Friday 24 June 2016

Is pair production only with $gamma$ photons?


in my revision guide the section on pair production only mentions it happening with gamma photons, so the question arose whether this is the only way it can happen?



This is what the book says: "Pair production is when a particle-antiparticle pair is produced from a single gamma photon. The gamma photon must have enough energy to produce that much mass. Pair-production usually happens near a nucleus, which helps to conserve momentum."


So does pair production only happen with gamma photons?


Thanks



Answer



Pair producing an electron and a positron requires an energy at least equal to their masses, $2m_ec^2$. This would just create them stationary, and you'd need an even greater energy to give them some momentum.


Since $m_e = 0.511$ MeV/c$^2$, the minimum energy required for pair production to occur is $\sim 1$ MeV.


What photons have an energy close to that value? Gamma rays.


Now, if you tried to do the maths of energy & momentum conservation, a single photon pair converting to an electron and a positron would never conserve both.


You can see it by noting that, for the outgoing electron+positron system, there exists a centre of mass frame where the total momentum is 0. But for the photon, there is no such thing since zero momentum would mean 0 energy ($E =pc$). The presence of a nucleus makes you have more 'elements' in the energy-momentum conservation calculations, which allows it to give/take some energy/momentum thus enabling the pair production process to occur.


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