Gaisser–Hillas function - Alchetron, the free social encyclopedia

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 N ( X ) as a function of traversed atmospheric depth X is expressed as

N ( X ) = N max ( X − X 0 X max − X 0 ) X max − X 0 λ exp ⁡ ( X max − X λ ) ,

where N max is maximum number of particles observed at depth X max , and X 0 and λ are primary mass and energy dependent parameters.

Using substitutions

n = N N max , x = X − X 0 λ and m = X max − X 0 λ

the function can be written in an alternative one-parametric (m) form as

n ( x ) = [ x m ] m exp ⁡ ( m − x ) = x m e − x m m e − m = exp ⁡ [ m ( ln ⁡ x − ln ⁡ m ) − ( x − m ) ] .

References

Gaisser–Hillas function Wikipedia

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