Gaisser–Hillas function
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The Gaisser–Hillas 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.[1]
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[2] as