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Hadronic Interactions and Cascades

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Extensive Air Showers

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Overview

After a brief introduction we discuss the hadronic cross sections for interactions that are of relevance for air shower and ultrahigh energy physics research, such as cross sections and the corresponding interaction mean free paths of nucleons, pions and nuclei on protons, air and other target nuclei that are encountered in cosmic ray experiments. Their energy dependence is summarized, accelerator and collider data are presented together with the results from cosmic ray and air shower experiments over the entire experimentally accessible energy range up to ~ 1019 eV. These topics are followed by a discussion of the projectile and target fragmentation at very high energies and of the basic properties of hadronic interactions, including particle production, secondary particle multiplicity, the nature of the secondaries, kinematic aspects of secondaries, longitudinal and transverse momenta, the phenomenon of large transverse momenta, the leading particle effect, elasticity/inelasticity of hadronic interactions, and correlations among the different observables. Subsequently a large variety of hadronic interaction models are discussed. Some emphasis is given to the early phenomenological-mathematical models that are scarcely documented and difficult to find in the literature, but played a relevant role initially to guide new pioneering experiments. A brief summary of the fast growing number of new models is given in the form of a catalogue, giving some emphasis on the currently relevant so-called event generators. The final part of this chapter is devoted to hadron cascades, outlining the analytical treatment of the problem and the Monte Carlo method for three- and four-dimensional cascade simulations (in space and time). The latter topic is treated in detail in Chap. 20.

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Notes

  1. 1.

    Approximately 2.2 GeV are dissipated per 1,000 g cm−2 of air traversed by a relativistic muon.

  2. 2.

    Nuclear emulsion is applicable up to ∼100 TeV. In some cases it had been used at mountain altitude as detector under LiH and carbon targets.

  3. 3.

    The author is grateful to Prof. Larry Jones for having called his attention to this significant difference.

  4. 4.

    Glauber theory of hadron–nucleus interactions had been used successfully for many years, yet it is the high energy limit of non-relativistic scattering theory and in fact not valid in the relativistic domain.

  5. 5.

    Caution must be taken when comparing data from different experiments with unaccompanied cosmic rays as the definition of the term “unaccompanied” (within a certain radius) varies from experiment to experiment.

  6. 6.

    According to Lindstrom et al. (1973) the partial cross section for the production of a particular fragment produced in a nucleus–nucleus collision depends strongly on the nature of the target nucleus, but the relative proportions of different fragments are not strongly target dependent.

  7. 7.

    A similar rise of the production cross section of strange particles, including hyperons was also observed at CERN \(\overline{p}p\), Tevatron and RHIC experiments.

  8. 8.

    We disregard here the comparatively rare occasional large transverse momentum events that are discussed below.

  9. 9.

    Cocconi et al. (1966) in their work used a value of \(2p_{0} \simeq 0.36\;\textrm{GeV/c}\).

  10. 10.

    See Eqs. (3.44) and (3.60), respectively, for definition.

  11. 11.

    See Chap. 21 for definitions.

  12. 12.

    At that time Minkowski predicted on the basis of QCD the existence of jets, direct gamma rays and lepton pairs with large transverse momenta that should exhibit a relatively flat distribution that goes asymptotically as p t −4 (Minkowski, 1973, private communication; Fritzsch and Minkowski, 1977).

  13. 13.

    For an early review see Feinberg (1972), and references listed therein.

  14. 14.

    It should be noted that in about 25% of all proton–nucleus interactions the most energetic hadron is a neutron (Jones, 1982).

  15. 15.

    Rough estimates are possible on the basis of the number of heavy tracks.

  16. 16.

    The charge Z can usually be determined but the problem is to distinguish minimum ionizing particles such as charged pions from protons, etc.

  17. 17.

    The only high energy cosmic ray experiment where a liquid hydrogen (H2) target had been used was the well known Echo Lake experiment (Jones et al., 1970, 1972).

  18. 18.

    So far no Centauro type events (Lattes et al., 1973; Bellandi et al., 1979) have been discovered in machine experiments (Alner et al., 1987) and neither so-called co-planar (co-linear) events (Slavatinski, 2003), nor the long flying component (Dremin et al., 1990; Yakovlev, 2003, 2005; Dremin and Yakovlev, 2006). Recently, Centauro-I had been re-analyzed by Ohsawa et al. (2004, 2006). A flaw in the initial scanning procedure had been discovered but the essential result, the unique gamma ray deficit, remains.

  19. 19.

    Large p t phenomena were unknown at that time.

  20. 20.

    In some cases the reconstruction of an event suggested a single emission center.

  21. 21.

    This model was actually first studied by Fermi (1950, 1951, 1953, 1954), Heisenberg (1949a, b), Landau and Pomeranchuk (1953a, b), and Belenkii and Landau (1956).

  22. 22.

    In the initial formulation of the CKP model it was assumed that all secondaries are pions.

  23. 23.

    For deeper insight the interested reader is referred to the books of Khristiansen (1980); Gaisser (1992), Rao and Sreekantan (1998), and references listed therein.

  24. 24.

    For details see the brief historical overview given in Sect. 4.6.

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Grieder, P.K. (2010). Hadronic Interactions and Cascades. In: Extensive Air Showers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76941-5_3

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