Pair production description: 8. Section 5.2.2 discusses pair production, the pro

Question

Pair production description:

8. Section 5.2.2 discusses pair production, the process where an energetic photon spontaneously decays.into an electron/positron pair a. Show that if the only elements of the interaction are the photon, the electron, and the positron, it is impossible simultaneously to con- serve energy and momentum. This is the confirmation of the fact that pair production can only occur near a nucleus. b. What is the miminum energy, and wavelength, a photon must have to be capable of initiating pair production?

Explanation / Answer

(a)

Let us say that the photon has created pair of particles. There must exist a reference frame ("center of mass") in which the total momentum of the two particles is zero. So by momentum conservation, in the same frame the photon had to have momentum zero. But photon cannot have momentum zero, because then it would have zero energy (since, p = E/c for photons). So momentum is not conserved in the center of mass frame, and, because of the Lorentz invariance, is not conserved in all frames. Therefore, the process is impossible.

(b)

The photon must have higher energy than the sum of the rest mass energies of an electron and positron i.e.(2 × 0.511 MeV = 1.022 MeV) for the production to occur.

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