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.

Hadron diffusion equations are solved using an alternative analytical method based on depth-like ordered exponential operators, similar to those used by Feynman. With this method, these equations are solvable for any form of the primary spectrum (an improvement compared with other methods). The muon fluxes generated by these hadronic showers are then obtained for zenith angles covering 0°–89°. A comparison of our calculations for the vertical and horizontal muon fluxes with experimental data and with another theoretical calculation is made. The agreement between them is in general very good, greater than 90%.

Atmospheric diffusion of high energy cosmic rays is studied analytically and the obtained integral electromagnetic fluxes are compared with the data measured by emulsion chamber detectors at mountain altitudes. We find a good consistency between them when the average nucleon inelasticity coefficient is varying between 0.50 and 0.65.

The main goal of this work is to pursue an investigation of cosmic string configurations focusing on possible consequences of the Lorentz-symmetry breaking by a background vector. We analyze the possibility of cosmic strings as a viable source for fermionic Cold Dark Matter particles. Whenever the latter are charged and have mass of the order of 10 13 GeV , we propose they could decay into usual cosmic rays.We have also contemplated the sector of neutral particles generated in our model. Indeed, being neutral, these particles are hard to be detected; however, by virtue of the Lorentz-symmetry breaking background vector, it is possible that they may present an electromagnetic interaction with a significant magnetic moment.

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