Some remarks about simulation of cosmic ray phenomena with use of nuclear interaction models based on the current SPS proton-antiproton data

The x-y controversy is studied by introducing models with as many features (except for x and y distributions) in common, as possible, to avoid an extrapolation problem, only primary energies of 500 TeV are considered. To prove the point, Monte Carlo simulations are performed of EAS generated by 500 TeV vertical primary protons. Four different nuclear interaction models were used. Two of them are described elsewhere. Two are: (1) Model M-Y00 - with inclusive x and y distributions behaving in a scaling way; and (2) Model M-F00 - at and below ISR energies (1 TeV in Lab) exactly equivalent to the above, then gradually changing to provide the distributions in rapidity at 155 TeV as given by SPS proton-antiproton. This was achieved by gradual decrease in the scale unit in x distributions of produced secondaries, as interaction energy increases. Other modifications to the M-Y00 model were made.