Does anti-matter Always annihilate with matter?

[Qentanglement]

So there seems to be an issue concerning the annihilation of an electron and a positron given the following scenario:

Say an electron has spin +1/2 or up, (say Z-axis is up) and a positron has spin +1/2 or up as well.

Now...
I know that a photon has to be a spin of 1. (This is important to note)

If the the electron and positron collide head on from opposite directions with exactly the same kinetic energy then there is an issue.

Momentum has to be conserved, momentum of the system is 0.

Energy has to be conserved, so two photons have to come out of this annihilation going in opposite directions with the same energy in order to conserve momentum and energy.

But "HOW could this be?" You can't have two photons! The total system would have either a total spin of +or- 2 or 0. (I say +or- 2 because one photon could have spin +or- 1 and the other also +or- 1)

We started out with an electron and positron with spin +1/2, SO either spin is not conserved, and two photons come out like usual or one photon comes out but doesn't move! This doesn't make sense, or they don't annihilate and bounce off each other. Or quark anti quark pairs are produced to preserve spin and momentum and energy.

What is the resolution to this scenario?

 

[Bob S]

Read about the two bound spin states of positronium (a bound electron-positron atom) at

http://en.wikipedia.org/wiki/Positronium

Bob S

 

[Qentanglement]

I have skimmed over the article you referred me to, however it leaves me even more confused. The article says that sometimes 1 or 2 or up to 5 photons can come out of the annihilation process! Well this makes sense depending upon the starting states of the electron positron pair.

However, You did not answer my question about my scenario You merely deflected me off to somewhere to get more confused.

I specifically asked what is the resolution to this scenario and it still remains unsolved.

The only thing that I can find in the Wikipedia article that can possibly answer my question is that an electron positron pair can annihilate into a neutrino anti neutrino pair, however it says that this interaction is negligible, 6.2×10−18.

Does this means that the answer to my question is that a neutrino anti-neutrino pair that will both have +1/2 spin will be created and fly in opposite directions? Is there anyone else that can verify this? Or what I think is more probable is that the electron positron pair will just bounce off each other?

 

[bcrowell]

But "HOW could this be?" You can't have two photons! The total system would have either a total spin of +or- 2 or 0. (I say +or- 2 because one photon could have spin +or- 1 and the other also +or- 1)

Two spin-1 photons can couple to make a spin with magnitude 0, 1, or 2 -- not just 0 or 2.

 

[Qentanglement]

Thank you very much bcrowell. You have answered my question directly. However, what is the mathematical equation that describes this? I don't understand how they are coupled. How does the math show that the coupling of two spin 1 photons can make it with a magnitude 1?

 

[dioib]

What bcrowell is referring to is the addition of angular momenta. A look at 1x1 table of this document might shed some light (taking the context for granted): http://cms.iafe.uba.ar/carmen/clebrpp.pdf
The idea also applies to the spin of electron-positron pair.

 

[bcrowell]

Suppose you said that two spin j's could only couple to spin 0 or spin 2j. For large j, you have to recover the classical limit, but that would be the same as saying that the spins had to lie along parallel axes, which isn't true. Since the statement can't hold true in the classical limit of large j, it doesn't seem reasonable to expect it to hold for j=1.

 

[Qentanglement]

Thank you very much everyone. I will look into this further. :)