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Elastic scattering question

  1. Nov 6, 2016 #1
    1. The problem statement, all variables and given/known data
    An electron collides with a particle with mass M at rest and scatters elastically through an angle θ (assume electron mass negligible).
    Show that the fraction of energy lost by the e- is:

    (Ee - Ee')/Ee = 1/[1+ Mc2/Ee(1-cosθ)]

    2. Relevant equations
    Conservation of Energy: Ee + Mc2 = Ee' + EM
    Conservation of momentum: Pe = Pe' + PM

    E2 = P2c2 + M2c4

    or for electron since mass negligible, E=Pc

    Previous parts of the questions required the rearrangements of these to get:
    PM2 = 1/c2[Ee2 +Ee'2 - 2EeEe'cosθ]

    3. The attempt at a solution
    I've tried to solve this so many times but the closest I can get is:

    (Ee - Ee')/Ee = Ee'(1-cosθ)/Mc2

    I don't know if I'm missing some kind of relation I can use to sub in Ee' for Ee because in the final expression I'm trying to get there seems to be way more Ee's than I would expect.

    I've also tried working backwards to find out what I'm missing from the answer but I just don't see it.

    I think I have tunnel vision from trying this so often and can't see another way, so thank you in advance for any help, it's greatly appreciated!
     
  2. jcsd
  3. Nov 6, 2016 #2

    mfb

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    Your situation is equivalent to Compton scattering (just with different particles), you should find derivations for this in textbooks and websites.
     
  4. Nov 6, 2016 #3

    vela

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    You're not missing any physics here. It's just algebra. Starting from the expression you got, solve for ##E_e'## in terms of ##E_e##, ##\theta##, and ##M##. Then plug the result into ##(E_e-E'_e)/E_e## and simplify.
     
  5. Nov 6, 2016 #4
    I hope this is helpful.
     

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