Cross-Section from Lab Frame to C-O-M Frame

In summary, The conversation discusses the search for a good explanation and worked example on how to convert an inelastic cross-section from the lab frame to the center-of-mass frame. This includes converting the energy and the corresponding dσ/dΩ values. The book "Atomic and Nuclear Physics" by Prof. S.N. Ghosal and the Review of Particle Physics are recommended as sources for further information on this topic.
  • #1
James_1978
37
3
Dear Forum,

I am searching for a good explanation and worked example that shows how to convert a inelastic cross-section from the lab frame to the center-of-mass frame. I need to first convert the energy (x-axis) from the lab frame to the COM frame. In addition, I need to convert the corresponding dσ/dΩ (y-axis) into the COM frame as well. I have been unable to find a good description of this in any book or notes.

Regards,
CJ
 
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  • #2
James_1978 said:
I am searching for a good explanation and worked example that shows how to convert a inelastic cross-section from the lab frame to the center-of-mass frame.

well one can see the treatment of nuc; reactions in
Atomic and Nuclear Physics . Vol.II, By Prof. S.N. Ghosal

Publisher :S. Chand & Co., New Delhi , India
(Chapter X -deals with the two descriptions- and as Dr. Ghoshal was an experimentalist he has dealt the interrelationship of two descriptions elaborately.)
 

What is a "Cross-Section from Lab Frame to C-O-M Frame"?

A cross-section from lab frame to center-of-mass (C-O-M) frame is a technique used in physics to analyze the behavior of particles in a collision or interaction. It involves transforming the reference frame from the lab frame, in which the particles have their initial velocities, to the C-O-M frame, which is a frame of reference where the total momentum of the particles is zero.

Why is the C-O-M frame used in cross-section calculations?

The C-O-M frame is used in cross-section calculations because it simplifies the analysis of particle interactions. In this frame, the total momentum of the particles is zero, which means that the initial and final momenta can be easily related. This allows for a more accurate measurement of the cross-section, which is a measure of the probability of a particular interaction occurring.

How is the C-O-M frame related to the lab frame?

The C-O-M frame is related to the lab frame through a coordinate transformation. The origin of the C-O-M frame is located at the center of mass of the system, and the axes are oriented along the initial direction of motion of the particles. The C-O-M frame moves with a velocity equal to the total momentum of the particles divided by their total mass, relative to the lab frame.

What are the advantages of using the C-O-M frame in cross-section calculations?

Using the C-O-M frame in cross-section calculations has several advantages. It simplifies the analysis of particle interactions, as mentioned earlier. It also makes it easier to compare data from different experiments, as the cross-section is independent of the reference frame. Additionally, the C-O-M frame allows for a better understanding of the underlying physics, as it is a more natural frame to consider for particle interactions.

Are there any limitations to using the C-O-M frame in cross-section calculations?

While the C-O-M frame is a useful tool in cross-section calculations, it does have some limitations. It is only applicable in situations where the total momentum of the particles is conserved. It also assumes that the particles are moving in a straight line with constant velocity, which may not always be the case. Additionally, the transformation to the C-O-M frame can be mathematically complex and may require advanced techniques to solve.

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