nuclear-physicspair-production
In order for a photon to decay into a pair of $e^+ e^-$, it must have at least $E_{\gamma}=1.022$ MeV and must be near a nucleus in order to satisfy the conservation of energy-momentum.
But would this happen even if the photon is near a neutron and not necesarily a nucleus? Does the fact that the nucleus is charged have anything to do with this decay? Who acts upon the photon to induce the interaction?
"Pair production is when a particle-antiparticle pair is produced from a single gamma photon. The gamma photon must have enough energy to produce that much mass. Pair-production usually happens near a nuclear, which helps to conserve momentum."
It is a hand waving way of describing pair production. Gammas are photons of high energy by definition. Gammas always have to interact with a field in order to produce a particle antiparticle pair , otherwise momentum will not be conserved. It is not a matter of help. The energy of the gamma must be a bit over the sum of the masses of the particle antiparticle to be created.
[Feynman Diagram of electron-positron pair production]. One can calculate multiple diagrams to get the cross section
Pair production can happen with other particles but not as easily studied .
Pair production is the creation of an elementary particle and its antiparticle, for example creating an electron and positron, a muon and antimuon, or a proton and antiproton. Pair production often refers specifically to a photon creating an electron-positron pair near a nucleus but can more generally refer to any neutral boson creating a particle-antiparticle pair
Quantum field theory does not offer a description of "how" its processes work, just like Newtonian mechanics doesn't offer an explanation of "how" forces impart acceleration or general relativity an explanation of "how" the spacetime metric obeys the Einstein equations.
The predictions of quantum field theory, and quantum electrodynamics (QED) in particular, are well-tested. Given two photons of sufficient energy to yield at least the rest mass of an electron-positron pair, one finds that QED predicts a non-zero amplitude for the process $\gamma\gamma \to e^+ e^-$ to happen. That is all the theory tells us. No "fluctuation", no "virtual particles", nothing. Just a cold, hard, quantitative prediction of how likely such an event is.
All other things - for instance the laughable description in the Wikipedia article you quote - are stories, in this case a human-readable interpretation of the Feynman diagrams used to compute the probability of the event, but should not be taken as the actual statement the quantitative theory makes.
There is no "how", what happens between the input and the output of a quantum field theoretic process is a black box called "time evolution" that has no direct, human-readable interpretation. If we resolve it perturbatively with Feynman diagrams, people like to tell stories of virtual particles, but no one forces us to do that - one may organize the series in another way, may be even forced to do so (e.g. at strong coupling), or one may not use a series at all to compute the probability. The only non-approximative answer to "how" the scattering processes happen in quantum field theory that QFT has to offer is to sit down and derive the LSZ formula for scattering amplitudes from scratch, as it is done in most QFT books. Which, as you may already see from the Wikipedia article, is not what passes as a good story in most circles.
But neither nature nor our models of it are required to yield good stories. Our models are required to yield accurate predictions, and that is what quantum field theory does.
Best Answer
Quantum mechanics says that everything that is not forbidden is compulsory. Any process that doesn't violate a conservation law will happen, with some rate or cross-section. However, this general principle doesn't tell you what the rate is. For example, it's theoretically possible for 124Te to decay into two 62Ni nuclei plus four electrons and four antineutrinos, but to predict the (very small) rate, you need to know the relevant nuclear physics.
In your example, the process probably would go at some rate determined by electromagnetic interactions, because the neutron has a magnetic field. But the rate would presumably be small because the magnetic field of a dipole falls off like $1/r^3$, and magnetic effects are usually down by $\sim v/c$ compared to electric effects.