  Most calculations of air shower development have been based on the
Bethe-Heitler cross sections for bremsstrahlung and pair production. However,
for energetic enough particles, a number of different external factors can
reduce these cross sections drastically, slowing shower development and
lengthening the showers. Four mechanisms that can suppress bremsstrahlung and
pair production cross sections are discussed, and their effect on extremely
high energy air showers considered. Besides lengthening the showers, these
mechanisms greatly increase the importance of fluctuations in shower
development, and can increase the angular spreading of showers.
