Meson cascade in the atmosphere,uncertainties in calculating the fluxes of high-energy muons,and data of direct measurements

A new calculation of the atmospheric fluxes of cosmic-ray hadrons and muons in the energy range 10–10⁴ GeV is performed on the basis of the method for solving nuclear-cascade equations with allowance for a nonscaling behavior of inclusive hadron-production cross sections, the growth of cross sections for inelastic hadron-nucleus collisions with increasing energy, and a non-power-law character of the primary spectrum. The fluxes of secondary cosmic rays at various levels in the atmosphere are calculated for three models of the spectrum and composition of primary cosmic rays. The effect of uncertainties in the spectrumand composition of primary cosmic rays on the flux of atmosphericmuons and their charge ratio at sea level is investigated. The calculated energy spectra of muons at sea level are compared with the results of previous experiments and the results of recent measurements performed by means of the L3 + Cosmic and CosmoALEPH spectrometers, as well as with the results of other calculations.     

High-energy cosmic ray muons in the Earth’s atmosphere

We present the calculations of the atmospheric muon fluxes at energies 10–10⁷ GeV based on a numerical-analytical method for solving the hadron-nucleus cascade equations. It allows the non-power-law behavior of the primary cosmic ray (PCR) spectrum, the violation of Feynman scaling, and the growth of the total inelastic cross sections for hadron-nucleus collisions with increasing energy to be taken into account. The calculations have been performed for a wide class of hadron-nucleus interaction models using directly the PCR measurements made in the ATIC-2 and GAMMA experiments and the parameterizations of the primary spectrum based on a set of experiments. We study the dependence of atmospheric muon flux characteristics on the hadronic interaction model and the influence of uncertainties in the PCR spectrum and composition on the muon flux at sea level. Comparison of the calculated muon energy spectra at sea level with the data from a large number of experiments shows that the cross sections for hadron-nucleus interactions introduce the greatest uncertainty in the energy region that does not include the knee in the primary spectrum.     

Temperature effect of the integral flux of cosmic-ray muons at high energies

The temperature coefficients of the integral fluxes of cosmic-ray muons arriving at sea level vertically and horizontally with energies of 10², 10⁴, and 3 × 10⁶ GeV are calculated. Decays of pions, kaons, and charmed particles are considered as sources of muon generation in the atmosphere (according to current data on the generation cross sections of pions, kaons, and charmed particles in interactions between nucleons and the nuclei of atmospheric atoms, obtained in experiments on accelerators and in quantum chromodynamics models). The uncertainties in the generation cross sections of charmed particles are quite high.     

Interaction of high energy muons in association with EAS,with rock and lead

An investigation on the interaction of high energy muons, associated with EAS and having energies greater than several hundred GeV, has been carried out at Kolar Gold Fields. A visual detector consisting of neon flash tube hodoscope has been used together with a scintillator detector to observe the muons and accompanying showers at the underground level. It has been found that nearly 90% of the showers observed at the underground level are generated in course of pure electromagnetic interactions of the muons with the matter traversed by them. The observed number of the showers is found to be consistent with the expected number calculated using the cross-sections for knock-on, bremsstrahlung and direct pair production processes. Rest of the observed showers do not appear to fit in the pure electromagnetic interaction scheme. Various possible production processes for these events have been discussed. Considering these events to be due to photonuclear interaction of muons in the rock, the observed number leads to a production cross-sectionσ _μ (?25 GeV) ?(1.6±0.75)10^?29 cm²/nucl.     

Fluxes of cosmic-ray muons and atmospheric neutrinos at high energies

The problem of charm generation in the interactions of nucleons with nuclei of air atoms at energies inaccessible at present-day accelerators is discussed. Both experimental data on cosmic-ray muons and the predictions of QCD-based theoretical models are used in analyzing the behavior of the differential cross sections for charmed-particle production at high energies. The calculated fluxes of muons and neutrinos arriving at sea level both along the vertical and along the horizontal direction are presented, together with their approximations for the interval 2×10²–10¹⁰ GeV.     

Derivation of muon spectrum at high energies from the recent JACEE primary cosmic-ray spectrum using Fermilab data on meson production

Summary The energy spectrum of sea level muons in the range (10²÷10⁴) GeV has been calculated from the latest directly measured JACEE primary spectrum using Fermilab results on pp→π^± X and pp→K^± X inclusive reactions. The conventional pion atmospheric diffusion equation after Bugaevet al. has been used in this analysis to account the flux of muons emerged from the multiple generation of mesons in air. The derived muon spectrum has been compared with the earlier magnetic spectrograph data of Durham and Kiel groups. The latest BAKSAN scintillator telescope data is well in agreement with the calculated integral spectrum originated from the meson decays in the range (1÷10⁴) GeV.     

Cosmic ray muons at a depth of 754 hg/cm2 in the Kolar gold Mines

A telescope of area 4 m², consisting of horizontal layers of plastic scintillators, neon flash tubes and absorbers was operated at a depth of 754 hg/cm² in the Kolar Gold Mines. New values for the vertical intensities of muons have been obtained from observations of the angular distribution over the slant depths ∼ 750–2300 hg/cm² and are compared with the existing measurements. From the angular distribution observed, we conclude that muons are produced wholly through the decay of pions and kaons up to energies of the order of 1 TeV. A value of 0.3±0.2 is estimated for theK/π ratio at production, for muon energies around 500 GeV. A decoherence distribution has been obtained for parallel muon events up to distances of the order of 10 m. From this we conclude that the averageP _t of the parents of muons of energy ∼ 250 GeV is of the order of 0.3 GeV/c. From an analysis of rock showers, we obtain the cross section for inelastic interaction of muons of mean energy 100 GeV as (3.8±1.5)×10⁻³⁰ cm²/nucleon.     

Nuclear spin conversion in diatomic molecules

A mechanism of the internal interaction in dimers that mixes different nuclear spin modifications has been proposed. It has been shown that the intramolecular current associated with transitions between electronic terms of different parities can generate different magnetic fields on nuclei, leading to transitions between spin modifications and to the corresponding changes in rotational states. In the framework of the known quantum relaxation process, this interaction initiates irreversible conversion of nuclear spin modifications. The estimated conversion rate for nitrogen at atmospheric pressure is quite high (10^?3–10^?5 s^?1).     

Far infrared spectral lines and absorptance calculation of NO

The positions and intensities of pure rotation lines of ¹⁴N¹⁶O have been calculated between 10–200 cm^-1 and are tabulated. The line by line absorption spectrum has been computed using tabulated parameters, and compared with experimental spectra measured by other authors. The spectral emission of atmospheric NO has been calculated for an altitude of 14.5 km, where some measurements have been carried out. After comparing the NO and the background H₂O+O₂+O₃ spectra, it is shown that the NO emission in the far i.r. spectrum of the lower stratosphere is negligible.     

A search for heavy leptons in cosmic radiation underground

An experiment to search massive long-lived, weakly interacting particles (leptons) in cosmic radiation has been conducted at Kolar Gold Fields at a depth of 7.6 hg cm⁻² (1 hg cm⁻²=100 g cm⁻²) below surface. The apparatus was senstive to sub-relativistic (velocity<0.75 c) charged leptons of mass greater than that of a proton and life times greater than a microsecond. The method consists of selecting charged particles using a scintillator counter telescope and vetoing relativistic particles (velocity >0.75 c) by using a water Čerenkov detector. The range of the particle is observed in arrays of neon flash tubes interspersed with iron absorbers. During 3000 hours of observation 28 events were recorded satisfying the trigger and event selection criteria. Bulk of these events were interpreted as due to recoil protons (low energy) from the inelastic scattering of high energy muons in the overhead absorber. The remaining events were interpreted as either atmospheric stopping protons or stopping muons that failed to generate a Čerenkov signal. The observed events are thus consistent with the background and no heavy leptons were seen. From our observations an upper limit of 2.12×10⁻⁷ (with 90% confidence level) is set on the ratio of the flux of heavy leptons to that of all muons at this depth.     

Study of condensed nitrogen by μSR method

The temperature dependences of parameters of the muon spin relaxation in liquid and crystalline nitrogen have been studied. It has been established that in condensed nitrogen there takes place a fast depolarization of muons. An anomalous behaviour of the amplitude and phase of muon precession is found in the vicinity of the orientation phase transition in solid nitrogen. It has been shown that muon spin relaxation parameters in nitrogen do not change at reduction of the oxygen impurity content from 0.7·10⁻⁴ to 10⁻⁶. The fast depolarization of muons in condensed nitrogen is apparently due to the formation of muonium atoms. To explain the phenomena observed, a model of the muonium chemical reaction is proposed. The initial phase of the muon precession has been measured as a function of the perpendicular magnetic field to determine the state of short-lived muonium in nitrogen. It has been determined that muonium in nitrogen is in an excited state. Consideration of the nuclear hyperfine interaction of muonium in condensed nitrogen makes it possible to give a qualitative explanation for the temperature dependence of the initial amplitude of the muon precession.     

Solar diurnal anisotropy measured using muons in GRAPES-3 experiment in 2006

The GRAPES-3 experiment at Ooty contains a large-area (560 m²) tracking muon detector. This detector consists of 16 modules, each 35 m² in area, that are grouped into four supermodules of 140 m² each. The threshold energy of muons is sec(θ) GeV along a direction with zenith angle θ and the angular resolution of the muon detector is 6°. Typically, it records ~4×10⁹ muons every day. The muon detector has been operating uninterruptedly since 2001, thus providing a high statistics record of the cosmic ray flux as a function of time over one decade. However, prior to using these data, the muon rate has to be corrected for two important atmospheric effects, namely, variations in atmospheric pressure and temperature. Because of the near equatorial location of Ooty (11.4°N), the seasonal variations in the atmospheric temperature are relatively small and shall be ignored here. Due to proximity to the equator, the pressure changes at Ooty display a dominant 12 h periodic behaviour in addition to other seasonal changes. Here, we discuss various aspects of a novel method for accurate pressure measurement and subsequent corrections applied to the GRAPES-3 muon data to correct these pressure-induced variations. The pressure-corrected muon data are used to measure the profile of the solar diurnal anisotropy during 2006. The data, when divided into four segments, display significant variation both in the amplitude (~45%) and phase (~42 m) of the solar diurnal anisotropy during 2006, which was a period of relatively low solar activity.     

Mass Composition of Cosmic Rays with Energies above 1017 eV According to the Data from the Muon Detectors of the Yakutsk EAS Array

The lateral distribution of muons in extensive air showers with energies above 1017 eV detected by underground scintillation detectors with a threshold of 1.0 GeV at the Yakutsk array in 1986–2016 has been analyzed. The experimental data on the muon flux density at a distance of 300 m from the shower axis have been compared to the calculations within various models of hadron interactions at ultrahigh energies. The experimental data are in the best agreement with the QGSJet01 and QGSJet II-04 models. The mass composition of cosmic rays in the energy range of (1–30) × 10¹⁷ eV changes from middle nuclei to a purely proton composition.

     

Study of the charge asymmetry in electromagnetic interactions of cosmic ray muons

The Durgapur cosmic ray spectrograph has been utilised to study the electromagnetic interaction of cosmic ray muons in iron in the momentum range 5–100 GeV/c. The dependence of the interaction cross section on the charge of the muons for the production of a single electron secondary due to the knock-on process and for two and more two electrons due to both knock-on and pair production has been investigated.The ratio of the interaction cross section for positive muons to that for negative muons in the magnetic-iron has been found to be 0.952 ± 0.045 for the production of one secondary particle. For production of two and more than two secondaries the ratios are 1.05 ± 0.09 and 0.91 ± 0.08 respectively. The present results do not indicate any charge asymmetry of cosmic ray muons in respect of electromagnetic interactions in iron.     

Variable composition of cosmic rays with E 0 ≥ 1017 eV according to the data from the muon detectors of the Yakutsk EAS array

The lateral distribution of muons with the threshold E _μ ≈ 1.0 secθ GeV (where θ is the zenith angle) in extensive air showers (EASs) with the energy E ₀ ≈ 10^17–19 eV in various observation periods from November 1987 to June 2013 has been analyzed. The experimental data have been compared to the calculations within various models of the development of EASs from the CORSIKA package. The experimental data are in the best agreement with the QGSJET II-04 model. The mass composition of cosmic rays with E ₀ < 2 × 10¹⁸ eV before 1996 was much lighter than that in a later time interval.     

Theory of muon spin depolarization in crystalline phases of 3He

As is obvious from the energetic point of view, positive muons must form the molecular ion ( He_2μ)⁺ in condensed phases of helium. A theory of positive muon spin depolarization in crystalline phase of ³He in this model is devised. The theory explains experimental results. It is shown that the abrupt temperature dependence of the muon spin depolarization rate at T < 2 K which is observed in experiments is explained by spin–phonon interaction. This interaction mechanism arises due to a modulation of the exchange interaction between host atoms of the ³He‐lattice. This revised version was published online in August 2006 with corrections to the Cover Date.     

A discrepancy between measured and calculated cosmic-ray spectra in the atmosphere

The flux of nucleons, pions, and muons in the energy range 1–1000 GeV and in atmospheric altitudes of 0–48 km has been calculated to a high degree of accuracy and without gross simplifications. Thus a discrepancy indicated already in 1964 byBrooke, Hayman, Kamiya andWolfendale has been firmly established. The discrepancy means, that it has proved impossible to derive the measured nucleon and muon spectra near sea-level from the measured primary nucleon spectrum unless the primary spectrum is reduced by a factor of about 2.5 or the high-energy collision models commonly used are changed. The latter would mean that the fraction of energy lost by the nucleon in a collision is passed over to the muon component to a minor extent than so far accepted, and this may be achieved in two ways: either the ratio of collision energy passed on to the electron-photon component to the energy passed on to the pion-muon component is increased in favour of the former, or about 10–20% of the collision energy are passed on to unspecified particles which do not contribute appreciably to the hard and weak components of cosmic rays. — The possibility is discussed that the missing fraction of 10–20% is spent in production of baryonantibaryon pairs.     

Experimental study of hadronic interaction models using coincident data from EAS-TOP and MACRO

The contemporaneous measurement of TeV muons in deep underground laboratories and of the e.m. component at the surface allows checking the hadron interaction models and the propagation codes used in EAS experiments in a primary energy range 10–50 TeV in which the primary spectra are measured by direct experiments. First results of such measurements between MACRO and EAS-TOP at the Gran Sasso laboratory, in this energy range, are here reported.     

Optical investigations of the metal-insulator transition in a low-dimensional organic conductor (EDT-TTF)4[Hg3I8]

The polarized reflectance spectra of single crystals of the low-dimensional organic conductor (EDT-TTF)₄[Hg₃I₈] undergoing a metal-insulator phase transition at a temperature T < 35 K have been presented. The spectral region of the study is 700–6000 cm^?1 (0.087–0.74 eV), and the temperature range is 300–9 K. It has been shown that the reflectance spectra are determined by a system of quasi-free electrons of the upper half-occupied molecular π-orbitals, which form a half-filled metallic band in the crystals. A high anisotropy of the spectra and their temperature dependences have been found. For two polarizations, the quantitative analysis of the spectra at 100 and 25 K has been performed in the framework of the phenomenological Drude model, the effective mass and the width of the initial metallic π-electron band have been deter-mined, and it has been found that the conducting system in the crystals has a quasi-one-dimensional character. As temperature decreases, the spectra demonstrate substantial changes indicating the formation of the energy gap (or pseudogap) in the spectrum of electronic states in the range of ～1500–2500 cm^?1. In the low-frequency region (700–1600 cm^?1), a vibrational structure has been observed, and the most intense feature of the structure (ω = 1340 cm^?1) is caused by the interaction of electrons with intramolecular vibrations of the C=C bonds of the EDT-TTF molecule. For temperatures of 15 and 9 K, the analysis of the spectra has been performed in the framework of the theoretical “phase phonon” model taking into account the interaction of electrons with the intramolecular vibrations. It has been concluded that the metal-insulator transition observed in the reflectance spectra of the crystals is similar to the Peierls dielectric transition that occurs in a system of electrons coupled with the intramolecular vibrations of the molecules forming the crystal.     

Determination of the atmospheric neutrino spectra with the Fréjus detector

The combined analysis of the final event set of data on neutrino interactions inside the detector, upward going stopping muons and horizontal muons recorded in the Fréjus experiment is presented. The absolute atmospheric neutrino spectra in the energy range for electron neutrinos and for muon neutrinos are determined. Based on the parameterization of Volkova for thev ^µ a spectral index of =2.66±0.05 is obtained from the ratio of horizontal muons over upward going stopping muons and from the measurement of the energy loss of horizontal muons inside the detector. The neutrino spectra are compared with various flux calculations. They do not show any evidence for neutrino oscillations in agreement with earlier analyses of the Fréjus data.Now atUniversity of Michigan, Ann Arbor, USA