The proton elastic form factor (nuclear physics)

[Liquidxlax]

Homework Statement

The elastic form factors of the proton are well described by the form

G(q²) = [itex]\frac{G(0)}{(1 + (\frac{q^{2}}{0.71})^{2}}[/itex]

with q^w in GeV². Show that an exponential distribution in the proton given by

ρ(r) = ρ_oe^-λr

Homework Equations

thought it to be the simple integral

The Attempt at a Solution

The integral

G(q²) = ∫∫∫ ρ(r)*e^(-iqrcosθ)*r²sinθ*drdθd∅

phi is 0 to 2pi

theta is 0 to pi

r is 0 to ∞

the problem is the r integral

G(q²) = a∫ r*sin(qr)*e^(-λr)

a are the constants combined into 1 term

I've done a problem similar with the Yukawa potential, but the Yukawa potential eliminated the r next to the sin(qr) which made it solvable.

not sure if i have done something wrong or what.

any help would be appreciated

 

[mark726]

Thank you for your post regarding the elastic form factors of the proton. It seems that you are trying to connect the given form factor equation to the exponential distribution in the proton. I can see that you have attempted to use an integral to solve this problem, but it seems that you are having trouble with the r integral.

Firstly, I would like to point out that the given form factor equation is in terms of q^2, not q. This may be causing some confusion in your integration. Also, the form factor equation is not a standard probability distribution, so it may not be appropriate to use it in the context of an exponential distribution.

If you are trying to show a connection between the two equations, I would suggest looking at the Fourier transform of the exponential distribution, which would give you a form similar to the form factor equation. However, I would also recommend consulting with your professor or classmates for further guidance on this problem.

I hope this helps. Good luck with your studies!