The Universe contains two types of electromagnetic radiation:

(a) the €˜micro-wave background€™ at T = 3 K, corresponding to photon energies E _{γ, 3K} ‰ˆ 1 meV,

(b) The Extra galactic Background Light (EBL) due to the stars, with a spectrum that is mainly in the infrared. The Universe is opaque to photons whose energy is such that the cross-section for pair production γ + γ †’ e⁺ + e^- is large. This already happens just above threshold

.

Compute the two threshold energies, assuming in the second case the photon wavelength λ = 1 μm.

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Cosmic Ray Spectra of Various Experiments 104 +. LEAP - eatellite 102 Proton - satelite (1 particle/m²-sec) Yakustk - ground array Haverah Park - ground array 101 Akeno - ground array AGASA - ground array Fly's Eye - air fluorescence 는 104 HIRes1 mono air fluorescence HIRES2 mono - air fluorescence HIRES Stereo - air fluorescence 107 Auger · hybrid 1010 Knee (1 particle/m-year). 10 13 10 16 10 19 1022 Ankle (1 particle/km-year). Courtesy Walter Hanlton 1025 ......CR Utah (1-particle/km-century) 10 28 .... 10° 1010 1011 1o12 1013 1014 1015 1015 1017 1018 1019 1020 Energy (ev) Flux (m? sr GeV sec)'