Electromagnetic cascade showers in lead with the Landau-Pomeranchuk-Migdal effect included: Average behavior of the one-dimensional LPM shower in lead

The numerical method developed by Fujimaki and Misaki can obtain solutions for an electromagnetic cascade shower, in which no restrictions on the forms of the differential cross sections for both bremsstrahlung and pair-production processes are made. By utilizing this method, the LPM showers (electromagnetic cascade showers in the presence of the Landau Pomeranchuk-Migdal effect) are calculated for primary energies in the range ${10}^{14}$-${10}^{17}$ eV in lead. Physical properties of the LPM showers, such as electron transition curves, track lengths, and fractional dissipated energies, are obtained in the cases with and without the inclusion of ionization losses. In order to compare LPM showers with ordinary electromagnetic cascade showers in the absence of the LPM effect [hereafter defined as Bethe-Heitler (BH) showers] and to clarify the characteristics of the LPM showers, all physical quantities which have been obtained in the LPM showers have also been obtained in the BH showers. We discuss the characteristics of the LPM showers, especially with reference to the BH showers. The results obtained by other authors are compared with the results obtained by the author.