The nucleon-air nucleus interaction probability law with rising cross section

Portella, H. M.; Gomes, A.; Lima, C. E. C.

doi:10.1088/0954-3899/27/2/305

Cited by 7 publications

(7 citation statements)

References 12 publications

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“…where λ(E) is the energy-dependent mean free path, η(E ) = E/E < 1 is the elasticity, u(η) is the elasticity distribution. Modelling the mean free path by a power index β [10],…”

Section: The Nucleon Casementioning

confidence: 99%

“…where λ (E) is the energy-dependent pion collision mean free path, b is the charge exchange probability of the incident pion and (E , E) dE is the probability of number of pions produced at energy E in the interval dE due to incident pion or nucleon of energy E . Modelling the mean free path by a power index β (the same as the nucleon case), equation (10) becomes…”

Section: The Charged Pion Casementioning

confidence: 99%

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Hadron cascade by the method of characteristics

Tsui

Portella

Navia

et al. 2005

J. Phys. G: Nucl. Part. Phys.

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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 expanded in a Taylor series to a first-order partial differential equation in atmospheric depth t and in transform parameter s. These equations are then solved by the method of characteristics. The hadron fluxes (nucleon and pion) in real space are 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 residue. Comparisons of our solutions are made with the nucleon flux measured at sea level and with the hadron fluxes measured at t = 840 g cm−2 and at sea level. The integral hadron flux is also compared with experimental data from the Mt Fuji Collaboration (t = 650 g cm−2). The agreement between all of them is very good in general, better than 90%.

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“…where λ(E) is the energy-dependent mean free path, η(E ) = E/E < 1 is the elasticity, u(η) is the elasticity distribution. Modelling the mean free path by a power index β [10],…”

Section: The Nucleon Casementioning

confidence: 99%

Section: The Charged Pion Casementioning

confidence: 99%

Hadron cascade by the method of characteristics

Tsui

Portella

Navia

et al. 2005

J. Phys. G: Nucl. Part. Phys.

Self Cite

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“…Instead of introducing mapping operators to the two terms on the right side of Eq. (A.3) to solve it formally in real space [26], we proceed to use the Mellin transform defined bỹ…”

Section: Appendix a Methods Of Characteristics For Nucleon Diffusion mentioning

confidence: 99%

Integral energy spectra of hadrons induced by one-single nucleon by the method of characteristics

Tsui¹,

Portella²,

Gomes³

et al. 2007

Braz. J. Phys.

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Hadron energy spectra induced by one-single nucleon are obtained solving diffusion equations by the method of characteristics. Our solutions are a generalization of earlier papers that allow us to calculate hadron fluxes including the energy dependence of the interaction lengths and inelasticities. A comparison with the integral hadron spectra of the so-called "halo events" detected by the Brazil-Japan Collaboration at Mt. Chacaltaya is made, in order to test our solutions. A reasonable agreement between then is obtained, considering the rising with energy of the nucleon inelasticity coefficient.

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“…Instead of solving Eq. (3) in real space [15,26], we use the integral transform approach. Before doing the η integral, we take the Mellin transform defined by…”

Section: Faltung Formulation Of Nucleon Diffusionmentioning

confidence: 99%

Faltung formulation of hadron halo event cascade at Mt. Chacaltaya

Tsui,

Portella,

Navia

et al. 2007

Preprint

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It is shown that the fundamental standard hadron cascade diffusion equation in the Mellin transform space is not rigorously correct because of the inconsistent double energy integral evaluation which generates the function < η s > with its associated parametizations. To ensure an exact basic working equation, the Faltung integral representation is introduced which has the elasticity distribution function u(η) as the only fundamental input function and < η s > is just the Mellin transform of u(η). This Faltung representation eliminates standard phenomenological parameters which serve only to mislead the physics of cascade. The exact flux transform equation is solved by the method of characteristics, and the hadron flux in real space is obtained by the inverse transform in terms of the simple and essential residues. Since the essential residues are given by the singularities in the elasticity distribution and particle production transforms that appear in the exponentials, these functions should not be parametized arbitrarily to avoid introducing non-physical essential residues. This Faltung formulation is applied to the charged hadron integrated energy spectra of halo events detected at Mt. Chacaltaya by the Brazil-Japan Collaboration, where the incoming flux at the atmospheric boundary is a single energetic nucleon.

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The nucleon-air nucleus interaction probability law with rising cross section

Cited by 7 publications

References 12 publications

Hadron cascade by the method of characteristics

Hadron cascade by the method of characteristics

Integral energy spectra of hadrons induced by one-single nucleon by the method of characteristics

Faltung formulation of hadron halo event cascade at Mt. Chacaltaya

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