We are going to talk about coordinate transform from “center of momentum frame” to “Laboratory frame”.

At the center of momentum [C.M.] frame, the total momentum is zero.

Refer here on Google Docs. for the Mathematica 7 code and calculation steps.

anyone want to have the .nb file, feel free to ask.

i am just discuss on the result.

  1. In the C.M. frame, energy of each particle reserved, there is no exchange in energy and momentum. after collision, they just change the moving direction.
  2. the energy is C.M frame is always smaller then Lab frame, or other fame. which is also from the face that, at the CM frame, total momentum is zero and the corresponding energy is the Proper Energy.
  3. In Lab frame, the scatter angle is always smaller than 90 degree for incident particle’s mass > target particle.
  4. In Lab frame, The larger the scatter angle, the smaller the momentum and larger the momentum transfer.