Consider two counter-rotating beams of electrons and positrons stored in the LEP collider both with energy E_e = 100 GeV. The beam intensity slowly decays due to beam–beam interactions and various types of losses. One of the losses (very small indeed) may be the interaction of the electrons with the photons of the cosmic microwave background. Assume the photon energy E_γ = 0.25 meV and a photon density ρ = 3 x 10⁸ m^-3. 

(a) Evaluate the energy for a photon E_γFT against an electron at rest to have the same CM energy. 

(b) Assuming the Thomson cross section 

evaluate the interaction length and the corresponding time. Considering that N_e = 1.6 x 10¹² electrons are stored in each ring, determine the rate of the considered events in the whole ring. Take the average value cos θ = 0 for the angle between the initial photon and the beam. 

(c) Determine the energy or the photons that scatter backward at 180° after a head-on collision.

Transcribed Image Text:

aħ 7.9 x 10-30 m2 mec