homework03 - momentum) ±rame. And is almost trivial i±...

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Phys 221 Homework III Due: Due Friday, February 10 1. Harris 3.14 2. Harris 3.23 3. Harris 3.26 4. Gamma Ray Cutof Let’s per±orm an estimate o± the cutof in the spectrum o± high-energy photons ( γ ’s) received at earth. The universe is permeated with radiation le±t over ±rom the Big Bang, the Cosmic Background Radiation (CBR). Gamma ray scattering of the CBR into e + e - pairs down- grades their energy. The CBR spectrum is a nearly per±ect blackbody with T =2 . 7 K. Con- sider a cosmic ray γ colliding with one o± these CBR photons, taking as a representative CBR γ the peak o± the blackbody distribution ±rom the Wien Law: λ max T =2 . 898 × 10 - 3 m · K . What is the minimum energy (in GeV) o± the cosmic ray γ (in the rest ±rame o± the galaxy) to produce a e + e - pair ±rom a direct collision with such a CBR γ ?( m e + c 2 = m e - c 2 = . 511 Mev). Hint : The problem can be simpli²ed by also considering the collision in the CM (center o±
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Unformatted text preview: momentum) ±rame. And is almost trivial i± you use 4-momenta and invariance. 5. Obtain Eq 3-8 in Harris by either doing problem 3.38, or, and this is easier (i± you don’t mind working in 4 dimensions): Write the 4-momentum conservation law ±or this problem as ˜ p e + ˜ p γ = ˜ p ± e + ˜ p ± γ . Take the momentum o± the ²nal state photon over to the other side ˜ p e + ˜ p γ-˜ p ± γ = ˜ p ± e . And “square” both sides (take the dot-product o± each side w/itsel±). You will ²nd that the algebra is very simple (the squares o± the individual 4-momenta are either 0 or ( m e c ) 2 , the crossterms present some small complexity). 6. Harris 3.33 7. Harris 3.43 8. Harris 3.46 Course Web Site: http://www.phys.cwru.edu/courses/p221/ $Date: 2012/02/04 19:04:36 $...
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This note was uploaded on 03/02/2012 for the course PHYS 221 taught by Professor Glob during the Spring '12 term at Case Western.

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