# Scattering in a central potential

• Logarythmic
In summary, the conversation discusses how to compute the differential scattering cross section for scattering in a central potential using classical mechanics. The technique is based on Rutherford's approach to alpha particles scattered on a Coulomb potential created by gold atoms. The first resource suggested is Appendix #9 from Max Born's "Atomic Physics", followed by a Google search for additional resources. The inverse cubic force mentioned is not the same as the inverse square force used in the technique. The book "Classical Mechanics" by Goldstein is also mentioned as a resource for deriving the Rutherford cross section.
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?

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? ;)

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.

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

## 1. What is scattering in a central potential?

Scattering in a central potential refers to the phenomenon of particles interacting with a central force field and being deflected in different directions as a result.

## 2. How does scattering in a central potential occur?

Scattering in a central potential occurs when particles, such as atoms or subatomic particles, come into contact with a central force field, such as an electric or gravitational field, and are deflected due to the force exerted on them.

## 3. What are the factors that affect scattering in a central potential?

The factors that affect scattering in a central potential include the strength of the central force field, the mass and velocity of the particles, and the distance between the particles and the center of the force field.

## 4. What is the difference between elastic and inelastic scattering in a central potential?

Elastic scattering refers to the scattering of particles in which their kinetic energy and momentum are conserved, while inelastic scattering involves a transfer of energy and momentum between the particles and the central force field.

## 5. What are the applications of scattering in a central potential in scientific research?

Scattering in a central potential is used in a variety of scientific research fields, including nuclear physics, astrophysics, and materials science. It allows scientists to study the properties and interactions of particles, as well as the nature of central force fields.

Replies
1
Views
883
Replies
1
Views
1K
Replies
5
Views
1K
Replies
2
Views
2K
Replies
6
Views
2K
Replies
1
Views
2K
Replies
11
Views
1K
Replies
2
Views
875
• Quantum Physics
Replies
5
Views
628