Definition of Common Observables

In the following we have adopted the notation used by Rossi (1948), which has been widely accepted in the literature.

1.6.1 Directional Intensity

The directional intensity, Ii(9,0), of particles of a given kind, i, is defined as the number of particles, dNi, incident upon an element of area, dA, per unit time, dt, within an element of solid angle, dO (Fig. 1.14). Thus,

Apart of its dependence on the zenith angle 6 and azimuthal angle <f>, this quantity also depends on the energy, E, and at low energy on the time, t. The time dependence is discussed in Section 1.8 and Chapter 6. Frequently, directional intensity is simply called intensity. Either the total intensity integrated over all energies, 7,(0, > E,t), or the differential intensity,

Electron- Hadran Muon

Photon Component Component

Component

Figure 1.12: Cascade shower: Schematic representation of particle production in the atmosphere. Shown is a moderately energetic hadronic interaction of a primary cosmic ray proton with the nucleus of an atmospheric constituent at high altitude that leads to a small hadron cascade. In subsequent collisions of low energy secondaries with atmospheric target nuclei, nuclear excitation and evaporation of target nuclei may occur. Unstable particles are subject to decay or interaction, as indicated, and electrons and photons undergo bremsstrahlung and pair production, respectively. For completeness neutrinos resulting from the various decays are also shown. Note that the lateral spread is grossly exaggerated.

Electron- Hadran Muon

Photon Component Component

Component

Figure 1.12: Cascade shower: Schematic representation of particle production in the atmosphere. Shown is a moderately energetic hadronic interaction of a primary cosmic ray proton with the nucleus of an atmospheric constituent at high altitude that leads to a small hadron cascade. In subsequent collisions of low energy secondaries with atmospheric target nuclei, nuclear excitation and evaporation of target nuclei may occur. Unstable particles are subject to decay or interaction, as indicated, and electrons and photons undergo bremsstrahlung and pair production, respectively. For completeness neutrinos resulting from the various decays are also shown. Note that the lateral spread is grossly exaggerated.

Ii(9,4>, E, t), can be determined. For 0 = 0° the vertical intensity Iv,i = Ii(0°) is obtained.

0 200 400 600 800 1000 1200 Atmospheric Depth [ g cm"2 ]

Figure 1.13: Altitude variation of the main cosmic ray components.

The flux, Jij, represents the number of particles of a given kind, z, traversing in a downward sense a horizontal element of area, dA, per unit time, dt. Dropping the subscript i, is related to I by the equation where fl signifies integration over the upper hemisphere (9 < 7r/2). If not specified otherwise the flux Ji is usually meant to be the integral flux J\ (> E).

1.6.3 Omnidirectional or Integrated Intensity

The omnidirectional or integrated intensity, J2, is obtained by integrating the directional intensity I over all angles,

1.6.2 Flux

0 0

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