61.5{L}_{\mathrm{cm}}$ TeV, where ${L}_{\mathrm{cm}}$ is the radiation length in centimeters. Two totally independent Monte Carlo computer programs have been developed which, in approximation A, agree with each other and with Konishi, Misaki, and Fujimaki. One of these programs (by Stanev and Vankov) has been extended to include calculations of the lateral and angular distributions of cascade particles; the other (by Streitmatter, Ellsworth, and Bowen) has been utilized in a hybrid Monte Carlo and analytic method to calculate the longitudinal development in approximation B.