Form Factor for Scattering (like muons off of protons)

[Martin89]

Homework Statement

Homework Equations

N/A

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.

 

[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.

 

[Martin89]

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

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

 

[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.