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Solid Angle Rutherford Scattering

  1. Jan 8, 2015 #1
    1. The problem statement, all variables and given/known data
    derive an equation for the solid angle for a Rutherford scattering detector given a detcor window area of [itex]A[/itex] and a distance to the detector of [itex]D[/itex] for some scattering angle [itex]\phi[/itex] given that [itex]d\Omega =2\pi sin\phi d\phi[/itex]

    2. Relevant equations
    [itex]d\Omega =2\pi sin\phi d\phi[/itex]
    [itex]A=Dd\phi [/itex]
    3. The attempt at a solution
    integrating [itex]d\Omega =2\pi sin\phi d\phi[/itex] to get solid angle gives [itex]\Omega =\frac{2\pi A}{D}\int sin\phi d\phi[/itex] howver this gives a negative value due to the integral of sine and shouldn't soild angle be positive? Is this correct or am i missing a step? Thank You
     
  2. jcsd
  3. Jan 8, 2015 #2

    BvU

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    You sure this gives a negative value ? Can you show how you get it ? Bounds, primitive ?
     
  4. Jan 8, 2015 #3

    haruspex

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    That's dimensionally incorrect. You have an area on the left and a distance on the right. And the dϕ looks wrong.
    Shouldn't it be ##A = D^2d\Omega##?
    As BvU posted, your problem with the negative sign will resolve itself when you put in the bounds on ϕ.
     
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