# Particle-antiparticle annihilation and spin

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?

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
Homework Helper
Gold Member
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.

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?

James - who said it doesn't?

Meir Achuz said:
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
Homework Helper
Kruger said:
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?

Meir Achuz said:
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?

juvenal said:
James - who said it doesn't?

Umm,Quantum Mechanics...?

Daniel.

Can u prove it?

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

oh oh, this is a dangerous one

drop it like it's hot...

marlon

dextercioby said:
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).

Last edited by a moderator:
dextercioby