# Form Factor for Scattering (like muons off of protons)

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1. Jan 7, 2019

### Martin89

1. The problem statement, all variables and given/known data

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. Jan 7, 2019

### mjc123

Consider the term in brackets. Express sin x and cos x as power series in x, and evaluate this term as far as q2.

3. Jan 13, 2019

### Martin89

Thanks for the help. I discovered that I had to express sinx in powers up to q3 to solve correctly.

4. Jan 14, 2019

### mjc123

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.