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 M. 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.
the function can be written in an alternative one-parametric (m) form as
Gaisser, T.K.; Hillas, A.M. (1977). "Reliability of the method of constant intensity cuts for reconstructing the average development of vertical showers". Proc. of 15th Int. Cosmic Ray Conf., 13–26 Aug 1977. 8. Plovdiv, Bulgaria. p. 353.
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