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# Does the "knee" in primary cosmic ray spectrum exist?

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The problem of the knee in primary cosmic ray at energy about 3-5 PeV is the most exiting problem in cosmic ray p h ysics. Since 1958 physicists try to solve this problem. On my opinion, the problem could be solved from the experimental point of view, whereas the primary spectrum would follow a pure power law. A key to the knee" problem lies in the hadronic structure of EAS and its propagation in the Earth's atmosphere. Neither exotic processes nor new physics are used. An explanation of the approach and some results of Monte Carlo simulations are given below.
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EXT-2003-026
04/04/2003

## Supplementary resource (1)

... This is a final stage of hadronic cascade development when the last cascading hadron lost its energy to a level below the threshold for pion production. We called these showers as coreless EAS [5,6]. Existence of this stage has a principle meaning for EAS phenomenology as it dramatically changes EAS properties and produces a knee in the EAS size spectrum at Ne ∼10 6 even at pure power law primary spectrum. ...
... These measurements as well as simulations have shown that primary cosmic ray energy where fast rising of neutron production is observed, coincides with hadrons appearance at observation level and coincides with the "knee" region independently of the observation level altitude. This confirms our previous claim that the "knee" is connected with a transition of coreless showers to normal EAS [5]. That is why measurement of the main (primary) EAS component (hadronic) is strongly needed for correct recovering of primary cosmic ray spectrum and mass composition in this energy region. ...
Article
Environmental neutrons originate from two sources: cosmic rays and natural radioactivity. They are in equilibrium with media and are therefore sensitive to many geophysical or Sun-Earth-Moon phenomena in accordance with the source of production. A history and some results obtained with the neutron technique are overviewed and discussed. The electron-neutron detectors (en-detectors) were developed at INR RAS in the framework of the PRISMA project to study Extensive Air Shower (EAS) hadronic component through thermalized neutrons. By continuous monitoring of neutron background with the en-detectors we have found interesting variation effects in the environmental thermal neutron flux, caused by geophysical phenomena. As shown, environmental thermal neutron flux could serve as a useful instrument to study cosmic rays, geophysical phenomena and many other applications.
... The phenomenological approach to the "knee" problem proposed by us in 2003 [3,4] allowed one to look to the problem from another point of view and could explain many "puzzles" observed around the "knee" during decades in cosmic ray physics, including the "multiple knees" problem. ...
... If the last cascading hadron lost its energy and stopped or decayed or captured by a nucleus, then N ch = 0 and the cascade becomes hadronless or coreless [4] and equilibrium between EAS components becomes broken [5] (actually it is broken when N ch < 10). Properties of such showers differ significantly from that of normal EAS. ...
Article
Primary cosmic ray energy spectrum around and above 1 PeV is of great interest due to its non-power-law behavior ("knee") in PeV region found many years ago using the indirect EAS (Extensive Air Shower) method. The method is based on secondary particles measuring on Earth's surface under a thick atmosphere. Traditionally, people use detectors sensitive to ionization produced mostly by secondary electromagnetic component and therefore any found changes in EAS size spectrum correspond to secondary components, which have to be recalculated to primary spectrum. Recently some new "knees" were claimed by high altitude experiments: at ∼45 TeV for all-particle spectrum (HAWC), for primary protons and helium: at ∼400 TeV (Tibet ASγ) and at ∼700 TeV (ARGO-YBJ) thus widening the "knee" region from ∼0.045 to 5 PeV. The natural explanation of such a strange spectrum behavior in a wide energy range could be found in the EAS phenomenological approach to the knee problem.
... Phenomenological approach to the "knee" problem proposed in 2003 [3,4] allowed us to look to the problem from another side and could explain many "puzzles" observed during decades in cosmic ray physics, including the "multiple knee" problem. Experimental data accumulated over a long period of ~ 70 years of EAS observations have a lot of contradictions and non-statistical dispersion. ...
... This is a discrete value and cannot be less than 1. If the last cascading hadron lost its energy and stopped or decayed or captured by a nucleus than N ch =0 and the cascade becomes hadronless or coreless [3] and equilibrium between EAS components becomes broken [4] (actually it is broken when N ch <10). Properties of such showers differ significantly from that of normal EAS. ...
Article
Full-text available
Primary cosmic ray energy spectrum around and above 1 PeV is of great interest due to its non-power law behavior found many years ago using the indirect EAS (Extensive Air Shower) method. The method is based on secondary particles measuring on Earth's surface under a thick atmosphere. Traditionally people use detectors sensitive to ionization produced mostly by electromagnetic component and so called "knee" was found for EAS size spectrum many years ago. Later it was assigned to a steepening of cosmic ray spectrum at 3-5 PeV. Recently some new "knees" were claimed by high altitude experiments, for primary protons and helium: at ~200-300 TeV (Tibet ASγ) and at ~700 TeV (ARGO-YBJ) thus widening the "knee" region from ~0.2 to 5 PeV and demonstrating disagreement with the existing experimental data. The natural explanation of such a strange spectrum behavior can be found in the phenomenological approach to the knee problem.
... 10.1029/2020GL090033 7 of 9 production in the soil from gamma-rays through the (γ, n) reaction. This means that the signature of neutron bursts should be expected from any large cosmic ray shower that has a sufficiently large electromagnetic component, even "coreless" showers (Stenkin, 2003) at lower altitudes. (3) A detectable RF signal with mainly east-west polarization was associated with the largest neutron burst observed, which produced 198 counts over 2 ms in our 7.62 × ⊘7.62 cm LaBr 3 scintillation detector, as well as a smaller burst, which produced 56 counts over the same time interval. ...
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... The application of the thermal neutron registration technique to the studies connected with the physics of extensive air shower was considered in detail in the publications [25,26,27] were a specialized scintillation neutron detector was proposed for the purpose. This detector is based on a thin layer of the ZnS(Ag) and 6 LiF (or 10 B 2 O 3 ) alloy grains covered with a thin transparent plastic film. ...
Preprint
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Article
Purposeful investigation of radiation fluxes strongly delayed in relation to the main particle front of extensive air shower (EAS) was undertaken at the Tien Shan Mountain Cosmic Ray Station. It was found that the passage of the EAS can be accompanied by the delayed thermal neutrons and by the soft (30–50) keV gamma rays, mostly concentrated within a region of about (5–10) m around the shower axis, where the integral radiation fluence can vary in the limits of $$(10^{-4}{-}1)$$ cm$$^{-2}$$ for neutrons, and of $$(0.1{-}1000)$$ cm$$^{-2}$$ for gamma rays. The dependence of signal multiplicity on the shower size $$N_\mathrm{e}$$ has a power shape both for the neutron and gamma ray components, with a sharp increase of its power index around the value of $$N_\mathrm{e}\approx 10^6$$, which corresponds to the position of the $$3 \times 10^{15}$$ eV knee in the primary cosmic ray spectrum. The total duration of detectable radiation signal after the EAS passage can be of some tens of milliseconds in the case of neutron component, and up to a few whole seconds for gamma rays. The delayed accompaniment of low-energy radiation particles can be an effective probe to study the interaction of the hadronic component of EAS.
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Examples of the power law spectra observations in the Nature are given. It is shown that the observed meteoroid mass spectrum is very similar to the observed cosmic ray energy spectrum. It is concluded that the "knees" observed in both spectra have a similar origin: the Earth's atmosphere. Both spectra are studied by indirect methods through secondary components and specific behavior of these components in the atmosphere could produce the "knee" even in a case when primary spectrum follows a pure power law.
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We report experimental results obtained by the emulsion chambers on board of the long duration balloon. We have been carrying out the trans-Siberian-continental balloon flight since 1995, and the results from 1995 to 1996 experiments are presented here. Total exposure of these two years amounts to 231.5 m2 h at the average altitude of ∼32 km.The energy range covers 10–500 TeV for proton-primary, 3–70 TeV/n for helium-primary, and 1–5 TeV/n for Fe-group (Z=26–28), though statistics of heavy components is not yet enough. Our preliminary data show that the spectra of the proton and the helium have nearly the same power indices ∼2.80, while those of heavier ones become gradually harder as the mass gets heavier, for instance the index is ∼2.70 for CNO-group and ∼2.55 for Fe-group.It is remarkable that a very high energy proton with multi-PeV is detected in 1995 experiment, and the estimated flux of this event coincides with a simple extrapolation from the energy spectrum with the power index 2.8 observed in the range 10–500 TeV. It indicates that there is no spectral break at around 100 TeV, in contrast to the maximum energy predicted by the current shock-wave acceleration model. This evidence requires some modification on the acceleration and/or propagation mechanism.Also we present all-particle spectrum and the average primary mass in the energy range 20–1000 TeV/particle. Our preliminary data show no drastic change in mass composition over the wide energy range, at least up to 1 PeV/particle, though the statistics is not yet enough to confirm it concretely.The flight performance and the procedure of the analysis, particularly the energy determination methods and the detection efficiency calculation are also given.
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The cosmic ray energy spectrum in the range E0 = 1015–1016eV (including the region of the steepening, “knee”) is studied by means of the EAS-TOP array (Campo Imperatore, Gran Sasso Laboratories, atmospheric depth 820 g cm−2). Measurements of the electromagnetic size (Ne = total number of charged particles at the observation level) are performed as a function of zenith angle with statistical accuracies of a few percent. The change of slope of the spectrum is observed in each bin of zenith angle at size values decreasing with increasing atmospheric depth. Its attenuation is compatible with the one of shower particles (Λe = 219 ± 3 g cm−2). This observation provides a consistency check, supporting a normal behaviour of showers at the break, that make plausible astrophysical interpretations based on an effect on primaries occurring at a given primary energy. The break has a “sharp” shape (i.e., within experimental errors is compatible with two intersecting power laws) that represents a constraint with which any interpretation has to match. The change of slope of the power law index reproducing the size spectrum is Δγ = 0.40 ± 0.09. The derived all particle energy spectrum is in good agreement with the extrapolation of the direct measurements at low energies and with other EAS data at and above the knee. Power laws fits to the energy spectrum below and above the knee give (in units of m−2 s−1 sr−1 TeV−1) S(E0) = (3.48 ± 0.06) × 10−10(E0/2300)−2.76±0.03 for 900 TeV < E0 < 2300 TeV and S(E0) = (3.77 ± 0.08) × 10−11(E0/5000)−3.19±0.06 for 5000 TeV < E0 < 104TeV. The systematic uncertainties connected to the interaction model and the primary composition are discussed.
Article
Frequency distributions of local muon densities in high-energy extensive air showers (EAS) are presented as signature of the primary cosmic ray energy spectrum in the knee region. Together with the gross shower variables like shower core position, angle of incidence, and the shower sizes, the KASCADE experiment is able to measure local muon densities for two different muon energy thresholds. The spectra have been reconstructed for various core distances, as well as for particular subsamples, classified on the basis of the shower size ratio Nμ/Ne. The measured density spectra of the total sample exhibit clear kinks reflecting the knee of the primary energy spectrum. While relatively sharp changes of the slopes are observed in the spectrum of EAS with small values of the shower size ratio, no such feature is detected at EAS of large Nμ/Ne ratio in the energy range of 1–10 PeV. Comparing the spectra for various thresholds and core distances with detailed Monte Carlo simulations the validity of EAS simulations is discussed.
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