Question on photon-nucleus pair production

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The discussion centers on the necessity of a nucleus for gamma ray photon-nucleus pair production, specifically in the context of creating electron-positron pairs. It is established that a photon must possess a minimum energy of 1.022 MeV to facilitate this process, which corresponds to the combined rest mass energy of the electron and positron. The conversation highlights the conservation of energy and momentum, emphasizing that the photon, being a massless particle, cannot produce massive charged particles without the presence of a nucleus to conserve momentum.

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I'm having a bit of trouble understanding why a nucleus is needed for a gamma ray to interact with in particle pair production. I know that all properties are conserved - spin, charge, etc. -, and I know that the photon must have at least the energy of twice the standing energy of the particle it creates (for electron-positron pairs this is 1.022 MeV, correct?), but why does a nuetral, massles particle (photon) create two charged, massive particles (i.e. an electron and positron), and why is a nucleus necessary?
I'm asking simply out of curiosity, and any answers would be highly appreciated.
Thanks!
 
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Try getting both total energy and total (vector) momentum before and after to add up. Remember that the energy-momentum four vector for the gamma ray is a null vector. Can you make a null vector from two time like massive particles' momenta?
 

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