Conservation of angular momentum in positron-electron annihilation

[Simon Bridge]

TL;DR Summary

if we have spin polarized electrons and positrons, how is the annihilation probability affected by spin orientation?

Pretty much in a nutshell... fielded a question about how spin affects electron positron annihilation... ie do the spins have to be opposite in order to conserve angular momentum for two-photon annihilation to happen?

Intuitively I figured that looks reasonable ... but decided to check, and found lots of discussions of electron-positron scattering re spin polarization, but nothing that seemed to come definitely to a clear conclusion on this. Standard texts on the matter to hand do not cover the spin part... so I am probably forgetting something obvious.

It's been a while.
Someone want to point me in the right direction?

I'll want to understand this fairly solidly (A), but be able to give a description to intermediate level (I).

 

[shjacks45]

Creation of electron positron pairs by photons conserved but Wikipedia e-p anhiliation article says conserved. But electron and positron are spin 1/2 and both emitted photons are spin 1.

 

[Meir Achuz]

The e-p pair must be in a spin zero state. The two photons cannot be in a spin one state, because the spin addition 1+1=1 is antisymmetric, and the photons are bosons.

 

[Simon Bridge]

ie. if the e-p pair had aligned spins, then the probability of 2-photon annihilation is zero?
Is there a paper to back this up?

I am thinking of thought experiment where the spins of both particles are deliberately polarized.
They could have prepared initial polarization angles to whatever angle we want.

If randomly aligned, could I argue that the particles interact magnetically so establishing a spin 1 or spin 0 measured combined state?

Spin 1 allowing odd-photon annihilation and spin 0 allowing even-photon annihilation?

I'm trying to get my head clear on this.