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| The '''Gaisser–Hillas function''' is used in [[astroparticle physics]]. It [[Parametrization|parameterizes]] the longitudinal [[particle density]] in a [[cosmic ray]] [[Air shower (physics)|air shower]]. The function was proposed in 1977 by Thomas K. Gaisser and Anthony M. Hillas.<ref name="isbn0-08-016724-1">{{cite book |author=Hillas, A. M. |authorlink= |editor= |others= |title=Cosmic rays |edition= |language= |publisher=Pergamon Press |location=New York |year=1972 |origyear= |pages= |quote= |isbn=0-08-016724-1 |oclc= |doi= |url= |accessdate=}}</ref>
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| The number of particles <math>N(X)</math> as a function of traversed atmospheric depth <math>X</math> is expressed as
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| :<math>N(X)= N_\text{max}\left(\frac{X-X_0}{X_\text{max}-X_0}\right)^{\frac{X_\text{max}-X_{0}}{\lambda}}\exp\left(\frac{X_\text{max}-X}{\lambda}\right),</math> | |
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| where <math>N_\text{max}</math> is maximum number of particles observed at depth <math>X_\text{max}</math>, and <math>X_0</math> and <math>\lambda</math> are primary mass and energy dependent parameters.
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| Using substitutions
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| <math>x=\frac{X-X_0}{\lambda}</math> {{spaces|5}} and {{spaces|5}} <math>x_\text{max}=\frac{X_\text{max}-X_0}{\lambda}</math>
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| the function can be written in an alternative one-parametric form<ref>{{cite journal |last= |first= |authorlink= |title= Lambert W Function for Applications in Physics|year= 2012|version= |accessdate= |author1= Darko Veberic |doi= 10.1016/j.cpc.2012.07.008 |journal= Computer Physics Communications |volume= 183 |issue= 12 |pages= 2622–2628|arxiv=1209.0735 }}</ref> as
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| :<math>N(x)=N_\text{max}\left[\frac{x}{x_\text{max}}\right]^{x_\text{max}}\exp(x_\text{max}-x).</math>
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| ==References ==
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| {{reflist}}
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| <div class="references-small">
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| {{cite conference
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| | last = Gaisser
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| | first = T.K.
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| | coauthors = Hillas, A.M.
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| | title =
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| | booktitle = Proceedings of the 15th International Cosmic Ray Conference, 13–26 Aug 1977
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| | place = Plovdiv, Bulgaria
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| | year = 1977
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| | volume = 8
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| | pages = 353
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| | url =
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| | accessdate = }}
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| </div>
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| {{DEFAULTSORT:Gaisser-Hillas function}}
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| [[Category:Cosmic rays]]
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| {{Physics-stub}}
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Latest revision as of 00:33, 26 September 2014
Alyson Meagher is the title her parents gave her but she doesn't like when people use her full title. To climb is some thing she would by no means give up. Distributing production is how he makes a living. I've always cherished residing in Mississippi.
my homepage ... telephone psychic (relevant internet page)