Observations on EAS are examined from the point of view of deriving the transverse momenta of the secondaries produced in ultra-high-energy collisions.The lateral distributions of muons for various threshold energies provide useful experimental data, and a detailed analysis of this characteristic has been made. The most extensive results have been reported by Earnshaw el al. (1967), and a theoretical treatment of the lateral distributions expected, as a function of the transverse momentum of the parent pions, has been given b y de Beer el al. (1966). A comparison appears t o indicate mean transverse momenta much greater than the value of -0.4 GeV/c found in the more direct observations on nucleon-nucleon collisions. However, a n examination of the fluctuations in lateral distribution expected theoretically suggests that there is bias with practical EAS arrays leading t o the selection of that fraction of the showers having unusually flat lateral distributions.The effect of applying a correction to allow for this bias is to reduce the derived mean transverse momenta considerably; the values being -0.6 f 0.2 GeV/c for pion interactions of mean energy -200 GeV and 1.0 f 0.3 GeV/c for interactions of mean energy -4 000 GeV. These values are still significantly higher than the values measured more directly.In view of the invariance of the transverse momentum of the secondaries from highenergy interactions its examination is of importance and significance. EAS studies of the lateral distribution of the muon and nuclear-active components will, in principle, give information about the transverse momentum of the parent particles (thought to be mainly pions) and of pions and nucleons respectively. Insofar as the muon component is easier to measure and the determination of lateral distance from the core should be relatively accurate, this coillponent will be considered in greater detail.The yardstick against which EAS transverse inomenta are compared is the value obtained froin studies using more direct methods (accelerators, ionization calorimeters, and nuclear emulsions). A number of experiments have shown that the distribution of pT can be represented to fair accuracy by the expression suggested by Cocconi et al. (1961) : \\illere the mean value is 2po. I t should be pointed out, however, that there is some evidence that this distribution may not be accurate for pT 0.2 GeV/c (de Beer et al.
Calculations have been made of the fluctuations in muon and electron numbers expected in air showers using different models of high-energy interactions and alternative assumptions about the mass composition of the primary particles. Comparison is made with the results of experiment, and it is concluded that the evidence concerning the suggested change in the mass composition of the primaries at energies above 1016 eV is inconclusive. Other consequences of fluctuations, in particular those in the lateral distribution of muons, are examined, and it is shown that such fluctuations can have a marked effect on the interpretation of experimental data.
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