Physics NotePublished
Hadron Cascade by the Method of Characteristics
H M Portella; K H Tsui; C E Navia; H Shigueoka
Publication details
- Authors
- H M Portella; K H Tsui; C E Navia; H Shigueoka
- Type
- Physics Note
- Status
- Published
- Publication date
- 20/12/2005
- Description
- 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.
- Year
- 2005
- Number
- CBPF-NF-005/05
- Linked to a thesis
- No
- Linked to a grant
- No