The extensive air shower muon number spectrum beyond the knee in the cosmic-ray energy spectrum

The extensive air shower (EAS) muon number spectrum is obtained with increased statistics using the central muon detector of the EAS MSU array, which records muons with energies above 10 GeV. The dependence of the mass composition of primary cosmic rays on the energy is considered. The conclusion is confirmed that for energies from 3 × 10¹⁵ eV (the primary energy spectrum knee) up to 10¹⁷ eV a change in the composition associated with an increase in the proportion of heavy nuclei occurs; however, after the energy of 10¹⁷ eV, the proportion of heavy nuclei begins to decrease and the composition becomes lighter. A comparison with similar data from other experiments is conducted. The existence of an additional component of cosmic rays is confirmed; earlier an indication of its presence was derived from data on the EAS electron number spectrum.     

Energy spectrum and mass composition of primary cosmic rays at energies 10<Superscript>15</Superscript>–10<Superscript>18</Superscript> eV

Data on muon and electron components of extensive air showers (EAS) (obtained with the EAS MSU array) were used to derive the primary cosmic ray (PCR) mass composition. It is shown that for energies beyond the knee at energy 3 × 10¹⁵ eV the abundance of heavy nuclei increases with energy. But at energies above 10¹⁷ eV the abundance of light nuclei starts to grow. The primary cosmic ray spectrum in the range 10¹⁵–10¹⁸ eV is analyzed. It is shown that at energies above 10¹⁷ eV the additional component appears and it differs from the bulk of Galactic cosmic rays generated by shocks in SN remnants.     

Radio signals from extensive air showers with the energies <Emphasis Type="Italic">E</Emphasis> <Subscript>0</Subscript> ≥ 10<Superscript>19</Superscript> eV according to data from the Yakutsk extensive air shower array

A radio instrument and results obtained from the measurements of the 32-MHz radio signal from particles of extensive air showers (EASs) with energies E₀ ≥ 1×10¹⁹ eV are reported in brief. The data were obtained at the Yakutsk EAS array in 1987–1989 (the first series of measurements) and in 2009–2014 (new series of measurements). The radio signal from EASs with energies above 10²⁰eV was detected at the Yakutsk EAS array for the first time, including the shower with the record energy of ~2×10²⁰ eV for the Yakutsk EAS array.     

Searching for preferential arrival directions of ultrahigh-energy cosmic rays on the Moscow State University EAS array

There is evidence for possible clustering in the arrival directions of extensive air showers (EASs). A program for analyzing EAS arrival directions has been developed to investigate this problem and the database of the Moscow State University EAS array for 1982–1989 has been analyzed. The distributions in equatorial coordinates have been derived for cosmic rays with energies E ≥ 2 × 10¹⁵ eV and zenith angles <40°. The uniformity of the derived distributions is verified using various statistical tests.     

Energy spectrum of primary cosmic rays at energies of 2 × 10<Superscript>13</Superscript> to 5 × 10<Superscript>17</Superscript> eV,according to Tien Shan data

The primary cosmic ray energy spectrum at energies of 10¹⁵ to 5 × 10¹⁷ eV is presented using the results from observations by the Tien Shan HADRON array. The spectrum was obtained from the spectrum of showers according to the number of electrons using a new way of determining the parameter of spatial distribution function S of electrons. The energy spectrum can be extended to low energies up to 2 × 10¹³ eV using data from separate experiments at the former Tien Shan array. Conclusions are drawn regarding changes in the form of the spectrum and its chemical composition at energies over 10¹⁶ eV. The spectrum is compared to the results from the TUNKA installation.     

Spatial distribution of EAS radio emission at 32 MHz

The results of the reprocessing of the experimental data on radio emission from extensive air showers (EAS) earlier obtained at the EAS facility (Moscow State University) are reported. The maximum depth distribution of showers is found from analysis of the width of the spatial distribution of radio emission. The average maximum depth is X _max = 655 ± 8 g/cm² for the primary particle energy E ₀ ～ (3–4) × 10¹⁷ eV. The normalized field strength at E ₀ = 10¹⁷ eV is 3.2 ± 0.6 and 2.8 ± 0.4 μV/(m MHz) at distances of 50 and 100 m from the axis, respectively. The accuracy of E ₀ determination from the radio emission field strength at 50 m from the axis is about 20%.     

Muons in extensive air showers of energies E 0=1016.6–1019.8 eV

Data on muons with the threshold energy E _μ≈1.0×secθ GeV in extensive air showers of energies E ₀≥4×10¹⁶ eV measured on the Yakutsk and Akeno arrays are jointly analyzed. The results are compared with the calculations by the quark-gluon-string model with jets. It is shown that this model does not contradict the data measured for energies E ₀≤10¹⁸ eV on both arrays under the assumption that the primary particle composition differs from the composition where heavy nuclei dominate over protons. Experimental data for energies E ₀≥3×10¹⁸ eV indicate that the shower development differs from that predicted by the quark-gluon-string model with jets.     

Radio emission of extensive air showers as a method for detecting ultra-high energy cosmic rays

Recording radio emission from extensive air showers (EASs) is considered now as a new promising method for detecting ultra-high energy (E ₀ > 5 × 10¹⁶ eV) cosmic rays. The results of calculation of EAS radio emission at frequencies from 40 to 80 MHz in the EAS energy range E ₀ = 10¹⁴–10¹⁷ eV are reported here, and the possibilities of determining EAS parameters from the radio emission lateral distribution are discussed.     

Estimate of the mass composition of cosmic rays above 4×10<Superscript>19</Superscript> eV

The arrival directions of extensive air showers are analyzed on the basis of world data. It is found that the zenith-angle distributions for energies E>10¹⁹ eV and E>4×10¹⁹ eV differ from each other. According to our estimates, the SUGAR array detects no showers above 10²⁰ eV. The mass composition of ultrahigh-energy cosmic rays is estimated. Cosmic rays with E>4×10¹⁹ eV most likely consist of superheavy nuclei.     

Electrons and muons in extensive air showers of energies E 0≥3×1017 eV: Yakutsk array data and QGSJET model

The results obtained from an analysis of the 1974–1998 Yakutsk array data on muons with threshold energy E _μ ≈ 1.0 × secθ GeV and on all charged particles (electrons and muons) in extensive air showers (EAS) are reported and compared with the results of calculations based on the model of quark-gluon strings with jets. For energies of E ₀≤3×10¹⁸ eV and zenith angles of θ≤45°, the results of the model calculations are consistent with the measured properties of the showers, while, for higher energy EASs, there are considerable discrepancies, which are probably due to the change in the development of the shower cascade in the region E ₀≥3×10¹⁸ eV.     

On EAS spectrum with extremely low content of hadrons in the primary-energy range ∼10<Superscript>14</Superscript>−10<Superscript>15</Superscript> eV

The distribution of energy fluxes of the hadron component of extensive air showers through an ion-ization calorimeter in the primary-energy range ～3 × 10¹³?10¹⁶ eV is considered. Extensive air showers with zero and minimum energy fluxes of the hadron component are selected. It is concluded that the primary-energy range E ₀ ≈ 1 × 10¹⁴?2 × 10¹⁵ eV contains isotropic γ radiation with a spectrum close to bell-shaped, having a maximum near E ₀ ≈ 2.2 × 10¹⁴ eV and an additional peak near E ₀ ≈ 1.6 × 10¹⁵ eV.     

Astrophysical and structural peculiarities of extensive air showers with energy E 0 ≥ 1017 eV from Yakutsk EAS array data

The astrophysical characteristics of primary cosmic rays (PCRs) and the structure of extensive air showers (EASs) with energy E ₀ ≥ 10¹⁷ eV are simultaneously analyzed using the Yakutsk EAS array data acquired in the period 1974–2005. Enhanced and reduced particle fluxes are shown to come from the disk of the Supergalaxy (the Local Supercluster of galaxies) at E ₀ ≥ 5 × 10¹⁸ eV and E ₀ ≤ (2?3) × 10¹⁸, respectively. The development of air showers with E ₀ ≥ (3?5) × 10¹⁸ eV differs significantly from that at lower energies. This is interpreted as a manifestation of the possible interaction between extragalactic PCRs and the matter of this spatial structure.     

Determining the primary cosmic ray energy from the total flux of Cherenkov light measured at the Yakutsk EAS array

We present a method for determining the energy of the primary particle that generates an extensive air shower (EAS) of comic rays based on measuring the total flux of Cherenkov light from the shower. Applying this method to Cherenkov light measurements at the Yakutsk EAS array has allowed us to construct the cosmic ray energy spectrum in the range 10¹⁵ ? 3 × 10¹⁹ eV.     

Mass composition of 1017- to 1018-eV primary cosmic rays according to data on the lateral distribution of radio emission from extensive air showers

Experimental data obtained for the lateral distribution of radio emission from extensive air showers (EAS) at the array of Moscow State University (30?C34 MHz) and the LOPES array (40?C80 MHz) were comparedwith the results of calculations performed within amicroscopic approach based on aMonte Carlo simulation of EAS (CORSIKA code). The same experimental data were used to reconstruct the distribution of the depth of the EAS maximum at cosmic-ray energies in the range of 1017?C1018 eV. The energy dependence of the depth of the EAS maximum was constructed for the case of data from the LOPES array, and the mass composition of cosmic rays was estimated for this case. From the resulting dependences, it follows that the mass composition shows a trend toward becoming lighter in the energy range being considered     

Electron impact ionization cross sections of beryllium and beryllium hydrides

We report calculated electron impact ionization cross sections (EICSs) for beryllium (Be) and some of its hydrides from the ionization threshold to 1 keV using the Deutsch-Märk (DM) and the Binary-Encounter-Bethe (BEB) formalisms. The positions of the maxima of the DM and BEB cross sections are very close in each case while the DM cross section values at the maxima are consistently higher. Our calculations for Be are in qualitative agreement with results from earlier calculations (convergent close-coupling, R matrix, distorted-wave and plane-wave Born approximation) in the low energy region. For the various beryllium hydrides, we know of no other available data. The maximum cross section values for the various compounds range from 4.0 × 10^?16 to 9.4 × 10^?16 cm² at energies of 44 to 56 eV for the DM cross sections and 3.0 × 10^?16 to 5.4 × 10^?16 cm² at energies of 40.5 to 60 eV for the BEB cross sections.     

Mass content of ultrahigh-energy cosmic rays within different time periods

Estimates obtained for the average atomic number 〈lnA〉 of nuclei of primary particles with energies in the region of E ₀ ? 10¹⁵ eV over the past 36 years at the Yakutsk array and other arrays worldwide for studying extensive air showers are presented. It is shown that these estimates are markedly different with in different time periods. Earlier than 1996, the composition of cosmic rays in the energy range of 5 × 10¹⁵–10¹⁸ eV was markedly lighter than in later years. After 2008, there appeared a trend toward a decrease in 〈lnA〉. This is likely to be a manifestation of some explosive process in the Milky Way Galaxy after 1996.     

Autoionization cross section of potassium atom excited by electron impact

The autoionization cross section of potassium atoms excited by electron impact is measured in the energy range from the first autoionization threshold at 18.72 eV to 202 eV. The data are obtained by deter-mining the total intensity of electron spectra resulting from the decay of the 3p ⁵ n ₁ l ₁ n ₂ l ₂ autoionizing states. The cross section has two maxima, 1.8 × 10^?16 and 2.2 × 10^?16 cm², at 21 and 32 eV, respectively. The excitation dynamics of autoionization states suggests that the first maximum is associated with the resonance character of the near-threshold excitation. The second maximum, as well as the behavior of the cross section at energies above 50 eV, reflects the dynamics of electron excitation of quartet and doublet autoionizing states. The measured autoionization cross section is compared with known data for the total single ionization cross section of potassium atom by electron impact. The relative contribution of the autoionization cross section to the total single ionization cross section is found to reach 30% at 32 eV.     

Estimation of the energy of the electron-photon component of cosmic rays on the basis of data for Cherenkov light from ultrahigh-energy extensive air showers

The energy fraction E _em/E ₀ dissipated to the electron-photon component of extensive air showers (EASs) for E ₀=10¹⁵?10¹⁹ eV is estimated using data on Cherenkov radiation and charged particles from the Yakutsk EAS array. The results are compared with models with different dissipations to the electron-photon component and with calculations for various primary nuclei. In the energy range 10¹⁵?10¹⁶ eV and 10¹⁸?10¹⁹ eV, the ratio E _em/E ₀ is equal to 77 ± 2 and 88 ± 2, respectively, in agreement with the mixed and proton contents of primary cosmic rays in the former and latter energy ranges, respectively.     

On the possibility of investigation of the mass composition and energy spectra of primary cosmic ray (PCR) in the energy range from 1015 to 1017 eV using EAS data

Summary A method allowing one to determine the mass composition of primary cosmic radiation by means of simultaneous analysis of model and experimental data is presented in this paper. The most important part of this work is the quantitative comparison of multivariate distributions and the use of methods of nonparametric statistics for probability density estimation in a multivariate space of features. To check the method offered, events withE ₀>500TeV were generated by the Monte Carlo method. The showers generated were preliminarily processed by algorithms used in experimental data handling. The apparatus-induced distortions of the measured EAS characteristics have been taken into account. The method allows one to select an experimental event initiated by primary protons and iron nuclei with an efficiency of (70÷80)%. Also a new multivariate method of incident particle energy estimation based on the nonparametric regression is described. The method proposed, together with the above-mentioned multivariate EAS classification, allows one to determine the energy spectrum of incident protons and nuclei. Detection and investigation of the products of interaction of these particles with the atmosphere will allow us to study proton-nuclei and nuclei-nuclei interactions at energies from 10¹⁵ to 10¹⁷ eV.