Creation of an Electron-Positron Pair by a Photon
1. The problem statement, all variables and given/known data
Show that the creation of an electron-positron pair (or any particle-antiparticle pair, for that matter) by a single photon is not possible in isolation, ie, that additional mass (or radiation) must be present. (Hint: Consider the reaction at threshold, then apply conservation laws.)
2. Relevant equations
hc/lambda - pc = 2m(e)c^2
at threshold, hf(min) = 2m(e) c^2
3. The attempt at a solution
I know this can't work b/c you can't find a Lorentz frame in which the e+ and e- have equal and opposite momenta, b/c then the photon would be at rest which would disobey the law of special relativity.
At threshold, all the energy of the photon becomes the mass of the electron and positron so the electron and positron have KE=0.
h/lambda = p- + p+
2m(e) c = m(e) u- + m(e) u+
2c= u- + u+