A Monte Carlo calculation of electromagnetic cascade showers over a wide lateral and energy range in lead

An extensive three-dimensional Monte Carlo calculation of electromagnetic cascade showers in a lead emulsion chamber is performed at energies from 1 GeV to 200 TeV, covering lateral distances up to 10 cm. We present the average electron longitudinal and lateral distributions in number as well as in energy loss in a thin film inserted in the chamber. For many practical applications the lateral distribution of the energy loss is more useful than that of the number. It is pointed out that approximation B of the cascade theory overestimates electron numbers and that the N-K or N-K-G function for the lateral distribution is too wide. However, their functional form is rather close to the lateral distribution of the energy loss measured at an optimal distance between two successive lead plates. Results are presented in graphic forms as well as by approximate formulas applicable for many experimental conditions. (orig.)