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Rutherford scattering problem

  1. Oct 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Alpha particle with kinetic energy 6MeV is scatterd on gold nucleus (A=197).
    Is Rutherford cross-section formula valid for this scattering? Explain !


    2. Relevant equations



    3. The attempt at a solution
    The Coulomb barrier is Ec=(1.03MeV)*(Z1*Z2)/(A1^1/3+A2^1/3)
    Z1=79 , Z2=2 , A1=197 , A2=4
    Ec=1.03MeV*158/7.41=22MeV
    The 6 Mev alpha particle will not go through the barrier, forces between alpha particle and gold nucleus will be coulombic so I think it is valid to use Rutherford cross-section.
    But I found that Rutherford cross-section formula is valid if
    [tex]Z1*Z2*\alpha<<1[/tex] is true.Since for Z1=79,Z2=2,alpha=1/137 this is not <<1 ,
    so rutherford cross-section is not valid.
    Where I'm going wrong?
     
  2. jcsd
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