That can't happen if the incoming particle is a single photon. One way to convince yourself is to realize that a closed system consisting of a single photon is

That can't happen if the incoming particle is a single photon. One way to convince yourself is to realize that a closed system consisting of a single photon is massless, therefore it cannot later contain a massive particle without violating conservation of mass (in the sense of E^2 - p^2). Another way to think about it is that a photon contains the maximum amount of momentum possible for a given amount of energy. (E = p). If you transform any of its kinetic energy into rest energy, there's nothing that can carry the excess momentum. However if the photon is in the presence of a massive particle, that particle can soak up the excess momentum, and pair production is possible. Alternatively if you have two photons, their momenta can cancel and pair production is again possible. A fun physics problem is a photon striking an electron and producing an electron-positron pair; what was the minimum energy of the photon, in terms of electron rest energies? It's not two, for the reasons given above!