# Compton Scattering Using Mandel-Stam Variables

• americanforest
In summary, the conversation discusses the use of Mandelstam variables in deriving Compton Scattering equations. The person speaking mentions using the CMS frame and lab frame for convenience and points out a mistake in the first equation. They also clarify that both systems need to be used in order to obtain the correct photon energies in the lab system. They also mention correcting the name of the person associated with Mandelstam variables.
americanforest

## Homework Statement

Not homework, just for fun. I want to derive Compton Scattering equations using Mandel-Stam variables as opposed to the way that I have done it in class using the usual energy and momentum conservation

## Homework Equations

$$(p_\mu+p_{ei}_\mu)^2=(p'_\mu+p_e_\mu)^{2}=s$$
p is the momentum of incoming photon and pei is of initially stationary electron. p' is final photon and p_e_\mu is final electron.

## The Attempt at a Solution

I'm going to try to do the right side in the CMS frame and the left side in the lab frame for convencience.

$$Em_e=2EE_e_$$
...skip a few easy steps using
$$E=\sqrt{p^{2}+m^{2}}$$
$$E^{2}-E'^{2}=\frac{p_e_^2}{me^{2}}$$

Which isn't right. What's wrong here?

Last edited:
You have to do both in the lab system because you need the photon energies in the lab system. Your first equation can't be right. You can't use the same E in each system.
Stanley's name is Mandelstam. He is only one person.

## 1. What is Compton Scattering?

Compton Scattering is a phenomenon in which a high-energy photon (particle of light) collides with a target, transferring some of its energy and changing its direction. This process was first observed by Arthur Compton in 1923 and is an important tool for studying the properties of subatomic particles.

## 2. What are Mandel-Stam Variables?

Mandel-Stam Variables, also known as Mandelstam variables, are a set of four variables used to describe the kinematic properties of a particle collision. They are named after physicists Stanley Mandelstam and Yakov Zeldovich who first introduced them in the 1950s. These variables are s, t, u, and v, and they represent different combinations of the energies and momenta of the particles involved in the collision.

## 3. How are Mandel-Stam Variables used in Compton Scattering?

In Compton Scattering, Mandel-Stam Variables are used to describe the energy and momentum of the incoming photon and the scattered photon. These variables are important for calculating the scattering angle and energy transfer of the photons in the collision. They also allow for the conservation of energy and momentum to be easily represented in equations.

## 4. What is the significance of using Mandel-Stam Variables in Compton Scattering?

Using Mandel-Stam Variables in Compton Scattering allows for a more elegant and compact way of representing the kinematic properties of the collision. They also make it easier to apply conservation laws and perform calculations. Additionally, Mandel-Stam Variables are used in many other areas of physics, making them a useful tool for understanding various phenomena.

## 5. Are there any limitations to using Mandel-Stam Variables in Compton Scattering?

One limitation of using Mandel-Stam Variables in Compton Scattering is that they only apply to two-body collisions, where two particles are involved in the interaction. For more complex collisions involving multiple particles, other variables or methods may be necessary. Additionally, Mandel-Stam Variables do not take into account the quantum mechanical nature of particles, so they may not accurately describe certain aspects of the collision.

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