Theoretical Analysis of Ionization Chamber Data on Large Air Showers

The decoherence curve of large air showers is analyzed under the simplifying assumption of a constant lateral structure function for all air showers. The following results emerge: (1) Contrary to statements found in the literature, ordinary shower theory leads one to expect a rise in the decoherence curve at distances much less than the characteristic laterla distance $r_1$. (2) The theoretical decoherence curve calculated under the assumption of a constant structure function rises more sharply near the origin than the experimental points. This indicates that the effective structure function is less peaked than the one we used (due to Molière). (3) The dependence of the structure function upon the age of the shower tends to lessen this discrepancy. However, quantitative estimates make it appear doubtful that one can get agreement between theory and experiment without assuming a rather high multiplicity of the event which starts the shower.