The vertical sea-level muon spectrum at energies above 1 GeV and the muon intensities at depths up to 18 km w.e. in different rocks and in water are calculated. The results are particularly collated with a great body of the ground-level, underground, and underwater muon data. In the hadron-cascade calculations, we take into account the logarithmic growth with energy of inelastic cross sections and pion, kaon, and nucleon generation in pion-nucleus collisions. For evaluating the prompt muon contribution to the muon flux, we apply the two phenomenological approaches to the charm production problem: the recombination quark-parton model and the quark-gluon string model. We give simple fitting formulas describing our numerical results. To solve the muon transport equation at large depths of a homogeneous medium, we use a semianalytical method, which allows the inclusion of an arbitrary (decreasing) muon spectrum at the medium boundary and real energy dependence of muon energy losses. Our analysis shows that at the depths up to 6-7 km w.e., essentially all underground data on the muon flux correlate with each other and with the predicted one for conventional (π, K)-muons, to within 10 %. However, the high-energy sea-level muon data as well as the data at high depths are contradictory and cannot be quantitatively described by a single nuclear-cascade model.

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Theoretical results representing further development of scaling formalism for the lateral distribution of electrons in atmospheric cascade showers are reported in this paper. A detailed study of the root mean square radius of extensive air shower electrons—the basic parameter of the lateral distribution function (LDF)—has been carried out. Comparisons of our predictions with CORSIKA simulation results and also KASCADE and AGASA experimental data are presented. A new method for cosmic ray primary composition deduction from the shape of electron LDF, applicable in wide primary energy range with weak sensitivity to hadronic interaction model, is introduced.

The polarization of the final electron for the nonlinear Compton effect in a field of a circularly polarized electromagnetic wave is considered. The complete set of formulas necessary for simulation of the e → γ conversion at future photon colliders is given. We note the possibility to transform the longitudinal polarization of the initial electron into transverse polarization of the final electron.

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