Gaisser–Hillas function
The Gaisser–Hillas function is used in astroparticle physics. It parameterizes the longitudinal particle [density (packed density)|particle density] in a cosmic ray Air [shower (physics)|air shower]. The function was proposed in 1977 by Thomas K. Gaisser and Anthony [Michael Hillas].
The number of particles as a function of traversed atmospheric depth is expressed as
where is maximum number of particles observed at depth, and and are primary mass and energy dependent parameters.
Using substitutions
, and
the function can be written in an alternative one-parametric form as