Three-dimensional development of cascade showers induced by 50-, 100-, and 300-GeV electrons

Five emulsion chambers were analyzed with two different dilution factors exposed to the 50-, 100-, and 300-GeV electron beams at Fermi National Accelerator Laboratory. The longitudinal development and lateral distribution of the number of shower tracks within a certain radius ({≤} 100 {μ} m) both roughly agree with the theoretical transition and lateral curves by Nishimura and Kidd connected by a spacing factor equal to the dilution factor. The error of the cascade energy measurement by the conventional way, using the transition curves within a radius 50 {μ} m, is 18-28% for 50-100 GeV and 13-14% for 300 GeV. Track length within a cylinder of the same radius gives less ambiguity than the above method, when the track length is summed up till the depth is greater than 1.4 times the depth of the maximum number of shower tracks within a radius 50 {μ} m. Other results with details are also described.