Why does pair production require a nucleus for momentum conservation?

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In pair production, an nucleus is needed to take away some momentum from the photon so momentum conservation is respected. correct?
 

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Right. Or at least a heavy charged particle. It's just that a nucleus is the most common such beast.
 
There is an alternative way for pair production to take place - it happened right after the big bang. Specifically, a pair of photons can interact to get a particle-antiparticle pair.
 

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