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Neutrino absorption in the Earth

Neutrinos with energies above a several TeV have a non-negligible probability to undergo a charged current interaction in the Earth before reaching the vicinity of the detector. The Earth is therefore opaque to very high energy neutrinos.

The amount of matter $\varrho$ that the neutrino encounters while traversing the Earth was taken from [#!Gandhi:1996tf!#] and is shown in figure 3.3 as a function of the zenith angle $\theta $. The column density seen by neutrinos with $\theta>145^{\circ}$ is enhanced due to the increased density of the Earth's core. The probability that the neutrino survives its journey through the Earth, $\pearth $, is given by

\begin{displaymath}
\pearth (E,\theta) = e^{-{\varrho(\theta)} N_A \sigma(E) }
\end{displaymath} (30)

and is shown in figure 3.3(right) as a function of the energy and zenith angle of the neutrino. As was mentioned in section 3.1, this probability is taken into account when in the calculation of the expected event rate.

Neutral current interactions of neutrinos in the Earth will result in a decrease in energy and a deviation of original direction. At the relevant energies, the neutral current cross-section is about a factor 2 smaller than the charged current cross-section. A rough estimate of the fraction of neutrinos undergoing a NC interaction but not a CC one, yields 15 % at most. This effect has been neglected.

Figure 3.3: Left: The density of the Earth, integrated over the path of the neutrino as a function of the direction of the neutrino expressed in water equivalent kilometres. The kink in the figure is caused by the density discontinuity associated with the boundary of the Earth's core. Right: The probability of a neutrino to traverse the Earth without undergoing an interaction as a function of the direction (zenith angle) of the neutrino and its energy.
\includegraphics [width=\figsize]{tools/figs/earth_pathlength.eps} \includegraphics [width=\figsize]{tools/figs/pearth.eps}


next up previous contents
Next: Muon propagation Up: Event generation Previous: Composition of the interaction   Contents
Aart Heijboer
2004-03-21