Sea Level Muon Research Articles

Terrestrial Effects of Nearby Supernovae: Updated Modeling

We have reevaluated recent studies of the effects on Earth by cosmic rays (CRs) from nearby supernovae (SNe) at 100 and 50 pc, in the diffusive transport CR case, here including an early-time suppression at lower CR energies neglected in the previous works. Inclusion of this suppression leads to lower overall CR fluxes at early times, lower atmospheric ionization, smaller resulting ozone depletion, and lower sea-level muon radiation doses. Differences in the atmospheric impacts are most pronounced for the 100 pc case with less significant differences in the 50 pc case. We find a greater discrepancy in the modeled sea-level muon radiation dose, with significantly smaller dose values in the 50 pc case; our results indicate it is unlikely that muon radiation is a significant threat to the biosphere for SNe beyond 20 pc, for the diffusive transport case. We have also performed new modeling of the effects of SN CRs at 20 and 10 pc. Overall, our results indicate that, considering only the effects of CRs, the “lethal” SN distance should be closer to 20 pc rather than the typically quoted 8–10 pc. Recent work on extended SN X-ray emission indicates significant effects out to 50 pc and therefore the case is now strong for increasing the standard SN lethal distance to at least 20 pc. This has implications for studies of the history of life on Earth as well as considerations of habitability in the Galaxy.

A Comparison of Muon Flux Models at Sea Level for Muon Imaging and Low Background Experiments

Cosmic-ray muons are a type of natural radiation with high energy and a strong penetration ability. The flux distribution of such particles at sea level is a key problem in many areas, especially in the field of muon imaging and low background experiments. This paper summarizes the existing models to describe sea-level muon flux distributions. According to different means used, four parametric analytical models and one Monte Carlo model, which is referred to as CRY, are selected as typical sea-level muon flux distribution models. Then, the theoretical values of sea-level muon fluxes given by these models are compared with the experimental sea-level muon differential flux data with kinetic energy values in the range of 1–1,000 GeV in the directions of zenith angles 0° and 75°. The goodness of fit of these models to the experimental data was quantitatively calculated by Pearson’s chi-square test. The results of the comparison show that the commonly used Gaisser model overestimates the muon flux in the low-energy region, while the muon flux given by the Monte Carlo model CRY at the large zenith angle of 75° is significantly lower than that of the experimental data. The muon flux distribution given by the other three parametric analytical models is consistent with the experimental data. The results indicate that the original Gaisser model is invalid in the low energy range, and CRY apparently deviates at large zenith angles. These two models can be substituted with the muon flux models given by Gaisser/Tang, Bugaev/Reyna, and Smith and Duller/Chatzidakis according to actual experimental conditions.

Comment on “‘Seed’ electrons from muon decay for runaway mechanism in the terrestrial gamma ray flash production,” by Gerson S. Paiva, Antonio C. Pavão, and Cristiano C. Bastos

Comment on “‘Seed’ electrons from muon decay for runaway mechanism in the terrestrial gamma ray flash production,” by Gerson S. Paiva, Antonio C. Pavão, and Cristiano C. Bastos

On inconsistency of experimental data on primary nuclei spectra with sea level muon intensity measurements

For the first time a complete set of the most recent direct data on primary cosmic ray spectra is used as input into calculations of muon flux at sea level in a wide energy range Eμ = 1 − (3 × 105) GeV. Computations have been performed with the CORSIKA/QGSJET and CORSIKA/VENUS codes. Comparison of the obtained muon intensity with the data of muon experiments shows that measurements of primary nuclei spectra conform to sea level muon data only up to several tens of GeV and result in essential deficit of muons at higher energies. As it follows from our examination, uncertainties in muon flux measurements and in the description of nuclear cascades development are not suitable to explain this contradiction, and the only remaining factor, leading to this situation, is underestimation of primary light nuclei fluxes. We have considered systematic effects, that may distort the results of the primary cosmic-ray measurements with the application of the emulsion chambers. We suggest, that re-examination of these measurements is required with the employment of different hadronic interaction models. Also, in our point of view, it is necessary to perform estimates of the possible influence of the fact that a sizable fraction of events, identified as protons, actually are antiprotons. Study of this cosmic-ray component begins to draw much attention, but today nothing definite is known for the energies >40 GeV. In any case, to realize whether the mentioned, or some other reasons are the sources of disagreement of the data on primaries with the data on muons, the indicated effects should be thoroughly analysed.

Estimation of Sea Level Muon Energy Spectrum at High Latitude from the Latest Primary Nucleon Spectra Near the Top of the Atmosphere

The vertical muon energy spectra at sea level have been estimated from directly measured primary cosmic-ray nucleon spectrum. The hadronic energy moments have been calculated from the CERN LEBC EHS data on the Lorentz invariant cross-section results on pp → π±X and pp → K±X inclusive reactions and are duly corrected for A–A collisions. Finally, the sea level muon energy spectra have been calculated from the decay of conventional mesons, using standard formulation. The estimated muon spectra are found to be in good agreement with the directly measured muon spectra obtained from the different experiments.

Estimation of the Sea Level Muon Spectra at Different Zenith Angles below 10 TeV Energy

The moderate energy primary cosmic ray nucleon spectrum has been calculated from the direct measurements of Webber et al., Seo et al., and Menn et al. along with the other results surveyed by Swordy. Using these directly measured primary mass composition results all particle primary nucleon energy spectrum has been constructed using superposition model to estimate the energy spectra of muons from the decay of the cosmic ray non-prompt and prompt mesons in the atmosphere. The Z-factors have been estimated from the CERN LEBC-EHS on the Lorentz invariant cross section results on pp → π±X and pp → K±X inclusive reactions and FNAL data on π±p → π ±X reactions, and duly corrected for A--A collisions. Using these Z-factors the meson energy spectra in the atmosphere have been calculated. The sea level muon energy spectra at zenith angles 0°, 45°, 72°, and 75° have been derived from the decay of non-prompt mesons by adopting standard diffusion equation of hadronic cascades. The contribution of charmed mesons to muon spectrum has also been accounted by adapting the conventional procedure. The derived differential sea level muon energy spectra for energies ≤10 TeV have been found to follow the power law fits of the form N μ(E)≈ const. E -γ. Our estimated muon energy spectra at zenith angles ≤75° have been found comparable with the global spectrograph muon flux results of MARS, DEIS, and MSU groups.

Sea level muon spectra at large zenith angles derived from the latest JACEE primary nucleon spectrum

Sea level muon energy spectra at large zenith angles have been derived from the latest JACEE primary spectrum using the Fermilab Single-Arm Spectrometer data on charged-meson production. The role of increasing total cross-section on the final result for the energy spectra has been investigated here with special emphasis. The inclusion of the rising total cross-section at cosmic range of energies, it is seen, has come into much use in explaining the observed data at very high energies.

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

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.

Derivation of muon range spectrum at different polar angles in deep underground from primary nucleon spectrum

The energy spectra of sea-level muons at different zenith angles have been estimated from the latest JACEE primary spectrum using ISR results modified for p-nucleus interactions. The theoretical results have been compared with the experimental results. Using the recent modified range-energy relation after Kobayakawa along with the fluctuation correction procedure after Kiraly, Kiraly and Osborne, the muon range spectra in deep underground at different polar angles have been calculated. The derived results are well in agreement with the latest Mont Blanc data after Bergamascoet al., Battistoniet al. and Utah experiments after Bergessonet al.

Sea Level Muon Spectrum Derived from the All Particle Primary Spectrum of GRIGOROV et al.

AbstractThe all particle primary spectrum of GRIGOROV et al. surveyed by HILLAS has been fitted by a power law fit of the form Iall particle(>E) = 1.3 E−1.65 (cm2 s sr)−1 where E is the energy in GeV/nucleus. Using our recently determined conversion factor for protonnuclei flux ratio of equal energies the primary proton spectrum has been calculated and the result agrees with the Goddard Space Flight Centre primary proton spectrum data satisfactorily. The primary nucleon spectrum has also been calculated and follows the form Nnucleons(E) dE = 2.664 E−2.75 dE (cm2 s sr GeV/nucleon)−1.Using this primary nucleon spectrum as the source of hadrons and accelerator data for various inclusive reactions viz. used for the estimation of hadronic energy moments in the frame work of FEYNMAN‐ Scaling, the differential meson spectra have been estimated. The meson atmospheric diffusion equation after Bugaev et al. has been considered for the derivation of sea level muon spectrum. The magnetic spectrograph data of Allkofer et al., Ayre et al., Green et al., and MUTRON group are in accord with the calculated muon spectrum.

Muon sea-level intensity and primary cosmic-ray nucleon spectrum in the (1÷100) TeV energy range from the Mt. Blanc underground experiment

We have measured the muon intensity underground up to 7100 hg/cm2 s.r. by means of a spark chamber apparatus. These intensities have been converted to a sea-level muon energy spectrum. An accurate description of the flux of hadrons and muons in the atmosphere allows us to derive the primary nucleon spectrum. If the validity of the superposition model and scaling in the fragmentation region is assumed, we find that the all nucleon spectrum is represented by a single exponent over the whole energy range (1°100) TeV and is given by the relationN(E)dE=(4.85±0.25)E −(2.79±0.04)dE.

Sea Level Muon Spectrum Derived from Bugaev Model Using the Primary Cosmic Ray Energy Spectrum of Grigorov et al

AbstractIn a recent paper BHATTACHARYYA has derived the pion and kaon production spectra in the atmosphere using a form of the primary nucleon energy spectrum of the measurements of GRIGOROV et al. and the interaction model of BUGAEV et al. The sea level muon spectrum derived from these meson spectra agrees with the magnetic spectrograph data of ALLKOFER et al. and AYRE et al.In this report a critical analysis of the paper has been made and some obvious mistakes in the formulation have been pointed out. The formulation of BUGAEV et al. and the data of GRIGOROV at al. have been misinterpreted by BHATTACHARYYA. The corrected results have been properly interpreted in this report.

The intercalation between the primary cosmic-ray nucleon and sea-level muon energies using the scaling model

An important numerical consequence of a recent calculation of the correlation between the energy spectra of primary cosmic-ray nucleons and sea-level muons using the scaling model is reported. The consequence interrelates between the energies of the two cosmic-ray species and may be stated specifically as Emedian=6.9(Emu +2) in contrast to the customary relation Emedian=10Emu , where Emedian is the median energy of primary nucleons responsible for sea-level muons of specific energy Emu .

Sea level muon spectrum derived from the primary nucleon spectrum using the Cocconi–Koester–Perkins model

In a recent paper Sarkar, Bhattacharyya, and Basu have derived the sea level muon energy spectrum from the measured nucleon spectrum of Ryan, Ormes, and Balasubrahmanyan using the Cocconi–Koester–Perkins model. They have found good agreement between this muon spectrum and the precisely measured spectrum of Ayre, Baxendale, Hume, Nandi, Thompson, and Whalley. In this report a critical analysis of the paper has been made and it is found that there are some obvious mistakes both in the formulation and in the calculation. The corrected results do not agree with the Ayre et al. spectrum. The unjustified values of some of the parameters used in their work are discussed.

Primary cosmic-ray nucleon spectrum from the sea-level muon spectrum using the scaling model

Using three values of the differential exponent, namely 2.65, 2.70 and 2.75, of the primary cosmic-ray nucleon spectrum, the scaling model of high-energy N-N collisions parametrised from the recent ISR data and a realistic model for the propagation of cosmic rays through the atmosphere, the sea-level vertical muon spectra in the energy range 0.5-103 GeV have been derived. By comparing the results with the recent muon data of Allkofer et al. (1971) it can be concluded that the primary cosmic-ray nucleon spectrum may be represented by a single exponent over the whole energy range 5-104 GeV, and is given by the relation D(EN)dEN=2.48EN-2.70dEN. This conclusion is not in agreement with the results of some recent similar calculations.

Sea Level Muon Spectrum and Muon Charge Ratio derived from CERN Results for Nucleon?Nucleus Inelastic Interactions

The sea level cosmic ray spectrum and muon charge ratio have been estimated by using the energy moments of the cross section for proton-air inelastic collisions. These energy moments have been determined by interpolation from CERN results for proton-nucleus inelastic interactions in pion production. The derived results are compared with previous work.

Sea-Level Muon Charge Ratio of Cosmic Rays at High Energies

The charge ratio fo cosmic-ray muons with energies up to 1 TeV in the zenith-angle range 68/sup 0/--82/sup 0/ has been measured. The data clearly show an enhancement of the charge ratio with increasing energy thus indicating a ''normal'' mass composition of galactic cosmic rays.

Cerenkov counter for spacecraft application

The design and performance of a Cerenkov telescope intended for the spectral analysis of protons and alphas from the GOES and TIROS spacecraft are described. Four proton data channels E p > 370 MeV and two alpha channels E α > 640 MeV/nucleon are provided. The response to cyclotron protons in the 350–570 MeV range is described relative to: angular response, energy response, energy resolution, and counting efficiency. The response to sea-level muons is also presented.

Kaon‐pion Ratio from ISR Results and the Derived Sea Level Muon Spectrum from MAEDA'S Model

Kaon‐Pion‐Verhältnis nach ISR (CERN)‐Resultaten und reduziertes Myonspektrum nach MAEDA'S ModellVarious authors have estimated the production spectrum of particles in the nuclear interactions of primary protons with air nuclei. In general pions have been considered by them as the parents of muons and kaon contribution to muon flux is neglected.Recently THOMPSON and WHALLEY [1] have studied the data of AYRE et al. [2] on 2 × 105 muons above 20 GeV which provided the impetus for the authors to consider and include muons produced as the result of kaon decay along with muons produced from the decay of pions. Later DAU et al. [3] have calculated the production spectrum of muons using the experimental results of the Kiel Group (ALLKOFER et al. [4]) and MAEDA'S [5] model. It is found from their investigation that the calculated results are not in fair agreement with the observed data for vertical incidence of muons. The adopted value of the kaon‐pion ratio in their calculations was 15% which is somewhat higher than the value obtained from the machine measurements by the CERN Intersecting Storage Ring Group (ANTINUCCI et al. [6]).In the present work we have used the kaon‐pion ratio from the CERN ISR data and calculated the spectral shape of the sea level muon spectrum from MAEDA'S [5] model. The derived spectrum is fitted to the magnetic spectrograph data of the Kiel and Durham Groups [2, 4]. χ2‐test has been performed to obtain an idea about the significance of the fit with the measured data.

Analytic representation of the proton-proton and proton-nucleus cross-sections and its application to the sea-level spectrum and charge ratio of muons

We have calculated the sea-level differential muon momentum spectrum and their charge ratio from 1 GeV/c to 5000 GeV/c, using all of the available accelerator data. We find an excellent agreement between our calculation and the existing experimental data. We see no need, at present, to invoke any change either in the cosmic-ray chemical composition or in the nature of the hadron-nucleus interaction at hadron energies above 1500 GeV.