Semigroup theory and diffusion of hadrons in the atmosphere

Portella, H. M.; Gomes, A.; Amato, N. M.; Maldonado, R. H. C.

doi:10.1088/0305-4470/31/32/010

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…These results are in agreement with that of L. Jones [18] based in an analysis on inclusive reactions data from accelerator, with analytical calculations on nucleon fluxes at sea level [9] and with hadron and electromagnetic fluxes at mountain altitudes [8,10].…”

Section: Discussionsupporting

confidence: 90%

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Estimative of Inelasticity Coefficient From Emulsion Chamber Data

Portella

Oliveira

Lima

2004

Int. J. Mod. Phys. A

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Section: Discussionsupporting

confidence: 90%

“…We assume that only the pions are generated in the multiparticle production neglecting the particles with small fractions such as kaons, heavy mesons, etc.. In this case the solutions are [8];…”

Section: Hadronic and Electromagnetic Cascades In The Earth's Atmospherementioning

confidence: 99%

Estimative of Inelasticity Coefficient From Emulsion Chamber Data

Portella

Oliveira

Lima

2004

Int. J. Mod. Phys. A

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“…Our value of κ , in the energy range 10 GeV E 10 TeV, shows a very good agreement with the results obtained from the mini-jet model [18]. There is also good accordance with analytical calculations concerning nucleon fluxes at sea level [12] and integral hadronic and electromagnetic fluxes at mountain altitudes [13,19].…”

Section: Discussionsupporting

confidence: 87%

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

Portella¹,

Gomes²,

Lima³

2001

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

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The diffusion equation of cosmic-ray nucleons is exactly integrated using the successive approximation method for a general distribution of the primary component, and taking into account the rising nucleon-air cross sections with energy. The interaction probability law for the nucleon in the atmosphere is obtained as a consequence of the respective diffusion equation. If the nucleon-air cross sections rise logarithmically, this probability law assumes a binomial form, and for the constant cross section, it is purely Poissonian. The well known approximate solution is compared with our exact solution. It is found that the former always gives a nucleon number greater than ours by, for example, 15-25% in the energy region 30-10 000 GeV at sea level in the case of the mean inelasticity ⟨κ⟩ = 0.60. It is also shown that a fairly accurate description of nucleon flux at sea level (1030 g cm-2) and hadron intensities at 840 g cm-2 and at 1030 g cm-2 are obtained with ⟨κ⟩ varying between 0.55 and 0.60.

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“…We have used the expression λ N (E) = λ N ( E B ) −β with B = 1 TeV , λ N = 83 g/cm 2 and β = 0.056 which are obtained from accelerator and EAS data in the region 1 TeV ≤ E lab ≤ 1000 TeV [25]. For the pion mean-free path, we assume that λ π /λ N 1.4, and that it has the same energy dependence like the nucleon case [32]. In the present calculation we have only one free parameter, A(TeV ), which is the normalization factor of the energy in Mellin's transform.…”

Section: Numerical Resultsmentioning

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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Semigroup theory and diffusion of hadrons in the atmosphere

Cited by 10 publications

References 16 publications

Estimative of Inelasticity Coefficient From Emulsion Chamber Data

Estimative of Inelasticity Coefficient From Emulsion Chamber Data

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

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

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