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

AI Thread Summary
To compute the differential scattering cross section σ(θ) dθ for a central potential V(r) = k/r² using classical mechanics, one can draw parallels to Rutherford's scattering approach. The Geiger-Marsden experiment is referenced as a foundational example, with suggestions to consult Max Born's "Atomic Physics" for detailed calculations. However, alternative resources are provided for those unable to access the book, including online links for further reading. The discussion highlights the challenge of applying techniques from inverse square forces to inverse cubic forces, while emphasizing that the underlying methodology remains similar. Mastery of these concepts may require additional study, particularly from Goldstein's "Classical Mechanics."
Logarythmic
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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?
 
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Ever seen Rutherford's approach to alpha particles scattered on a Coulomb potential made by the gold atoms ?

Just mimick the computations.

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

Daniel.
 
Well, that book is not a part of my collection so can you help me in any other way? ;)
 
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.
 
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Sorry, I can't figure this out. This is an inverse qubic force, not an inverse square force.
 
Yes, but the technique is the same.

Daniel.
 
Goldstein's "Classical Mechanics" derives the Rutherford cross section.
 
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That's the book I'm using but it seems like I don't understand it.
 
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