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Form Factor for Scattering (like muons off of protons)

  1. Jan 7, 2019 #1
    1. The problem statement, all variables and given/known data
    Form factor.png

    2. Relevant equations
    N/A

    3. The attempt at a solution
    I am trying to complete the last part of this question, part 5(c). My professor has told me that the form factor $$F(q)\rightarrow1$$ as $$q\rightarrow0$$ but I am unsure how to show this.

    I believe that $$\lim_{{q }\rightarrow0} \frac{\sin\left( qRh/\hbar\right)}{q^3}=\infty,$$ and $$
    \lim_{{q }\rightarrow0} \frac{\cos\left( qRh/\hbar\right)}{q^2}=\infty.$$ Is someone able to please show me where I am going wrong? Thanks.
     
    Last edited by a moderator: Jan 7, 2019
  2. jcsd
  3. Jan 7, 2019 #2

    mjc123

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    Consider the term in brackets. Express sin x and cos x as power series in x, and evaluate this term as far as q2.
     
  4. Jan 13, 2019 #3
    Thanks for the help. I discovered that I had to express sinx in powers up to q3 to solve correctly.
     
  5. Jan 14, 2019 #4

    mjc123

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    Yes, but as the sin term is divided by q, the whole term in brackets goes up to q2. That's what I meant.
    The key point is that if you treat the sin and cos terms separately, they both tend to infinity, but the whole term does not.
     
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