Thickness of the particle swarm in cosmic-ray air showers

Abstract

The average dispersion in arrival time of air-shower particles detected with a scintillator at an impact parameter r is described with accuracy 5-10% by the empirical formula ( sigma t)= sigma t0(1+r/rt)b, where sigma t0=1.6 ns, rt=30 m b=(2.08+or-0.08)-(0.40+or-0.06)sec theta +(0+or-0.06)log(E/1017 eV), for r<2 km, 1017 <E<1020 eV and theta <60 degrees . (E is the primary energy and theta is the zenith angle). The amount of fluctuation in sigma t due to fluctuations in the level of origin and shower development is less than 30%. These results provide a basis for estimating the impact parameters of very large showers with data from very small detector arrays (mini arrays). The energy of such showers with data from very small detector arrays (mini arrays). The energy of such showers can then be estimated from the local particle density. The formula also provides a basis for estimating the angular resolution of air-shower array-telescopes.