The GaisserâÂÂHillas function is used in astroparticle physics. It parameterizes the longitudinal particle density in a cosmic ray 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 (m) form as