Observations on extensive air showers VI. The ratio of the soft to penetrating components and their attenuation in the atmosphere

Cranshaw, T. E.; Beer, J.; Galbraith, W.; Hillas, A. M.; Norris, S. J.; Porter, N. A.

doi:10.1080/14786435808237019

Cited by 10 publications

(2 citation statements)

References 16 publications

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“…On the other hand, the altitude variation curves in our previous papers were averaged over the fluctuation in the level of shower-initiation for fixed energies and could not be compared directly with experimental results. Cranshaw et al 3 ) have suggested the possible existence of mixture of showers arising in several ways, viz. a mixture of primaries, the primary interaction distributed along a considerable depth of atmosphere, and large fluctuations in the development of the nuclear cascade.…”

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A Study on the Extensive Air Showers

Ogita

1962

Prog. Theor. Phys.

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With the totally inelastic and half elastic collision models in our previous paper, various quantities in extensive air showers (EAS) are given as functions of the depth from the starting point of EAS. The effect of the fluctuation in the level of shower initiation is illustrated. The calculated results are compared with the experimental ones, taking into account the above fluctuation, and the value of the average inelasticity is estimated. Furthermore, the consistency between the attenuation length obtained by using the correlation diagrams in some quantities and that of the shower intensity is examined in connection with the form of the energy spectrum of the primary particles.

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A Study on the Extensive Air Showers

Ogita

1962

Prog. Theor. Phys.

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“…Since the probability that an A-particle makes the first collision at depth between x1 and x1 + dx1 is given by (4) where LA is the interaction mean free path of the A-particle, the frequency with which A-particles g1ve rise to EAS with sizes between N and N + dN at x' is given by…”

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On the Structure of Extensive Air Showers. II

Ueda¹

1960

Prog. Theor. Phys.

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1231The structure of extensive air showers (EAS) is examined in detail, in particular in it~ dependence upon the characteristics of the high-energy nuclear interactions and the primary energy spectrum. The following effects are taken into account: (1) The fluctuation in the depth at which the primary particles make their first interaction.(2) The fluctuations in the first interaction made by heavy primary particles.The main results are summarized as follows: (i) Shower curves are derived which are consistent with experiments, by a proper choice of the parameters involved in our model of the high-energy interaction. (ii) Under the assumptions that the relative abundance o:· various groups of primary nuclei at the top of the atmosphere is the same as measured at lower energies and that all groups have the same energy spectra as the proton spectrum, the calculated shower size spectrum is not inconsistent with the observed one even if there is a cutoff in the primary energy at about 5 ·108 Mc2 per nucleon. (iii) Under the same assumptions, the fluctuation in the ratio between numbers of muons and of electrons is, at sea level, almost entirely governed by the fluctuation in the depth of the first interaction of protons. At mountain altitudes the fluctuation in the ratio is governed nearly equally by both the fluctuations due to protons and that due to heavy nuclei. (iv) Under the same assumptions, the shower rate due to primary nuclei heavier than protons is, at mountain altitude, equal to or greater than twice that due to protons. (v) There is a possibility that high-energy nuclear active particles (:2:10 12 ev) in EAS initiated by a proton are as abundant as those in an EAS initiated by a heavy nucleus.Additional remarks which would be useful for further investigations are also given. pointed out independently the importance of the fluctuation in the depth at which the f1rst nuclear interaction occurs. Krau shaar showed that the conventional conversion of the size spectrum into a primary energy spectrum led to an overestimation of the energy by a factor of 1.4. A more refined analysis made by Miyake showed that the attenuation length of the shower rate is intimately related to the interaction mean free path of primary particles with air nuclei,* and that the intensity of the primary particles decreases more rapidly at high energies than does the intensity hitherto considered and that the practical upper limit of the energy spectrum would be about 5 ·10 17 ev. Recent experiments made by the Japanese 5 l and Russian groups 6 J also show that the lateral distribution of charged particles and the ratio between numbers of muons and of all charged particles fluctuates rather widely from shower to shower.The purposes of the present paper are to examine quantitatively the effect of the fluctuations on various quantities, taking into account the shape of the primary energy spectrum and the characteristics of the high-energy interactions and to get at least a first approximation to a consistent picture of EAS.The important so...

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