Distributions of the charged particles multiplicities in the electromagnetic showers initiated by 10 to 1000 GeV electrons in lead

Distributions of the charged particles multiplicities in the electromagnetic showers initiated by 10 to 1000 GeV electrons in lead are calculated using GEANT4. It is shown that they are well fitted by the inverse sum of two exponents. The evolution of the multiplicity distribution shapes as a function of the lead depth is discussed. An estimate of the energy resolution of a simple e,{\gamma} detector consisting of a high Z convertor and a counter of the shower electrons and positrons is presented.