hw9 - Physics 226 Assignment#9(Final HW Due FRIDAY June 3...

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Physics 226 Assignment #9 (Final HW) May 15, 2016 Due FRIDAY , June 3, 2016 1. There are strong reasons to believe that very high energy cosmic rays reaching the Earth originate outside our galaxy, and are mostly protons. As one of these protons propagates through space, it can scatter off photons of the 3 cosmic microwave background. Such photons have energies of about k B T , where k B is Boltzmann’s constant and T 3K. [Recall that kT at room temperature ( 300 K ) is about 1 40 eV.] (a) Photons in the microwave background are travelling in all directions. However, for simplicity, assume that our cosmic ray proton collides head-on with a microwave background photon (i.e. they are going in opposite directions). What is the smallest proton energy E min needed for such scattering to produce a π 0 plus a proton? In other words, when can the reaction p + γ p + π 0 occur? [Hint: If the required energy is very large compared to the proton rest energy, you can neglect relative corrections suppressed by the ratio of the proton rest energy to its total energy.] (b) A cosmic ray proton undergoing such a scattering event will typically lose 10% or more of its energy. Explain why this process may produce an upper limit (known as the GZK cutoff) on the observed cosmic ray spectrum at an energy of E min . What would observation of such a cutoff in the energy spectrum imply about the source of high energy cosmic rays? 2. In this question assume that m u = m d , so that the strong interactions exactly conserve isospin, implying that the initial and final states of each process must have the same total isospin and the same total I z .
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