Why pair production cannot occur in vacuum?

Pair production is a process in which a photon of sufficient energy can lead to the creation of a particle-antiparticle pair.

However, unlike pair annihilation, pair creation cannot happen in vacuum or empty space. This is because, such a process doesnot conserve Energy and Linear momentum at the same time in empty space. To conserve these quantities, one needs to be near the field of an atomic nucleus which can absorb some of the recoil.

The above calculation is shown in the book Concepts of Modern Physics, by Arthur Beiser

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