Particle-antiparticle annihilation and spin

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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?
 

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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.
 
  • #3
Meir Achuz
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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.
 
  • #4
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?
 
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James - who said it doesn't?
 
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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?
 
  • #7
dextercioby
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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...? :rolleyes:

Daniel.
 
  • #8
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Can u prove it?
hehe. No. You learned me that spin has not to be conserved. Only total angular momentum has to be conserved.
 
  • #9
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oh oh, this is a dangerous one


drop it like it's hot...

marlon
 
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dextercioby said:
Umm,Quantum Mechanics...? :rolleyes:

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).
 
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dextercioby
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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.
 
  • #12
Meir Achuz
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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.
 

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