Show that the reaction ? -> e+e- cannot happen in free space. Take ?, the photon

Question

Show that the reaction ? -> e+e- cannot happen in free space. Take ?, the photon,
with mass m? = 0, energy E0 and momentum k along x only, while the produced
couple of the electron e- and anti-electron e+ have mass me each. To show this, you
can use the energy-momentum invariant m2 c4 = E2 - p2c2
which is the same quantity in all frames and before and after the reaction. Note: For some reason, the gamma's keep showing up as ?.
which is the same quantity in all frames and before and after the reaction. Note: For some reason, the gamma's keep showing up as ?.

Explanation / Answer

? --> e-    + e+ in this process if the ? ray photon is completely absorbed Acccording to law of cosevation of energy m0c^2     --->   2m_ec^2 The photon must have energy 2 m_ec^2   = 2*0.511 Mev = 1.022 MeV Here m_e is rest mass of the electron or positron According to law of coservation of momentum the two photons must be moving in the opposite directions Hence   a    single photon can 't produce the electron and positron , to conserve energy and linear momentum   we must have another photon

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