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Coupling Functions, Integral Multiplicities, and Inverse Transformations

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Cosmic Rays in the Earth’s Atmosphere and Underground

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 303))

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Abstract

The intensity of any CR component of type (e.g. total neutron counting rate and different neutron multiplicities, muon component on the ground and underground at different depths and different directions, electron-photon component, frequency of External Atmospheric Showers (EAS), and others), observed at cut off rigidity R c (t) at the level h o (t) in the atmosphere at some moment of time t can be determined from

$$ N_i \left( {R_c \left( t \right),h_0 \left( t \right),t} \right) = \int\limits_{R_c \left( t \right)}^\infty {D\left( {R,\,t} \right)m_i \left( {R,h_0 \left( t \right),g\left( t \right),T\left( {h,t} \right),E\left( {h,t} \right)} \right)dR} $$
(3.1.1)

. Here D(R,t) is the primary CR spectrum out of the atmosphere, and m i (R, h o (t), T (h, t), E(h, t)) is the integral multiplicity (number of total secondary CR particles of type i generated from one primary particle with rigidity R), which depends on the mass of air h o (t) in the vertical column under the point of observations. (Note that atmospheric pressure is usually used instead of vertical column mass. This is correct only if the velocity of the wind is zero or very small. Otherwise it is necessary to take into account the Bernoulli effect; see Chapter 6 for details). The integral multiplicity depends also on the value g(t) of gravitational acceleration which is a function of the latitude and varies with time because of the gravitational influence of the Moon and the Sun, and on the vertical distribution of air temperature T(h,t) and atmospheric electric field E(h,t).

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  1. Israel Cosmic Ray Center, Space Weather Center, and Emilio Segrè Observatory, Tel Aviv University, Israel Space Agency, and Technion, Qazrin, Israel

    Lev I. Dorman

  2. Cosmic Ray Department of IZMIRAN, Russian Academy of Science, Troitsk, Russia

    Lev I. Dorman

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Dorman, L.I. (2004). Coupling Functions, Integral Multiplicities, and Inverse Transformations. In: Cosmic Rays in the Earth’s Atmosphere and Underground. Astrophysics and Space Science Library, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2113-8_3

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