[en] Signals in the surface and underground scintillation detectors from the extensive air shower particles at the Yakutsk array are measured in some practical units. These units are signals in detectors caused by the near vertical muons. These signals from the near vertical muons in the surface and underground detectors have been simulated with the help of the GEANT4 package. These simulations follow up the real experimental calibration of the surface and underground detectors carried out at the Yakutsk array. Results of simulations show the noticeable difference of ∼5% in energies deposited in these two types of detectors. This difference should be taken into account to interpret correctly data on the fraction of muons observed at the Yakutsk array and to make real conclusions about the composition of the primary cosmic radiation at ultra-high energies.

[en] An original method for calculating the spectrum of atmospheric muons with the aid of the CORSIKA 7.4 code package and numerical integration is proposed. The first step consists in calculating the energy distribution of muons for various fixed energies of primary-cosmic-ray particles and within several chosen hadron-interaction models included in the CORSIKA 7.4 code package. After that, the spectrum of atmospheric muons is calculated via integrating the resulting distribution densities with the chosen spectrum of primary-cosmic-ray particles. The atmospheric-muon fluxes that were calculated on the basis of the SIBYLL 2.1, QGSJET01, and QGSJET II-04 models exceed the predictions of the wellknown Gaisser approximation of this spectrum by a factor of 1.5 to 1.8 in the range of muon energies between about 10"3 and 10"4 GeV.Under the assumption that, in the region of extremely highmuon energies, a dominant contribution to the muon flux comes from one to two generations of charged π"± and K"± mesons, the production rate calculated for these mesons is overestimated by a factor of 1.3 to 1.5. This conclusion is confirmed by the results of the LHCf and TOTEM experiments

[en] New formulas for estimating the energy of inclined extensive air showers (EASs) on the basis of signals in detectors by means of an original method and detailed tables of signals induced in scintillation detectors by photons, electrons, positrons, and muons and calculated with the aid of the GEANT4 code package were proposed in terms of the QGSJETII-04, EPOS LHC, and GHEISHA models. The parameters appearing in the proposed formulas were calculated by employing the CORSIKA code package. It is shown that, for showers of zenith angles in the range of 20◦–45◦, the standard constant-intensity-cut method, which is used to interpret data from the Yakutsk EAS array, overestimates the shower energy by a factor of 1.2 to 1.5. It is proposed to employ the calculated VEM (Vertical Equivalent Muon) signal units of 10.8 and 11.4 MeV for, respectively, ground-based and underground scintillation detectors and to take into account the dependence of signals on the azimuthal angle of the detector position and fluctuations in the development of showers.

[en] A classic procedure for estimating the energy of giant air showers in terms of the parameter s(600) (density of energy deposition in a scintillator at a distance of 600 m from the shower axis) is analyzed on the basis of the model of quark-gluon strings. A simulation of the signal s(600) by means of the CORSIKA code leads to estimates of energy that are approximately 1.6 times lower than those adopted at the Yakutsk array. Estimates of energy on the basis of Cherenkov radiation agree with experimental data within the errors. Calculations of the distributions of energy deposited in the atmosphere indicate that more than 20% of this energy can be deposited at distances in excess of 100 m from the shower axis

[en] Fluctuations of lateral distributions of signals in the surface scintillation detectors of the Yakutsk array are found to be large. New estimates of the inclined shower energy had been suggested. In view of these estimates the Yakutsk energy spectrum becomes quite comparable with the spectra observed at the Pierre Auger Observatory and the Telescope Array. The shower energy calculated using the data of only one detector may be overestimated if fluctuations are neglected.

[en] The more accurate original calculations of the atmospheric vertical muon energy spectra at energies 10² - 10⁵ GeV have been carried out in terms of DPMJET and VENUS models. The Gaisser-Honda approximations of the measured energy spectra of primary protons, helium and nitrogen nuclei have been used. The package CORSIKA has been used to simulate cascades in the standard atmosphere induced by different primary particles with various fixed energies E . Statistics of simulated cascades for secondary particles with energies (0.01−1)· E was increased up to 10⁶. It has been shown that predictions of the DPMJET and VENUS models for these muon fluxes are below the data of the classical experiments L3 + Cosmic, MACRO and LVD by factors of ∼ 1.6-1.95 at energies above 10² GeV. It has been concluded that these tested models underestimate the production of the most energetic secondary particles, namely, π-mesons and K -mesons, in interactions of the primary protons and other primary nuclei with nuclei in the atmosphere by the same factors. (paper)

[en] The composition of the primary cosmic radiation should be studied by various alternative approaches. A promising way is to exploit a dependence of the fraction of muons in an extensive air shower on the atomic number of the primary nuclei. A comparison of the fraction of muons at 600 m from the shower axis observed at the Yakutsk array in the vertical air showers at ultra-high energies with results of simulations in terms of QGSJET-II and Gheisha-2002d models carried out with the help of the CORSIKA 6.616 and GEANT4 codes showed rather heavy composition of the primary radiation. But some errors in these models should be taken into account. At last, one has to allow for the fact that signals in the surface and underground scintillation detectors of the Yakutsk array from various particles of extensive air showers are measured in different units. All these corrections taken together show the proton composition of the primary radiation in the energy region of ∼2.·10¹⁸ – 10¹⁹ eV. At lower energies a composition is heavier. The change from the heavy composition to the primary protons occurs in the energy interval of 9.·10¹⁷ – 2.·10¹⁸ eV. It is not excluded that at energies above 1.1·10¹⁹ eV the composition may be also heavier as illustrated by a trend of data.

[en] The muon lateral structure functions in giant air showers induced by primary photons have been simulated with the help of original codes. Particularly, the densities of muons with energies above 0.5 and 1 GeV at a distance of 1000 m from the shower core have been estimated for gamma-induced showers of various energies. A comparison with the results of calculations for hadronic showers shows a considerable deficit of muons in the gamma-induced showers. The density of muons at a distance of 1000 m from the shower core happened to be ≥ 10 times larger for the hadronic showers. Some possible constraints of the source models with superheavy-dark-matter particles and topological defects are discussed

[en] A viable description of experimental data on cosmic rays in the energy range 10¹⁸-10¹⁹ eV is obtained on the basis of the quark-gluon-string model. The Landau-Pomeranchuk-Migdal effect and interactions of neutral pions are taken into account in this description. Data on the fraction of muons in inclined and vertical showers, as well as on the longitudinal development of showers, are adequately reproduced by calculations performed under the assumption that primary cosmic radiation consists of protons. For the energies of three huge showers reported in the literature, previous estimates in the range (3-5)x10¹⁹ eV are confirmed. The slope parameter b_μ of the spatial distribution of muons is found to be dependent on the distance from the shower core. Novel minimax approaches to interpreting experimental data and, in particular, to verifying the anomalous energy dependence of b_μ are advocated

[en] Uncertainties of the model energy spectra of the most energetic secondary charged mesons are discussed. Computer simulations of the partial energy spectra of the atmospheric vertical muons induced by primary cosmic particles with various fixed energies in terms of hadronic interactions models had been carried out with the help of the CORSIKA package. These partial spectra have been convolved with the contemporary spectra of the primary cosmic particles in the energy range 0.1-10 000 TeV. Results of simulations are compared with the contemporary data of the atmospheric vertical muon flux. Comparison shows that all models underestimate the production of secondary charged π^±-mesons (and K^±-mesons) by a factor of ~ 1.4 ÷ 2 at the highest energies. This underestimation induces a more rapid development of extensive air showers in the atmosphere and results in uncertainties in estimates of energy and composition of the primary cosmic particles.