"A high-energy photon creates a pi+ pi- pair." ???

[mr. vodka]

1. The problem statement, all variables and given/known data
"A high-energy photon creates a pi+ pi- pair. What is the minimal frequency of the photon?" (+ other side questions)

2. Relevant equations
E = hf
E = mc²

3. The attempt at a solution
Well superficially it looks very easy, just taking hf = 2mc² with m the mass of a pion, but... How can one photon create a pair, this is not possible. Or am I missing something?
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[Phrak]

"A high-energy photon creates a pi+ pi- pair. What is the minimal frequency of the photon?"

It can, all by itself? Where did you get this quote? Does the statement assume a catalyst--a target?

Both energy and momentum need to be conserved, in which case the target energy and momentum are changed.

[mr. vodka]

The phrase is an exact translation from an old exam question from a course (introductory physics III [about quantum, particle, nuclear, ... physics) I'm taking... Maybe the catalyst is (very) implicit? If so, I don't see how we'd compute the minimal energy the photon has to carry...

[Phrak]

It must be glazed-over. A photon will not spontaneous decay into a particle and it's antiparticle: Consider a pi+ and pi- in the center of mass frame, in vacuum. They annihilate to photon(s). To conserve momentum, there must be at least 2 photons produced. So must this be true of the reverse reaction; two or more photons must go in , to get two pions out.

However, for the level of this problem, I think you just pretend that the total energy of the pions, where E=2mc^2, is equal to E = h nu of the single output photon.

[vela]

This gets back to your other problem regarding pair production. It has to happen in the vicinity of other matter. Do you understand why the presence of other matter allows pair production to happen?