quantum mechanics - Why does a photon colliding with an atomic nucleus cause pair production?

I understand that the photon needs to have enough energy to produce a lepton and it's antimatter partner, and that all of the properties are conserved, but why does the photon do this in the first place? What's going on "behind the scenes" to transform a single, neutral particle (the photon) into two charged particles (i.e. electrons)? Why is the nucleus necessary?

Answer

This process is the result of the cooperation of two theories of nature:

(i) Special relativity: This is a huge topic to study but we shall only need a small part of it, and perhaps the most famous one, which tells us this

$E=mc^2$.

This equation shows us that matter and energy are equivalent and interchangeable. For example, if an amount of energy $E = 2m_ec^2$ becomes available in a very small region of space, where $m_e$ is equal to the mass of the electron (or positron,) then it is possible to convert it into two particles, the electron and the positron.

(ii) Quantum mechanics: This tells us that electromagnetic waves are represented by “particles called photons,” which carry the energy of the electromagnetic field. The amount of energy carried by a photon is given by the famous equation

$E=hf$ where $h=6.63\times 10^{-34}$Js and $f$ is the frequency of the photon. So if the photon caries the amount of energy $E=2m_ec^2$ as it is emitted by a source (usually $gamma$)-emitter then the following can happen:

As the photon travels in space, QM allows the creation of an electron positron pair which lives only for a very short time, because they annihilate again into the original photon – this process is called “vacuum polarisation.” These two particles exist in virtual states and cannot be separated just like that, as that would violate the principle of conservation of momentum.

However, if an atomic nucleus is near by, then it is possible that a second photon coming from the nucleus can separate the two particles, before they annihilate again to give the original photon that generated them. I.e. the Coulomb field of the nucleus “pushes” the positron away, while it “pulls” the electron towards it. Hence the two particles became real, and can be guided into magnetic fields for storage and further use.

These processes are “behind the scenes” of a pair creation. The part of physics dealing with these fascinating quantum phenomena is called Quantum Electrodynamics.

Expansion: By the paragraph that begins “However, if an atomic…” I mean the following:

Imagine a $\gamma$-photon with sufficient energy approaching an atomic nucleus at a very close range. As the photon creates the $e^--e^+$ pair, the positron is scattered away from the nucleus while the electron flies towards the nucleus, in a virtual state, where it absorbs a virtual photon, effectively interacting with the Coulomb field of the nucleus and gets scattered to a new momentum state. During this process the nucleus carries some of the momentum of the virtual electron away. The presence of the atomic nucleus facilitates the splitting of the pair while the principle of momentum conservation is obeyed.