A detailed simulation of vertical showers in atmosphere produced by primary gammas and protons, in the energy range 11100 TeV, has been performed by means of the FLUKA Monte Carlo code, with the aim of studying the time structure of the shower front at different detector heights. It turns out that the time delay distribution can be fitted using few parameters coincident with the distribution central moments. Such parameters exhibit a smooth behaviour as a function of energy. These results can be used both for detector design and for the interpretation of the existing measurements. Differences in the time structure between gamma and proton induced showers are found and explained in terms of the nonrelativistic component of extensive air showers. c 1998 Elsevier Science B.V.
IntroductionRecent papers concerning calculations of Extensive Air Showers (EAS) [1] include results on time delay of particles from the shower front, in view of the comparison with existing recent measurements [21 4]. As a matter of fact, the first measurements of the structure of the EAS front were attempted by Bassi, Clark and Rossi in 1953 [5], but many other have contributed [6112]. As far as the many simulation works on EAS are concerned, a part from the quoted Ref.[1], only a limited fraction of them has considered the question of the time structure [13123].The interest in this topic has been renewed by recent experimental data concerning the detection of an anomalous delayed component [24]. In this framework it is therefore important to achieve a better and more detailed knowledge of this time structure. Furthermore, eventual fast simulation tools based of simple parametrisations constructed on this knowledge can be helpful not only for analysis, but also for design of new detectors, trigger evaluation, etcetera.When a full shower simulation is considered, the structure of the time front depends to a large extent on the details of particle transport algorithms. Therefore, it can be useful to consider the outputs of very detailed codes, and compare it with the results of the codes optimized for the cosmic ray physics, which often contain simplifications in order to reduce the computer time. A valuable study of the time structure of Extensive Air Showers, for very high energies, based on the use of the CORSIKA code [25] has been presented in [3].Here we present the study of the time structure of the e.m. secondary component generated by a photon or proton, as calculated mainly with the FLUKA96 code.0927-6505/98/$ -see front matter c 1998 Elsevier Science B.V. All rights reserved. PII S 0 9 2 7 -6 5 0 5 ( 9 8 ) 0 0 0 5 2 -8 ASTPHY 429