The muon lateral distribution function as a transformation of the height-of-origin distribution in hadronic extensive air showers

Starting from the parametrized energy and transverse momentum spectra at the height of the muon origin taken from the simulations, the lateral distribution function of the muons is represented within a simple geometry model, as an integral transformation of the height distribution of the muon origin. The kernel of this transformation depends on the energy threshold, shower zenith angle and observation level depth, while it is universal for different primary types and primary energies in the knee region. The validity of this representation is discussed in connection with the assumptions of the model.