How to Compute Differential Scattering Cross Section in a Central Potential?

[Logarythmic]

How can I compute the differential scattering cross section $$\sigma (\theta) d \theta$$ for scattering in the central potential
$$V(r) = \frac{k}{r^2}$$
using classical mechanics?

 

[dextercioby]

Ever seen Rutherford's approach to alpha particles scattered on a Coulomb potential made by the gold atoms ?

Just mimick the computations.

Daniel.

 

[Logarythmic]

If you mean the Geiger-Marsden experiment, I have read about it but never seen any calculations. Any tip on where I can find it?

 

[dextercioby]

Appendix #9 from Max Born's "Atomic Physics" is the first i could come up with.

Daniel.

 

[Logarythmic]

Well, that book is not a part of my collection so can you help me in any other way? ;)

 

[dextercioby]

Google for it. Here http://www.du.edu/~jcalvert/phys/ruther.htm

http://www2.kutl.kyushu-u.ac.jp/seminar/MicroWorld1_E/Part2_E/P25_E/Rutherford_scattering_E.htm

Daniel.

 

[Logarythmic]

Sorry, I can't figure this out. This is an inverse qubic force, not an inverse square force.

 

[dextercioby]

Yes, but the technique is the same.

Daniel.

 

[Meir Achuz]

Goldstein's "Classical Mechanics" derives the Rutherford cross section.

 

[Logarythmic]

That's the book I'm using but it seems like I don't understand it.