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I am studying the phenomenon of pair production and I learned that it cannot occur in a vacuum. Rather it occurs near a nucleus which absorbs momentum to keep the momentum conserved.

Instead of a nucleus, can we have pair production with two photons? For example, the two photons collide to produce an electron-positron pair.

cconsta1
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Anindita Sarkar
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Yes the process you are saying is absolutely possible $$\gamma + \gamma \rightarrow e^+ +e^-$$ Is a lowest order process that can occur in QED, since it involves two vertex, and as you know the QED respects time reversal or t-parity the process

$$ e^+ +e^- → γ +γ$$ must be time reversal.

EDIT: Pair Annihilation the process may be interpreted as a incoming photon giving a positron and an electron and one of them absorbing another photon for momentum corrections in that case one of the fermion will become a propagator.

Just hold your screen upside down (reverse time direction) and you'll see the process just replace the $e^-$ and $e^+$ accordingly.

For more details refer to Chapter 9 of Lahiri & Pal A first book of Quantum Field Theory