Abstract
Determination of the primary particle mass using air fluorescence or a Cherenkov detector array is one of the most difficult task of experimental cosmic ray studies. The information about the primary particle mass is a compound of the produced particle multiplicity, inelasticity, interaction cross-section and many other parameters, thus it is necessary to compare registered showers with sophisticated Monte-Carlo simulation results. In this work we present results of the studies of at least three possible ways of extrapolating proton- Nucleus and Nucleus-Nucleus cross sections to cosmic ray energies based on the Glauber theory. They are compared with experimental accelerator and cosmic ray data for the proton-air cross section. We also present results of the EAS development with the most popular high-energy interaction models adopted in the CORSIKA program with our cross section extrapolations. The average position of the shower maximum and the width of its distribution are compared with experimental data and some discussion is given.
Highlights
The hadronic interaction cross section is one of the parameters playing a major role during an Extensive Air Shower development
To calculate the integral in Eq 9 we used the fluctuation of the nucleus shape ρA(d) adopted from Lund model [3] in the form of Woods-Saxon (2-parameter Fermi) distribution leading us to following form of eikonal function: χopt(b) = i d2d ρA(d) 1 − eiχ(b−d)
As a result we present plots of Xmax position versus primary energy for each case compared with results for cross sections currently existing in CORSIKA and experimental data (Fig. 3)
Summary
The hadronic interaction cross section is one of the parameters playing a major role during an Extensive Air Shower development. Calculations of hadronic cross sections at ultra high energies require their extrapolation from lower energies where accelerator data are available. Such extrapolations forces the building of a phenomenological models based e.g. on Glauber diffraction theory [1, 2]. Glauber approximation consists of introducing an eikonal function, χ, representing all phase-shifts related to all possible scattering acts. Eikonal χ(b) represents the opacity of two colliding objects. A knowledge on the form of hadron matter distribution allows for calculations of elastic, inelastic and total cross sections
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