I Evaluating Scattering Integral

1. Apr 1, 2016

Waxterzz

Hi,

I really don't have a clue to solve this.

I tried something like the dirac function identity:

But then I saw it's dk' not dk' and couldn't got it straight.

Can someone help me with this?

2. Apr 1, 2016

Staff: Mentor

As it is said, you have to change to spherical coordinates. The Dirac delta will then only affect the integral over r.

3. Apr 1, 2016

Waxterzz

I don't see it. dk' is not a volume element?

4. Apr 1, 2016

Waxterzz

dk' is a vector. Then I have an integral comprising of 3 terms each involving unit vectors.

I really don't have a clue.

5. Apr 1, 2016

Waxterzz

Wait wait, I am extremely confused.

I just have to integrate over the k' first?

6. Apr 1, 2016

Waxterzz

Mr
6 hours and I still have no clue, can you please hold my hand and solve it with me. I mean, just say what I have to do, I will solve it, but give me instructions.

I mean what's the deal with the dirac function and the dk', it's supposed to be a volume element and the dirac term, why isnt it delta(k-k')

7. Apr 1, 2016

blue_leaf77

$d\vec{k}$ is a volume element. Write it as a volume element in spherical coordinate. To make the integrand even more transparent, use the cosine law to express $|\vec{k}-\vec{k'}|^2$ in terms of $k$, $k'$, and $\theta$.

8. Apr 1, 2016

Waxterzz

How come dk' is a volume element, it's the derivative of a vector. Most textbooks, the volume element is called a d tau or a dV

My head is a mess. It's like I completely forgot how to calculus.

Good news: I know I'm wrong.

Really don't see it

9. Apr 1, 2016

Staff: Mentor

What happened to the Dirac delta? You should do the integral over k' first.

10. Apr 1, 2016

Staff: Mentor

It's not a derivative, it is an infinitesimal vector element.

11. Apr 1, 2016

Waxterzz

It's been this the whole time?, with r being k'

Ps: After this I'm going to finally learn LaTeX

12. Apr 1, 2016

blue_leaf77

Why did the Dirac delta disappear in the second equation from the last one?

13. Apr 1, 2016

Waxterzz

This is what I got uptil now, but I have to leave.

Thanks for help, give me feedback if you want to, and I will post update when I'm back, probably tomorrow. Thanks for the patience anyway!!

14. Apr 18, 2016

Waxterzz

Hi,

Hope this is somewhat more clear, because last post was a bit messy. Still haven't learned LaTex.

Is this valid?

I couldn't evaluatie the last integral, because of the square.

Do I need to use partial fractions?

Thanks

15. Apr 18, 2016

Waxterzz

Hi myself,

I found out I need to include something like 1- ( stuff going in the z direction after k scattering) / (stuff that would go in z direction if there was no scattering at all), so 1 - k' projected on z axis /k = 1 - (k cos theta) / k

Yes, I'm a noob.

So I'll start over. :')