Expedient treatment of three-dimensional electron-photon cascade showers observed in emulsion chambers

Emulsion chambers with different inhomogeneity parameters were exposed to the 50, 100 and 300 GeV electron beams at Fermilab to study the cascade shower profiles systematically. Measured shower profiles near the axis are presented, and are shown to satisfy the similarity relation well if the dilution and reduction factors, which describe the inhomogeneity effects caused by the gap in the chamber, are appropriately conjoined with the radial spread of showers. Also an analytic expression is given which allows an extrapolation of the measured data up to higher energies and also up to other chambers with different inhomogeneous structure.