J Wdowczyk

A theoretical analysis of extensive air showers I. Near-vertical showers at sea level

Calculations have been made of some features of extensive air showers expected in the near-vertical direction at sea level for three models for the nucleon-air-nucleus, and pion-air-nucleus interaction. The models have been chosen with regard to known experimental features of interactions of energy up to some few thousand GeV and the calculations have been made for primary protons and heavy nuclei, the latter using a simple fragmentation model. Detailed comparison between prediction and experiment has been made for the energy spectrum and lateral density distribution of muons in showers of size in the region of 106 particles. All the models predict the measured shape of the energy spectrum to several hundred GeV, indicating that the propagation model and the energy spectrum adopted for all three models are acceptable. For muon energy thresholds up to about 10 GeV the predicted lateral distributions agree in shape at radial distances above about 50 m but show a considerable excess over observation at small distances. Much of the discrepancy can be removed by allowing for uncertainty in core location in experimental arrangements and the residue can be eliminated if it is assumed that collisions in which secondaries are emitted with small transverse momenta (pt [less, similar] 0.1 GeV/c) are rare. Only one experiment appears to have been carried out at a high energy threshold (Eμ > 40 GeV) and the resulting lateral distribution is somewhat flatter than predicted even after allowance is made for the factors mentioned. If substantiated the most likely explanation is the existence of an excess of interaction secondaries with transverse momenta above several GeV/c.

THEORETICAL ANALYSIS OF EXTENSIVE AIR SHOWERS. IV. MUON SHOWERS DEEP UNDERGROUND.

For Pt. III see ibid vol.2, No.3, (1969) 354-64. Studies of muon showers deep underground by the Utah group have stimulated an extension of the previous calculations of the present authors into the region covered by the underground experiment: viz. muon threshold energies of the order of 1000 gev and zenith angles in the region of 60 degrees . The effect of varying some of the more important parameters of the high- energy nucleon-air-nucleus collision has been examined, and it is concluded that a multiplicity law of the form Ep1/4 is preferred to an Ep1/2 law and that there is no evidence for a significantly greater mean transverse momentum than the value of 0.4 Gev/c, which relates to the parents of muons of lower energy. An increase in the fraction of kaons generated with increasing nucleon energy is not favoured. Concerning the mass spectrum of the primary particles, there is some support for the contention that the primaries above 1015 ev are largely protons, but none for the conclusion of Grigorov et al. in 1967 that the proportion of heavy nuclei commences to increase at 1012 ev. However, a problem that affects all the conclusions is that significantly fewer multiple events are observed than expected.

The possibility of detectable fluxes of cosmic ray γ rays with energy above 1019 eV

Under the assumption that cosmic rays are of extragalactic origin above 1018 eV it is shown that the presence of the 2.7K black body radiation may lead to a detectable flux of very energetic gamma rays.

Theoretical analysis of extensive air showers V. General analysis of muons above 1000 GeV

For Pt IV see abstr. A. 3283 of 1970. Previous calculations by the present group (Adcock et al. in 1969) have been extended to yield predictions of the frequencies of multiple muons in the comprehensive experiment of Cannon and Stenerson (see ibid., vol 4, 266, 1971). It is shown how comparison with experiment can give information about the magnitude of the mean transverse momentum (pt) of the parent pions, the form of the multiplicity law and the magnitude of the primary cosmic ray intensity, all in the region of 2*105 GeV primary energy. Comparison is also made with the previous experiments and the areas of agreement and disagreement are explored.

The mean transverse momentum of secondaries from cosmic-ray interactions in the region of 2 × 105 GeV

The variation with separation of the rate of pairs of cosmic-ray muons of energies above 1000 GeV has been measured at a mean angle to the vertical of 45 degrees by Coats et al (1970). The variation is most sensitive to the mean transverse momentum of the parent pions in the initial nucleon-air nucleus interactions and the value determined from comparison with a theoretical analysis is (pt)=0.60+or-0.05 GeV/c, the median primary energy in question being approximately 2 × 105 GeV. The form of the distribution in transverse momentum giving a best fit to the experimental data is that proposed by Elbert et al. (1968). The value found for (pt) lends confirmation to the slow increase in this quantity with increasing interaction energy suggested by previous work.

A theoretical analysis of extensive air showers. III. Muon showers at large zenith angles

For Pt. II see abstr. A15896 of 1968. A theoretical analysis has been made of the muon component of extensive air showers incident at large angles to the vertical. Using the model described previously, calculations have been made of the expected numbers of muons reaching ground level as a function of threshold energy and zenith angle for primary particles of various energies. The data have been combined with alternative primary spectra of cosmic rays, with and without an enhanced contribution from heavy nuclei, to give the expected muon density spectra. It is found that the density spectrum is sensitive to the distribution of transverse momentum among the parents of the muons and to a lesser extent to the mass composition of the primaries. There is thus the possibility of deriving information about the mean transverse momentum, and perhaps setting limits on the mass composition, from a comparison with experiment.

An analysis of experimental results on fluctuations of muon and electron numbers in extensive air showers

The theoretical results derived in the previous paper by de Beer et al. in 1968 have been compared with experimental observations, with reference to the fluctuations in the total numbers of muons and electrons and to the variation of the mean number of muons with shower size. It is found that the derivation of accurate parameters from experimental data is very difficult in view of the presence of a variety of bias effects. However, good agreement appears, in general, when comparison is made of the predictions of our preferred model (which assumes a CKP type of energy distribution for the secondary pions from high-energy interactions). The nature of the mass composition of the primaries is still unclear in view of the rather low sensitivity of most parameters to the mass spectrum. What evidence there is, from the (Nμ, Ne) relation, gives only a very slight indication of a change in the primary composition above 1015 eV.

A theoretical analysis of extensive air showers II. Fluctuations of muon and electron numbers

The results reported form a continuation of the analysis given by de Beer et al. in 1966. In the present work an examination is made of the fluctuations expected in the electron and muon components from shower to shower, with particular regard to the number, lateral distribution and height of origin of the muons. It is shown that fluctuations can affect considerably the picture of showers drawn from results with practical air shower arrays, largely through the correlations that exist between the various components. The important problem of deriving results of significance to high-energy nuclear physics and to astrophysics is studied, and it is shown that the relative fluctuation of the muon number in showers of fixed size has some sensitivity to the characteristics of high-energy interactions, whereas the relative fluctuation of the shower size for constant muon number is sensitive to the mass composition of the primary particles.