Properties of the Shower Maximum
Two properties of the shower maximum are important to note. First, at maximum, an EAS typically contains ~1-1.6 particles for every GeV (109 eV) of energy carried by the primary cosmic ray. Second, the average "slant depth"at which the shower maximum occurs, varies logarithmically with the energy of the primary cosmic ray.{multithumb thumb_width=250}
The "slant depth" refers to the amount of materials penetrated by the shower at a given point in its development, and is customarily denoted by the symbol "X". The value of X is calculated by integrating the density of air from the point of entry of the air shower at the top of the atmosphere, along the trajectory of the shower, to the point in question. Hence X has units given as density (g/cm3) multiplied by distance (cm). An air shower traveling along an exactly vertical, downward trajectory traverses ~1,000 g/cm2 in reaching sea-level. This value of 1,000 g/cm2 can also be interpreted as an atmospheric pressure. Obviously, an inclined shower will traverse more than 1,000 g/cm2 to reach sea-level.
Following the above convention, the depth of shower maximum is denoted "Xmax". With a value of about 500 g/cm2 at 1015 eV, the average Xmax for cosmic ray showers increases by 60-70 g/cm2 for every decade of energy.
Various hadronic shower models tend to predict significantly different absolute values for average Xmax. This makes direct comparison of measured Xmax to theoretical predictions somewhat problematic as a means of studying composition. However, nearly all the models predict (a) the same slope dXmax/dLog10E ~ 55 g/cm2 for any single element, and (b) roughly the same separation in Xmax between heavier and lighter elements. A deviation in the measured slope dXmax/dLog10E, referred to as the "Elongation Rate", from the canonical single-component value would be a clear indication of an evolution in the composition mix with energy.
