Compton Scattering Angle - CM FRAME

In summary, the problem involves finding the scattering angle of an incoming photon with energy 10 MeV and an angle of 25 degrees in the CM frame. Using Compton scattering formulas, the scattering angle of the electron was found to be 35 degrees, with energies of 4.02 MeV for the electron and 5.47 MeV for the photon. To proceed in the CM frame, the Lorentz transformation can be used to find the four-vectors of the photon and electron and determine the speed of the CM frame.
  • #1
unscientific
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Homework Statement


Given incoming photon has energy 10Mev and scatters at angle 25 degrees, find the scattering angle in CM frame.
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Homework Equations

The Attempt at a Solution


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In lab frame, let the energy of incoming photon be ##E##. Total 4-vector would be ##P + Q = (\frac{E}{c},\frac{E}{c}) + (mc,0)##.

Using compton scattering formulas, I solved the scattering angle of electron ##\alpha = 35 ^o##, energy of scatted electron ##E_e = 4.02 ~MeV##, energy of scattered photon ##E' = 5.47~MeV##.Having solved this completely in the lab frame before/after scattering, how do I proceed in CM-frame?

In CM frame, total momentum is ##0##, so 4-vector would be ##P_{cm} + Q_{cm} = (\frac{E_{p,cm}+E_{e,cm}}{c},0)##.

Even when I assume that in CM frame they are both scattered along the same line it doesn't help.
 
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  • #2
Did you mean ##\alpha=35^\circ## or is that a typo?

Since you know everything the lab frame, you can simply use the Lorentz transformation to find the four-vectors in the CM frame. Suppose the CM moves with speed ##\beta=v/c##. Get expressions for the three-momentum of the photon and the electron in the CM frame. As you noted, their sum should be 0, which will allow you to determine ##\beta##.
 
  • #3
Solved.
 

Related to Compton Scattering Angle - CM FRAME

What is Compton Scattering Angle in the CM frame?

The Compton Scattering Angle in the CM frame is the angle at which a photon is scattered after colliding with an electron in the center-of-mass frame. It is an important concept in particle physics and is used to study the properties of particles and their interactions.

How is the Compton Scattering Angle in the CM frame calculated?

The Compton Scattering Angle in the CM frame is calculated using the conservation of energy and momentum equations. The angle can be determined by measuring the energies and momenta of the particles before and after the collision.

What factors affect the Compton Scattering Angle in the CM frame?

The Compton Scattering Angle in the CM frame is affected by the energy of the incoming photon and the mass of the scattering particle. It also depends on the scattering angle in the lab frame and the angle between the initial and final momenta in the CM frame.

Why is the Compton Scattering Angle in the CM frame important in particle physics?

The Compton Scattering Angle in the CM frame allows us to study the properties of particles and their interactions. By measuring this angle, we can determine the mass and energy of particles involved in the collision, providing valuable information about the fundamental building blocks of matter.

What are some real-world applications of the Compton Scattering Angle in the CM frame?

The Compton Scattering Angle in the CM frame has various applications in fields such as medical imaging, material science, and astrophysics. It is used in X-ray and gamma-ray spectroscopy techniques to study the structure and composition of materials. It is also used in medical imaging techniques such as positron emission tomography (PET) to detect and diagnose diseases.

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