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

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Homework Help Overview

The discussion revolves around computing the differential scattering cross section for a particle scattering in a central potential described by V(r) = k/r², with references to classical mechanics and historical approaches such as Rutherford's scattering theory.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss mimicking Rutherford's approach to scattering problems and seek resources for calculations. There are questions about the applicability of techniques for different types of forces, specifically contrasting inverse cubic and inverse square forces.

Discussion Status

The discussion is ongoing, with participants sharing resources and references. Some express difficulty in understanding the material, while others suggest alternative sources and approaches without reaching a consensus on the best method to compute the cross section.

Contextual Notes

There is mention of specific texts and resources that may not be accessible to all participants, which could impact their ability to engage fully with the problem. Additionally, there is a noted confusion regarding the type of potential being analyzed.

Logarythmic
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How can I compute the differential scattering cross section [tex]\sigma (\theta) d \theta[/tex] for scattering in the central potential
[tex]V(r) = \frac{k}{r^2}[/tex]
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.
 
Last edited by a moderator:
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.
 
  • #10
That's the book I'm using but it seems like I don't understand it.
 

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