Particle-antiparticle annihilation and spin

[Nicky]

I have a question regarding particle-antiparticle annihilation, such as electron-positron, proton-antiproton, etc. Can the annihilation still occur if the two particles are in opposite spin eigenstates, i.e. if the pair has zero net spin?

 

[Kruger]

The spin of the whole system has to be conserved.

The particle and the antiparticle will annihilate into two photons. Because of spin conservation (one photon has spin of 1 and particle antiparticle has in your sense net spin of 0). You see? Two photons also with net spin zero.

 

[Meir Achuz]

For positronium (electron-positron bound state), the state with total spin 0 annihilates much faster than the state with spin 1, because the spin 1 state must annihilate into three photons, with 1+1+1=1.
Incidentally, the two particles are NOT in opposite spin eigenstates.
If they are in an eigenstate of total spin (1 or 0), the individual particles can not be in spin eigenstates.

 

[James Jackson]

Sorry, I'm missing something very obvious that I do know, but can't put my finger on right now (note to self - drinking heavily the night before doing Physics doesn't work...). Why can't the spin 0 positronium state decay to two photons with spin +1, -1 respectivaly? That conserves the spin surely?

 

[juvenal]

James - who said it doesn't?

 

[Nicky]

For positronium (electron-positron bound state), the state with total spin 0 annihilates much faster than the state with spin 1, because the spin 1 state must annihilate into three photons, with 1+1+1=1.

Does the spin 1 state decay in two stages? Maybe spin 1 positronium -> spin 0 positronium + photon, then spin 0 positronium -> two photons?

 

[dextercioby]

The spin of the whole system has to be conserved.

The particle and the antiparticle will annihilate into two photons. Because of spin conservation (one photon has spin of 1 and particle antiparticle has in your sense net spin of 0). You see? Two photons also with net spin zero.

Can u prove it?

For positronium (electron-positron bound state), the state with total spin 0 annihilates much faster than the state with spin 1, because the spin 1 state must annihilate into three photons, with 1+1+1=1.

Why?

James - who said it doesn't?

Umm,Quantum Mechanics...?

Daniel.

 

[Kruger]

Can u prove it?

hehe. No. You learned me that spin has not to be conserved. Only total angular momentum has to be conserved.

 

[marlon]

oh oh, this is a dangerous one


drop it like it's hot...

marlon

 

[juvenal]

Umm,Quantum Mechanics...?

Daniel.

Maybe you're misunderstanding my point, and I'm not sure why you are since it's pretty explicit.

You're saying that spin 0 positronium CANNOT decay to two photons? That is what I'm referring to.

If so, I beg to differ:

http://rockpile.phys.virginia.edu/mmod27.pdf

Bottom of page 3. (Further up may lie the answer to your inquiry of Meir Achuz's post).

 

[dextercioby]

I didn't say that,i missinterpreted your question,since you simply asked it without quoting what in James Jackson's post you were referring to.

Daniel.

 

[Meir Achuz]

So far we have left out charge conjugation invariance, which was tacitly assumed in my original answer. Photons have C=-1. Positronium of spin 0 has C=+1, and so can decay into two photons. Positronium of spin 1 has C=-1, and cannot decay into two photons. Three is the next lowest number. If this leads to more questions, I will try to answer them as asked.