# Strong force, low energy proton scattering

1. Jan 7, 2008

### opous

1. The problem statement, all variables and given/known data

A beam of low energy protons is observed to scatter elastically from a target of neutrons. Sketch the variation of the differential cross section with the resulting scattering angle and comment on a characteristic feature of the strong force than can be deduced.

2. Relevant equations

N/A

3. The attempt at a solution

I've attached a graph of what I think this looks like, roughly (differential cross section y (mb/sr), angle x (deg))

However I'm more interested in the second part of the question... all I have in my notes here is that the "strong force matter distribution is well fit by a Saxon-Woods potential", but that doesn't tell me what characteristic the graph is highlighting. Can anyone familiar with this area suggest anything? Thanks in advance

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2. Jan 8, 2008

### malawi_glenn

Your text book in nuclear physics does not cover wood saxon and scattering? Can you tell me what book you use?

A wood saxon potential is on the form:
$$V(r)=\dfrac{-V_0}{1+\exp ((r-a)/R)}$$

where V_0 is a constant, a is the "thickness" and R is the half density radius. You can plug this in and play with the paramaters to get a feeling. This potential is used since one model is that the nuclear matter have this distribution. So you can set the nuclear matter distribution equal to the wood-saxon, but remove the minus sign in front.

Now the differential cross section into play. You can straight forward solve this by the Born approximation. That is the often the first relation we learn how to relate the potential with the diff cross section.

Try find something in your text book how to relate differential cross sections with the potential. =)

3. Jan 8, 2008

### pam

That graph looks more like scattering from a nucleus than a neutron.
The wiggles look like diffraction bumps that are related to scattering from a hard core or a W-S potential which smooths the hard core a little.

4. Jan 8, 2008

### malawi_glenn

And a target of neutrons are pretty hard to create..

5. Jan 9, 2008

### opous

I'm using Das and Ferbel Intro. To Nuclear and Particle Physics (II ed). I'm aware of the Wood-Saxon potential and it's uses in describing these models, I was trying to express that I'm unsure how it's related to a characteristic of the strong force. ie, is the graph telling me that the strong force is short ranged? strong? saturating? I'm not at all sure how I'm supposed to decipher the property...

6. Jan 9, 2008

### malawi_glenn

For the properties of the strong force you want to perform p-n scattering, and differential cross section for this has nothing to do with wood saxon as I know of it.

As Pam pointed out, your diff cross section looks more like a cross section for proton/electron scattering of a nucleus.

7. Jan 9, 2008

### opous

^ Oh, I do apologise. I was misreading your post. I probably didn't express my original point very clearly. The graph I attached there wasn't included in the question, it was simply the only one I could find which had the required axes (differential xs/angle) and mentioned scattering (labelled "scatter low energy neutrons (14MeV), the SF matter distribution is well fit by Saxon-Wells").

I'm afraid I'm not very au fait with the cross section beyond the loose definition of it describing the probability of an interaction.

From a textbook I see that

$$\frac{d \sigma}{d \Omega} = \left(\frac{zZe^_2}{8\pi \epsilon_{0}\mu v^{2}_{1}}\right)^{2} cosec^{4}(\theta / 2)$$

8. Jan 9, 2008

### malawi_glenn

what is "Saxon-Wells" ?

I still cant see the purpose of this task and what they want from you, since you cant make a material with just neutrons, so in order to derive information about the strong force you do free n + p scattering.

But IF you could, then the potential will be somthing like wood-saxon, just as in the nucleus.
And the graph that you have posted looks like (as Pam said) a differential cross section from a wood saxon potential.