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Applications of Special Relativity
Problems on Collisions and Decays
Problem 3.1:
What is the 4-vector inner product of (E/c, (2E cosθ)/c, (2E sinθ)/c, 3E/c) with the 4-
momenta of a photon with energy G traveling in the x - z plane at an angle θ to the x-axis?
[Solution]
Problem 3.2:
The opposite to matter-antimatter annihilation is
called 'pair creation.' This occurs
when an photon 'decays' into one matter particle and one antimatter particle. Consider the simpler situation
in which two photons, each with energy E, collide at an angle θ and create a particle of mass M.
What is M in terms of E and θ?
[Solution]
Problem 3.3:
A particle with mass m and energy G collides with a stationary particle of mass M. What is the
speed of the frame in which the total momentum is zero?
[Solution]
Problem 3.4:
A particle with mass MA decays into two particles with masses MB and MC respectively. What
are the energies and momenta of MB and MC?
[Solution]
Problem 3.5:
We can apply what we know about collisions to an analysis of Compton scattering. A photon of energy E = hν = hc/λ in incident on a particle of mass m. The photon scatters off at an angle θ
with respect to its original direction. What is the new wavelength λf of the photon?
[Solution]
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