Differential cross section/simple integral

[jonwell]

At least it should be a simple integral...

Homework Statement

The whole text is here- http://i35.tinypic.com/2nisnp.jpg

Basically (I think) I need to integrate the differential over all angles theta and phi, and get sigma(naught) back out.

Homework Equations

given in pic

The Attempt at a Solution

If I use the given substitution and integrate I get log(tan(pi/2)) which is log(0) which is broken... I don't really know where to go other than that.

Thanks! Been reading the forum for a long time but this is my first question :)

 

[gabbagabbahey]

You shouldn't be getting any Log terms when you integrate; if you show me your work, I can tell you where you are going wrong.

 

[jonwell]

I substitute sin(theta) for d(omega), and the integral for 1/sin(theta) is log(tan(theta/2)) at least as given by mathematica and the back of my book.

I kind of figured I shouldn't be getting that, which is what makes me think I'm approaching the problem all out of whack.

 

[gabbagabbahey]

You should be substituting $sin(\theta) d \theta d \phi$ for $d \Omega$ not just $sin(\theta)$...$d \Omega$ is a differential, $sin(\theta)$ is just a function...you should have:

$$\frac{d \sigma}{d \Omega}=\frac{d \sigma}{sin(\theta) d \theta d \phi}=\frac{\sigma_0}{4 \pi}$$

$$\Rightarrow d \sigma=\frac{\sigma_0}{4 \pi} sin(\theta) d \theta d \phi$$

...do you follow?

Then just integrate both sides of the equation.

 

[jonwell]

You should be substituting $sin(\theta) d \theta d \phi$ for $d \Omega$ not just $sin(\theta)$...$d \Omega$ is a differential, $sin(\theta)$ is just a function...you should have:

$$\frac{d \sigma}{d \Omega}=\frac{d \sigma}{sin(\theta) d \theta d \phi}=\frac{\sigma_0}{4 \pi}$$

$$\Rightarrow d \sigma=\frac{\sigma_0}{4 \pi} sin(\theta) d \theta d \phi$$

...do you follow?

Then just integrate both sides of the equation.

I figured it was something simple. I follow perfectly, thank you very much :)

[...I need to figure out that LaTeX code stuff, that's pretty cool.]

 

[gabbagabbahey]

Your welcome. There's an introduction to LaTeX here