A large area (128 m^2) Muon Tracking Detector (MTD), located within the KASCADE experiment, has been built with the aim to identify muons (E_mu > 0.8 GeV) and their directions in extensive air showers by track measurements under more than 18 r.l. shielding. The orientation of the muon track with respect to the shower axis is expressed in terms of the radial- and tangential angles. By means of triangulation the muon production height H_mu is determined. By means of H_mu, a transition from light to heavy cosmic ray primary particle with increasing shower energy Eo from 1-10 PeV is observed. Muon pseudorapidity distributions for the first interactions above 15 km are studied and compared to Monte Carlo simulations.
Muons have never been used up to now to reconstruct the hadron longitudinal development of EAS with sufficient accuracy, due to the difficulty of building large area ground-based muon telescopes [1]. Muons are produced mainly by the decay of charged pions and kaons in a wide energy range. They are not always produced directly on the shower axis. Multiple Coulomb scattering in the atmosphere and in the detector shielding may change the muon direction. It is evident that the reconstruction of the longitudinal * corresponding author, e-mail: paul.doll@kit.edu † now at: Instituto de Física y Matemáticas, Universidad Michoacana, Morelia, Mexico 2 now at: Max-Planck-Institut für Physik, München, Germany 3 now at: Universidade São Paulo, Instituto de Física de São Carlos, Brasil 4 now at: Dept. of Astrophysics, Radboud University Nijmegen, The Netherlands 5 now at: Institute for Space Sciences, Bucharest-Magurele, Romania 6 deceased 7 now at: University of Trondheim, Norway development of the muon component by means of triangulation [2,3] provides a powerful tool for primary mass measurement [4] , giving an information similar to that obtained with the Fly's Eye experiment, but in the energy range not accessible by the detection of fluorescence light. Muon tracking allows also the study of hadron interactions by means of the muon pseudorapidity [5]. Already in the past, analytical tools have been developed which describe the transformation between shower observables recorded on the ground and observables which represent directly the longitudinal shower development [7]. Fig. 1 in ref [8] shows the experimental environment. Measured core position distributions for showers inside KASCADE range from 40 -120 m and inside Grande from 250 -360 m.The shower core position ranges cover full trigger efficiency as confirmed by investigations of muon lateral density distributions [6]. With CR studies very high energies are accessible in the 'knee' energy region 10 15 -10 ter (rise of < p T >) which is transformed to geometric scaling [14] by the color-glass-condensate theory.
The angular correlation of the muon tracks with respect to the shower axis is expressed by the ρ and the τ angles [1]. The ρ angle contains some scattering which is represented by the τ angle value exhibiting a σ τ ∼ 0.2 o . Fig. 1 shows ρ angle distributions for specific muon number lg(N µ ) bins corresponding to different shower energy bins [4]. The ρ angle distributions are plotted for ’light’ and ‘heavy’ primary CR mass enriched showers, employing the lg(N µ )/lg(N e ) ratio (corrected for attenuation) [9] [4] to be larger (‘heavy’) or smaller (’light’) than 0.83. The distributions show a dependence on the primary mass range, however, masked by the energy dependent penetration.
Based on ρ and τ angles and the distance of the muon hit to the shower core R µ , the muon production height h µ along the shower axis is calculated:
The MTD-KASCADE system with its dense array grid and 80 -120 m core distance range for the muon track allows to study the muon momenta in the 100 -200 GeV range. h µ will be considered for ρ > τ which we can extend up to 20 km for a shower core muon hit distance window 80 -120 m (note 100 m/20000 m ∼ = 0.28 o ) employing, according to simulations, ∼ 200 GeV muons from above 15 km. Fig. 2 shows muon production height distributions for different muon size bins and different lg(N µ )/lg(N e ) ratio above 0.83 (‘heavy’) and below 0.83 (’light’). CORSIKA [12] simulations based on QGSjetII+FLUKA2002.4 (slope -2.7 and -3.1 below and above the knee, respectively) for Hydrogen and Iron are shown in the Fig. 2 as well. In the low h µ range the low energy interaction model (FLUKA2002.4) seems capable to describe the h µ distribution. The experimental distributions are getting more narrow with increasing energy but differently for ’light’ and ‘heavy’ CR primaries. The S N N numbers quote the CM energies assuming A=1 CR primary. In the course of the analysis in [4], h µ is transformed to H µ [g/cm 2 ] and after subtracting from each H µ an ’energy’ dependent penetration depth the remaining depth H A µ exhibits [4] the mass A sensitivity.
Fig. 2 shows strong reduction of muons from above 15 km for ’light’ primary CR particles with respect to Monte-Carlo especially for the highest energy interval, which corresponds to a CM energy of ∼ 8 T eV . Standard Monte-Carlo (see above) predicts for a nucleon-nucleon collision charged particle multiplicities < N ch > ∼ 40 (2T eV ) -70 (8T eV ). As a consequence, a fraction out of ∼ 70 × 200GeV parent pions are missing. Very recent results from LHC at 7 T eV report also [10] smaller < N ch > at midrapitity compared to QGSjetII. It would be worthwhile to study to which extent the simulated distributions in Fig. 2 above ∼ 15 km scale with the inelastic cross sections of H and Fe primary masses. At 10 16 eV on Nitrogen σ H inel amounts to ∼ 400 mb and σ F e inel is about 5 times larger. The ratio of charg
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