What is the minimum opening angle between two photons in a neutral pion decay?

[schattenjaeger]

I forget the problem exactly but the general solution is good. I believe it was a neutral pion decaying into two photons

I don't know the numbers but I'm given momentum and it's gigantic, some GeV, opposed to the wussy pion mass so it's way relativistic

I could do the first part easy, it was like find out far the pion travels given its lifetime before decay(and then it gave me the lifetime)

However then it wanted the minimum opening angle between the two photons in the LAB frame. >_> I dunno, I figured I could assume both photons get half the pion's momentum, but then it seems like they should both be going in the same direction to conserve energy and momentum(although obviously I'm wrong)I know in the pion's rest frame to conserve momentum they both go out at 180 degrees apart(if they have half the momentum each I guess)but I don't know from there

 

[OlderDan]

Can you do it assuming the angles are equal for the two photons from the line of motion of the pion? The energy momentum relationships E² = p²c² + (mc²)² and the conservation laws should get you the equal angle solution fairly easily. By symmetry, that has to be the minimum or maximum opening angle. It should not be too hard to show which it is.