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title: "Hadron Cascade by the Method of Characteristics • CBPF Index"
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**Physics Note****Published**

# **Hadron Cascade by the Method of Characteristics**

**H M Portella; K H Tsui; C E Navia; H Shigueoka**

12/20/2005

[**Download PDF **0.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adba818/pdf) [**Contact owner**](mailto:oliveira@cbpf.br?subject=Hadron%20Cascade%20by%20the%20Method%20of%20Characteristics)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>H M Portella; K H Tsui; C E Navia; H Shigueoka</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>20/12/2005</dd>

<dt>Description</dt>
<dd>Hadron diffusion equations with energy-dependent interaction mean free paths and inelasticities are solved using the Mellin transform. Instead of using operators on the finite difference terms, the Mellin transformed equations are Taylor expanded into a first order partial differential equation in atmospheric depth $t$ and in the transform parameter $s$. Then, these equations are solved by the method of characteristics. The hadron fluxes (nucleon and meson) in real space is evaluated by the method of residues. For the case of a regularized power law primary spectrum these hadron fluxes are given by simple residues and one, never before mentioned, essential singularities. A comparison of our solutions with the nucleon flux measured at sea level and with the hadron fluxes measured at $t=840\, g/cm^2$ and at sea level are made. The agrement between them is in general very good, greater than $ 90\% $. In order to check the accuracy of our calculations, a comparison between our solution and the simulated nucleon cascades is also made.</dd>

<dt>Year</dt>
<dd>2005</dd>

<dt>Number</dt>
<dd>CBPF-NF-005/05</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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