L. G. Dedenko

The composition of the primary particles at energies 3 ×10 17 -3 ×10 19 eV observed at the Yakutsk array

Signals in the surface and underground scintillation detectors of the Yakutsk array from particles of extensive air showers and a fraction of muons at 600 m from the vertical shower axis have been simulated. Calculations have been carried out in terms of QGSJET-II and Gheisha-2002d models with the help of the CORSIKA 6.616 and GEANT4 codes at energies 3×1017–3×1019 eV. A comparison of the results of these simulations with data observed at the Yakutsk array shows rather heavy composition of the primary radiation in this energy region. But it was shown that the number of muons is underestimated by ~15% if the QGSJET-II model was used at energies above 100 GeV and by ~ 10% if the Gheisha-2002d model was used at energies below 100 GeV. Besides, signals in the surface and underground detectors from a muon differ by 3%. A comparison of the results with these corrections taken into account with data favors rather a light (maybe a proton-dominated) composition of the primary radiation in the energy region of 2.3×1018–1.14×1019 eV. In the energy interval of 3×1017–2.3×1018 eV, the composition is heavier. At energies above 1.14×1019 eV, a composition may also be heavier as illustrated by a trend of data.

Test of hadron interaction models in the most important energy range of secondary particles in spectra of atmospheric muons

A simple method has been proposed for testing hadron interaction models, which are used to simulate extensive air showers, in observed spectra of atmospheric muons. It has been shown that muon flux intensities in the energy range of 102–104 GeV that are calculated within the SIBYLL 2.1, QGSJETII-04, and QGSJET01 models exceed the data of the classical experiments L3 + Cosmic, MACRO, and LVD on the spectra of atmospheric muons by a factor of 1.5–2. It has been concluded that these tested models overestimate the generation of secondary particles with the highest energies in elementary events of interaction between hadrons in agreement with the LHCf and TOTEM accelerator experiments.

Employing Cherenkov radiation and fluorescence light in calibrating the energy of giant air showers

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.

Cosmic rays of ultrahigh energy

A new phenomenon—giant air showers of energy above 1020 eV,which lie beyond the Greisen-Zatsepin-Kuzmin cutoff—was discovered by various detection methods. The mechanism of particle acceleration to such high energies is still a puzzle. The arrival directions of giant showers do not contradict the hypothesis of their isotropic distribution. There are indications of their correlations with distant objects. It is obvious that only observations at new arrays can clarify the problem. The observed events must be reanalyzed within a more elaborate scheme. Verification of slight deviations from Lorentz invariance is possible.

Testing model energy spectra of charged particles produced in hadron interactions on the basis of atmospheric muons

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 103 and 104 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.

Investigation of the structure of a muon disk for E0 ≥ 5 × 1016 eV according to data of the Yakutsk array for studying extensive air showers

The results are presented that were obtained at the Yakutsk array by investigating the time structure of a muon disk in extensive air showers of primary energy in the region E0 ≥ 5 × 1016 eV at distances of 250 to 1500 m from the shower core. The measurements were performed with a large muon detector that has an area of 184 m2 and a detection threshold of Eµ≈0.5secθ GeV and which began operating in November 1995. Two components having different muon-disk thicknesses were discovered, and this requires strong modifications in the currently prevalent idea of the development of extensive air showers. The problem of the existence of E0 ≥ 1020 eV events is considered.

The new energy estimates of giant air showers

Abstract A new model of interpretation of data has been suggested. All responses of scintillation detector stations should be interpreted in terms of this model to estimate the energy of giant air shower correctly. It has been calculated that the main contribution to responses of scintillation detector stations at large distances that are important for observations of giant air showers was caused by photons. The ratio of signal in units of vertical equivalent muon to the charged particle density happens to be equal to 2.5 in electron-photon showers at distances above 500 m from the shower core. Calculations in terms of the quark-gluon model string for showers observed by the Yakutsk array showed 4 events with energies above 102 20 eV.

New estimates of extensive-air-shower energies on the basis of signals in scintillation detectors

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.

Testing of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 hadronic interaction models via help of the atmospheric vertical muon spectra

The recent results of the very precise measurements of the primary cosmic protons and helium nuclei energy spectra by AMS-02 and some rather accurate estimates of these energy spectra generated in SNR allow us to elaborate the new approximation of the pimary nucleon energy spectra. As the acuracy of this approximation is rather high we can use it to test various models of hadronic interactions with the help of atmospheric muon energy spectra. The atmospheric vertical muon energy spectra have been calcullated in terms of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models in the energy range 102 ÷ 105 GeV with help of the CORSIKA package and this new approximation of the primary nucleon spectrum. The comparison of calculations with the muon spectra observed by collaborations L3+Cosmic, LVD and MACRO has shown that all models predict approximately two times lower intensity of the muon energy spectra. As these muons are products of decays of the most energetic π ± and K ± mesons in the atmosphere, we can conclude that production of these π ± and K ± mesons is underestimated by EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models.

Signals in the underground scintillation detectors of the Yakutsk array from muons of extensive air showers

A model of the underground part of the Yakutsk array was developed. The signals from muon scintillation detectors were calculated using the GEANT4 code within this model. It was shown that the signals strongly fluctuate and may be several times higher that the mean ionization energy losses by a single muon. These large losses imitate high muon multiplicity in the case of a low muon density. It was also shown that there are many gamma particles near the shower axis, which significantly contribute to signals in underground detectors and thus make data interpretation difficult.