Form Factor for Scattering (like muons off of protons) (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 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.
 

Attachments

Last edited by a moderator:

mjc123

Science Advisor
671
293
Consider the term in brackets. Express sin x and cos x as power series in x, and evaluate this term as far as q2.
 
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

Science Advisor
671
293
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.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top