Primary Nucleon Spectrum Research Articles

The sea-level muon spectrum and charge ratio and their relationship with high-energy accelerator data

The sea-level muon spectrum and charge ratio have been calculated using the available high-energy accelerator data. The calculated muon spectrum is inconsistent with a primary nucleon spectrum of the form AE- gamma but is consistent with a spectrum of the form A(E- gamma 1+X0E- gamma 2). Consideration of the sea-level muon spectron and the primary iron spectrum suggests a primary nucleon spectrum 1.73 (E-2.70+or-0.05+1.35* 10-3*E-2.00+or-0.10)s-1 sr-1 cm-2 GeV-1. This spectrum is in better agreement with the observed muon charge ratio than a spectrum with a single exponent, but the predicted ratio is 7%in excess of the measured ratio at a sea-level momentum of 10 GeV/c, and this is attributed to a breakdown in the limiting fragmentation hypothesis or a difference in the charge distribution of secondaries between nucleon and nucleus targets. The predicted and observed variation of the ratio are in good agreement assuming that the spectrum of nuclei (Z approximately 26) cuts off in the region of 104GeV.

Sea Level Muon Spectrum Derived from Bugaev Model

AbstractThe pion and kaon spectra in the atmosphere are derived from primary nucleon spectrum determined by GRIGOROV et al.; they satisfy the relations N(Eπ) dEπ = 0.187 EdEπ and N(Ek) dEk = 0.017 E dEk, respectively. By using the pion‐kaon atmospheric diffusion equation the sea level muon spectrum is calculated and the result compared with the magnetic spectrograph data of ALLKOFER et al. and AYRE et al.

Bose-type distribution and primary cosmic ray nucleon spectrum from sea-level muon spectrum

The recent CERN Intersecting Storage Ring cross section data on the p+p to pi +or-+X inclusive reactions have been analysed using the Bose-type distribution of the form E(d3 sigma )/(d3p)=(Axs12/)/(exp( epsilon ( lambda )/T)-1) proposed by Hoang (1973). This formula has been used to derive the cosmic ray primary nucleon spectrum from the sea-level muon spectrum. It is found that the primary spectrum obeys the following relation: N(Ep)dEp=2.06Ep-2.64dEp. The result has been compared with the recent experimental data and theoretical predictions given by different authors.

Cosmic-ray spectra and Hagedorn’s thermodynamic model

The sea-level muon and proton spectra were computed by using Hagedorn's model for the production of nucleons, pions and kaons in nucleon-nucleus collisions. The multiplicities and partial inelasticities of these particles were calculated in the range (5÷40000) GeV of proton laboratory energy. The predicted muon and proton spectra show agreement ((0÷20)%) with recent measurements in the range (5÷5000) GeV. Thus Hagedorn's model is very useful in cosmic-ray physics. The results also confirm the absolute primary nucleon spectrum which was built up for this purpose from two recent experimental spectra.

Absolute calculation of secondary cosmic gamma rays at the top of the atmosphere

Starting from the primary nucleon and the primary electron spectra the vertical secondary gamma spectra in 0–30 g/cm2 atmospheric depth and the energy range 1–1000 GeV are calculated and compared with experimental data. The calculated spectra largely depend on the properties of the primary-nucleon—air-nucleus collision. The collision model is considered in detail. The influence of the relevant collision parameters, which are not very well known, on the gamma spectra is studied. In addition the influence of the solar cycle and of the geomagnetic cutoff is shown. The conventional values of the collision parameters together with a lowered primary nucleon spectrum, as suggested by recent measurements by Schmidtet al., give theoretical gamma spectra which lie within the wide range of the experimental data. In the same way the above assumptions can help to remove a discrepancy noticed a few years ago between measured and calculated muon and nucleon spectra in the atmosphere.

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.

The energy spectrum of cosmic-ray neutrons at sea level in the range 20-4000 GeV

A study has been made of the production of bursts by neutral cosmic-ray particles, presumably neutrons, in the energy range 20-4000 GeV. The energy spectrum is found to exhibit a deficiency above 100 GeV when compared with that derived from the primary nucleon spectrum, given by a number of authors, assuming a constant attenuation length. The discrepancy most likely represents a change of attenuation length with energy, but an alternative explanation involving quark production cannot be ruled out.

A Deduction of the High Energy Spectrum of Cosmic-Ray Primary Nucleons from the Observed Muon Spectrum

Fermi's theory of pion production is extended to treat collisions of nucleons with air nuclei. The energy distribution of the created pions and their daughter muons is approximately calculated, and is applied to correlate the observed muon spectrum in the energy range 10-100 Bev with the primary nucleon spectrum. The results and limitations of this procedure are discussed.