Indications for the new unitarity regime in the extensive air showers   measurements
  We note that the new unitarity regime when scattering amplitude goes beyond the black disc limit (antishadowing) could help in the explanation of the regularities such as knee in the energy spectrum, existence of penetrating and long-flying particles and other features observed in the measurements of the extensive air showers which originate from cosmic particles interactions with the atmosphere. 
S.M. Troshin, N.E. Tyurin