Study of cascade showers generated by near-horizontal muons in the water Cherenkov detector with a dense array of optical modules

The method for reconstructing the cascade curve by the Cherenkov radiation in water of the NEVOD detector with a dense spatial array of optical modules is discussed. Cascades are generated by near-horizontal muons which are separated by the DECOR coordinate detector. The cascade curves and the cascade energy spectrum measured in an ～8000-hour measurement series are presented.     

Energy spectrum of cosmic-ray muons

Summary The energy spectrum of cosmic-ray muons at sea-level is calculated by the numerical integration of a diffusion equation by assuming a scaling model. The calculated spectrum is in good agreement with the observed data of muons with the zenith angles of 0° and nearly 90°. Furthermore, by this comparison, it is concluded that the scaling model is valid up to the muon energy of 6.9 TeV. It is also found that the survival probability of muons at large zenith angles is in favour of that calculated by Ramana Murthy rather than that obtained by Dau, Carstensen and Jokisch. Two production spectra of muons obtained by Thompson and Whalley and Dauet al. are analysed in reference to the recent experimental data. As a result, it is concluded that the power law exponent of the differential-energy spectrum of muon parent particles is 2.75±0.15 in the muon energy range from 100 GeV to 6.9 TeV.

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Riassunto Si calcola lo spettro di energia dei muoni dei raggi cosmici per mezzo dell'integrazione numerica di un'equazione di diffusione assumendo un modello a scala variabile. Lo spettro calcolato è in buon accordo con i dati osservati dei muoni con angoli di zenith di 0° e quasi 90°. Inoltre da questo confronto si conclude che il modello a scala variabile è valido fino ad energie muoniche di 6.9 TeV. Si trova anche che la probabilità di sopravvivenza dei muoni ad angoli di zenith grandi è in favore di quella calcolata da Ramana Murthy piuttosto che di quella ottenuta da Dau, Cartensen e Jokisch. Si analizzano due spettri di produzione dei muoni ottenuti da Thomson e Whalley e Dauet al. rispetto a recenti dati sperimentali. Come risultato si conclude che l'esponente della legge di potenza dello spettro di energia differenziale delle particelle genitrici dei muoni è 2.75±0.15 nell'intervallo di energia muonica compreso tra 110 GeV e 6.9 TeV.

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Резюме Вычисляется энергетический спектр мюонов космических лучей на уровне моря, использия численное интегрирование уравнения диффузии и предполагая модель подобия. Вычисленный спектр хорошо согласуется с наблюденными данными для мюонов с зенитными углами вблизи 0° и 90°. Из этого сравнения делается вывод, что модель подобия справедлива для энергии мюонов вплоть до 6.9 ТэВ. Отмечается, что вероятность выживания мюонов при больших зенитных углах отдает предпочтение вычислениям Рамана Мурти, а не Дау, Карстенсена и Джокиша. Два спектра образования мюонов, полученные Томпсоном и Валлеем и Дау и др., сравниваются с недавними экспериментальными данными. Из сравнения получено, что показатель степенного закона в дифференциальном энергетическом спектре равен 2.75±0.15 в области энергий мюонов от 110 ГэВ до 6.9 ТэВ.

     

Delayed muons in extensive air showers and double-front showers

The results of a long-term experiment performed in the period between 1995 and 2006 with the aid of the MUON-T underground (20 mwe) scintillation facility arranged at the Tien Shan mountain research station at an altitude of 3340 m above sea level are presented. The time distribution of delayed muons with an energy in excess of 5 GeV in extensive air showers of energy not lower than 106 GeV with respect to the shower front was obtained with a high statistical significance in the delay interval between 30 and 150 ns. An effect of the geomagnetic field in detecting delayed muons in extensive air showers was discovered. This effect leads to the asymmetry of their appearance with respect to the north-south direction. The connection between delayed muons and extensive air showers featuring two fronts separated by a time interval of several tens of to two hundred nanoseconds is discussed. This connection gives sufficient grounds to assume that delayed muons originate from the decays of pions and kaons produced in the second, delayed, front of extensive air showers.     

Production of high-energy muons in gamma showers

We have calculated the number of high-energy muons in gamma showers generated by photoproduction and by muon pair creation. The prompt muons have flatter energy spectrum than the muons, which come from photoproduction and contribute significant fraction of the total muon rates for E_μ ? 1 TeV. The total rate of high-energy muons in gamma showers is, however, very low.     

Spatial distribution of Cherenkov light from cascade showers in water

The spatial distribution of the Cherenkov light generated by cascade showers is analyzed using the NEVOD Cherenkov water detector. The dependence of the Cherenkov light intensity on the depth of shower development at various distances from the shower axis is investigated for the first time. The experimental data are compared with the Cherenkov light distributions predicted by various models for the scattering of cascade particles.     

Low-energy muons in extensive air showers (EAS)

Summary A small air shower array of 21 detectors in conjunction with two shielded muon magnetic spectrographs has been operated for detection of muons of momentum in the range (2÷500) GeV/c at a geomagnetic latitude of 26^o 45′ N at North Bengal University Campus. The array is sensitive to air showers initiated by cosmic-ray primaries of energy in the range (10¹⁴÷10¹⁶) eV. The initial results on muons with a comparison of other recent measurements have been given to infer information on the characteristics of high-energy interaction. An evaluation on the Monte Carlo simulation and observational data on muons in air showers have also been given to indicate the present status of the study of muons in air showers.

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Riassunto Si utilizza un piccolo insieme di ventuno rivelatori di sciami cosmici congiunto a due spettrografi muonici magnetici schermati per rilevare muoni con momento nell'intervallo (2÷500) GeV/c ad una latitudine geomagnetica di 26^o 45′ N al North Bengal University Campus. L'insieme è sensibile a sciami cosmici iniziati da primarie con energia nell'intervallo (10¹⁴÷10¹⁶) eV. Si effettua un confronto dei risultati iniziali sui muoni con altre misure recenti per riferire informazioni sulle caratteristiche dell'interazione ad alta energia. Si dà una valutazione della simulazione di Monte Carlo e dei dati osservativi sui muoni negli sciami cosmici per indicare lo stato attuale dello studio dei muoni nei raggi cosmici.

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Реэюме НеболъшАя из 21 детектора атмосферных яяивней, соедненная с двумя мюонными магнитными спектрогафами, используется для детектектирования мюонов с импульсами в области (2÷500) ГзВ/с на геомагнитной широте 26° 45′ N в камрусе Северного ьенгалъского университета. Детектируюшая система чувстви-телъна к атмосферным ливням, образованным космическими частицами с знергиями в интервале (10¹⁴÷10¹⁶) зВ. Сравнение полученных резулътатов с данными других недавних измерений позволяет получитв информациу о характеристиках взаимо-действий при оченъ вюсоких знергиях. Проводится такзе сравнение моделирования по методу Монте Карло с данными наблюдений для мюонов в атмосферных ливнях.

     

Hadrons and other secondaries generated by cosmic-ray muons underground

Summary The production of nuclear-active and electromagnetic particles, as well as long-lived isotopes in nuclear and electromagnetic showers generated by cosmic-ray muons at different depths underground is discussed. Characteristics of the secondary components and their dependence on the depth and the muon energy, obtained in experiments and calculations, are presented.     

Energy spectrum of cosmic ray muons above 10 TeV according to BUST data

The energy spectrum of cosmic ray muons in the range of several TeV to PeV obtained through the analysis of multiple interactions of muons (the pair meter technique) in the Baksan Underground Scintillation Telescope (BUST) is presented. Results are compared with prior BUST data on the muon energy spectrum measurements and data of other experiments, along with calculations for different muon spectrum models.     

Energy spectrum of electron pairs in a high energy photon-electron cascade

The energy spectrum of electron pairs generated in a high energy photon-electron cascade up to a depth of 1·5 c. u. was measured and the possible influence of the medium on the shape of the spectrum according to Landau-Pomeranuk-Ter Mikaelyan and Migdal was investigated. Two procedures were used for the analysis; no significant deviation from the Bethe-Heitler spectrum could be observed. Different ways of estimating the primary energy were applied; the resulting value, 2×10¹²eV, was accepted as the primary energy.

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The authors wish to thank Dr. Lanius for kindly lending them the necessary plate from the Berlin part of the I-stack.     

The energy spectrum of neutrons produced by cosmic ray muons in LVD

The energy spectrum of neutrons produced by cosmic ray muons in the underground detector LVD (3650 m.w.e.) is obtained for the energy range of 30–450 MeV. The spectrum is derived using the energy release spectrum of neutron interaction products in 1.5 m³ scintillation counters.     

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.     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

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实验研究了超短超强激光与7μm薄膜Cu靶的相互作用中靶背法线方向产生的质子和碳离子的能量分布。实验中采用CR39和Thomson磁谱仪相结合测量质子和碳离子能谱。实验中观察到了质子和C4+、C3+、C2+和C1+离子。实验结果表明:离子沿着靶背法线方向发射,离子在一定能量处出现截断;质子的产额远远高于碳离子产额;C4+、C3+、C2+和C1+最大截止能之比约为4:3:2:1。     

Energy loss of electron-induced showers in oriented tungsten crystals

The development of the shower induced by 26- and 28-GeV electrons in the oriented tungsten crystal results in strong absorption of the shower energy by the crystal and an increase in the energy fraction of shower particles scattered between the crystal and detector. The ratios of total shower energy losses in oriented tungsten crystals to total losses in misoriented crystals 1, 2.7, 5.8, and 8.4 mm thick were 3.9, 2.6, 2.1, and 1.9, respectively.     

Energy losses of high-energy muons and τ-leptons in inelastic scattering by nuclei

A hybrid model is used to calculate the losses of muons and τ-leptons in inelastic scattering by nuclei in water and in ground. The model includes soft and semihard photoprocesses and also hard scattering with an exchange by a γ-photon and a Z₀-boson. In the calculations, nuclear effects, such as shading and antiscreening of nucleons, the EMC effect, and the Fermi motion of nucleons in a nucleus, are considered. The distinction in scattering between a particle and an antiparticle, conditioned by an admixture of a weak neutral current, is discussed. Comparison with other calculations is given. Formulas for the coefficients of energy losses of muons and τ-leptons in water and in ground are obtained which approximate the calculation results over a wide interval of energies: 10²–10⁹ GeV. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 82–86, March, 2006.     

Cosmic ray energy spectrum from measurements of air showers

This review focuses on high-energy cosmic rays in the PeV energy range and above. Of particular interest is the knee of the spectrum around 3 PeV and the transition from cosmic rays of Galactic origin to particles from extra-galactic sources. Our goal is to establish a baseline spectrum from 1014 to 10^20 eV by combining the results of many measurements at different energies. In combination with measurements of the nuclear composition of the primaries, the shape of the energy spectrum places constraints on the number and spectra of sources that may contribute to the observed spectrum.     

Variations of neutrons and muons generated by cosmic rays in the atmosphere and in thunderstorm electric fields

We investigate the interrelation between cosmic rays (CRs) and the electric field of the Earth during thunderstorms established by various investigators. The data from simultaneous measurements by spectrograph of CRs and the electric field in Yakutsk are used. It is noted that in seven recorded events of prolonged (up to 9 hours) variations in the electric field by ±5 kV m⁻¹ and in one event of a one-hour increase in the field value up to +20 kV m⁻¹ the CR index rose substantially. During the thunderstorm of the latter event, the intensity of neutrons fell by a considerable 1%. At the same time, a drop of ∼0.3% was observed in the CR muon component. Such effects was not observed for higher energy muons.     

Cascade showers in the NEVOD Cherenkov water detector

A technique for measuring the cascade shower energy in the NEVOD Cherenkov water detector with a spatial lattice of quasi-spherical modules is discussed. The technique allows the number of cascade particles that move near the shower axis to be reconstructed on the basis of analysis of response amplitudes of triggered photomultiplier tubes. The technique of cascade-curve reconstruction was applied to cascade showers generated by near-horizontal high-energy muons extracted by means of the DECOR coordinate-tracking detector arranged around the Cherenkov water detector. The first results of measuring the energy spectrum of cascade showers of 10–1000 GeV are presented.