Relativistic collisions - different frames, threshold energy

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Homework Help Overview

The discussion revolves around relativistic collisions, specifically focusing on energy and momentum in different reference frames. The original poster presents a series of questions related to Lorentz invariance and the interactions between an ultra-relativistic electron and a photon, including calculations for threshold energy and back-scattered energy.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants inquire about the assumptions regarding the electron's motion during collisions and whether it can be treated as stationary. There is also uncertainty about the kinetic energy of the electron in its rest frame.

Discussion Status

The discussion is ongoing, with participants seeking clarification on specific aspects of the problem. Some have expressed a need for more targeted assistance, indicating that not all areas of the problem have been addressed yet.

Contextual Notes

There appears to be a lack of clarity on certain assumptions, such as the treatment of the electron's kinetic energy in its rest frame and the conditions of the collisions. Participants are encouraged to specify where they need help to facilitate more effective guidance.

unscientific
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Homework Statement



(a) Show that E2 - p2c2 is a Lorentz invariant, where E is the total energy, p is the momentum, c is speed of light.

(b) In the lab frame, an utlra-relativistic electron with γ = 100 collides head-on with a photon of energy E. Find the threshold energy E required to create an electron-positron pair.

(c) In another head-on collision with the same setup, the path of the photon is reversed. Find the photon's energy in the electron's rest frame.

(d) Find the back-scattered energy of the photon in the same frame.

(e) Find the KE of the electron in the same frame.

(f) Find the back-scattered energy of photon in LAB frame.

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Homework Equations






The Attempt at a Solution


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Any help would be very appreciated!
 
unscientific said:
Any help would be very appreciated!

Help would be more forthcoming if you said where it's needed.
 
clamtrox said:
Help would be more forthcoming if you said where it's needed.


Part (d): Is it alright to assume the electron remains stationary throughout the collision (Like a tennis ball rebounding against the wall)

Part(e): I'm not sure if this is a trick question, but in the elctron's frame, shouldn't it's own KE = 0?
 
bumpp
 
anyone?
 

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