# Goldstein Central Force Repulsive Scattering

• decerto
In summary, on page 108 in Goldstein 3rd edition, it is stated that the function ##\psi## can be derived from the orbit equation (3.36) by setting the limits as ##r_0=\infty##, ##r=r_m##, and ##\theta_0=\pi##. In the accompanying diagram, the angle being calculated, ##\theta##, appears to be the same as ##\psi##, but the author notes that ##\psi=\pi-\theta##. This is because when starting at ##r=\infty## and ##\theta=\pi## and moving to ##r=r_m##, the corresponding angle traced out is ##\theta=\psi##.
decerto
On page 108 in Goldstein 3rd edition in the paragraph after equation (3.94) he says that ##\psi##` can be obtained from the orbit equation (3.36) using the limits as ##r_0=\infty## ##r=r_m## which the distance of closest approach and ##\theta_0=\pi## which is the initial direction.

So looking at the diagram on the top of the page this angle he is calculating ##\theta## seems to me to be exactly ##\psi## but he says that ##\psi=\pi-\theta##

When we start at ##r=\infty , \theta = \pi## and move to ##r=r_m## on the diagram the corresponding angle traced out is ##\theta=\psi## where am I going wrong/The book is here for anyone who doesn't have it.

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decerto said:
When we start at r=∞,θ=πr=\infty , \theta = \pi and move to r=rmr=r_m on the diagram the corresponding angle traced out is θ=ψ\theta=\psi where am I going wrong/
You start out at an angle of ##\pi## and trace out an angle ##\psi## so you must end up at an angle ##\pi-\psi##.

## 1. What is the Goldstein Central Force Repulsive Scattering?

The Goldstein Central Force Repulsive Scattering is a concept in classical mechanics that describes the motion of a particle under the influence of a central repulsive force, such as the Coulomb force between two charged particles.

## 2. How is the Goldstein Central Force Repulsive Scattering different from other scattering processes?

The Goldstein Central Force Repulsive Scattering is unique because it involves a central force that is always directed radially outwards from the center. This results in a specific type of trajectory for the scattered particle.

## 3. What are the key equations involved in the Goldstein Central Force Repulsive Scattering?

The key equations involved in the Goldstein Central Force Repulsive Scattering include the central force equation, which describes the force acting on the particle, and the equation of motion, which describes the trajectory of the particle.

## 4. What are some real-world applications of the Goldstein Central Force Repulsive Scattering?

The Goldstein Central Force Repulsive Scattering has applications in various fields, including nuclear physics, atomic physics, and astrophysics. It is used to understand the behavior of particles in scattering experiments and to study the structure of atoms and nuclei.

## 5. What are some limitations of the Goldstein Central Force Repulsive Scattering model?

The Goldstein Central Force Repulsive Scattering model assumes that the scattered particle is a point mass and that the central force acting on it remains constant throughout the interaction. This may not accurately describe all real-world scenarios, such as when the scattered particle has a non-negligible size or when the central force changes during the interaction.

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