Science Homework Help

CH1: The Particles- Macroscopic to Subatomic

question: Repeat Example 1.1 but for a cosmogenic neutrino. Assume isotropy.

here is example 1.1: Estimate the ratio of atmospheric neutrinos to incoming cosmic rays of the same energy.

From Figure 1.10, there is a peak in the curve for atmospheric neutrinos around 108 eV so we will adopt this energy for a comparison with CRs. At higher and lower energies, the number of atmospheric neutrinos declines rapidly (note the logarithmic scale) so this energy should be sufficient for a rough estimate. From the figure, we read that there are ≈10−8 neutrinos eV−1 cm−2 s−1. Conversion to ‘per GeV’ gives us 10 neutrinos GeV−1 cm−2 s−1 and to ‘per square metre’ gives 105 neutrinos GeV−1 m−2 s−1. Atmospheric neutrinos are isotropic since they can pass through the ‘transparent’ Earth. We can therefore divide by 4 (see Appendix B of the online material) to convert to a value per unit solid angle (‘per steradian’) to find ≈8 × 103 neutrinos GeV−1 m−2 s−1 sr−1 . We can now compare this value to CRs as given in the same units in Figure 1.8. At the same energy, there are ≈104 GeV−1 m−2 s−1 sr−1 incoming CRs. Thus, the ratio is close to one as a rough estimate.

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