# Pair Production in static fields

1. Jul 1, 2012

### FunkyDwarf

Hello,

I have a [probably silly] question regarding particle pair production in strong static fields.

Take for instance the finite Coulomb field (of say an extended nucleus) and the Dirac equation. One can compute the bound states of such a system and see that at a certain value of Z the energy of one of the levels (say the ground state for arguments sake) is equal to -mc^2. Using a sort of energy conservation argument one can say that now pair production is allowed because if your particle drops into this state from at least +mc^2 to this state of -mc^2 you have enough energy to create two (real) particles and perhaps detect them at infinity. (ok so far?)

My question is, how does this transfer to QFT? Let's say you still have a static central potential (as a function of Z) but now one must consider a time dependent field (of particles), correct? In this case is it possible to get pair production (and by that i mean particles that can be detected at infinity as said before) before the critical Z (-mc^2 level) is achieved? I guess ultimately what i'm asking is when you go to QFT is such creation before Zcritical still forbidden or just strongly suppressed? (if it's just suppressed, how does energy conservation fit into all this?)

Cheers,
-Z