Measuring the energy spectrum of neutral pions in ultra--high--energy proton--air interactions

Fluctuations in the muon content of extensive air showers are anti-correlated to the fluctuations of the energy taken by the neutral pions which emerge from the first interaction of the cosmic ray in the atmosphere. We demonstrate that the high-energy tail of the neutral pion spectrum produced in the first proton-air interaction can be measured, within the uncertainties of present cosmic ray experiments, through the analysis of the probability distribution of showers over the shower muon contents.