Question 6

An electron and a positron can collide and produce a proton and an antiproton,

$$e^- + e^+ \rightarrow p + \bar{p}.$$

Find the minimum kinetic energy of the positron needed for this reaction in a frame of reference in which the total momentum of the particles is zero.

Find the minimum kinetic energy of the positron needed for this reaction in a frame of reference in which the positron collides with a stationary electron.

[The masses of the electron and the positron are identical, both being 0.51 MeV/$c^2$. The masses of the proton and the antiproton are also identical, and are 938.3 MeV/$c^2$.]

[Numerical answers can be found here.]

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]