The relation of the lateral distribution of Cerenkov light from cosmic-ray showers to the distance of maximum development

Abstract

The lateral distribution of Cerenkov light intensity from EAS at sea level has been calculated and its dependence on the distance to maximum development, Hm, investigated. The distribution separates into two regions: outside approximately 125 m radius, the intensity Q decreases as R- gamma with gamma dependent on Hm as found previously; more important, inside 125 m, the steepness decreases markedly for showers with large values of Hm. Several functional forms, for example an exponential Q(R) approximately e-bR and a power law (R+R0)- gamma as well as the intensity ratio Q(50)/Q(150), were tried to define the shape in this region. The parameter b and this intensity ratio are equally suitable estimators for Hm les than 5 km. For Hm>or approximately=5 km, where the shape becomes sensitive to the late development of the shower, to the presence of aerosols and to the photocathode spectral response, the ratio is preferred. Typical errors expected are Delta Hm>or approximately=0.4 km below 4 km, increasing to >or approximately=1 km near Hm approximately 7 km. Differences between this theory and that of McComb and Turver (1982) are discussed.