Pair Production
Calculate the threshold energy for a gamma-ray to create an electron-positron pair in an interaction with an electron at rest.
Solution From the conservation of lepton number
$$\gamma + e^{-} \longrightarrow e^{+} + e^{-} + e^{-}$$
At threshold the invariant mass squared is
$$S = \left(E_{\gamma} + m_{e} \right)^{2} - p_\gamma^2 = \left(3m_{e}\right)^{2}$$
As $E_{\gamma} = p_{\gamma}$ it follows
$$E_{\gamma} = 4m_{e} = 2.044 MeV$$
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Last modified: 2022-10-01 21:02:28 by mustafa
