Ortho- and Para-Positronium Decays

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In summary, the decay of ortho- and para-positronium involves the emission of at least two photons to conserve 4 momentum, with the additional requirement of conserving overall angular momentum of 1 for ortho-positronium. This leads to the simplest answer of 3, 5, 7, etc. photons being created with alternating spins. However, it is also possible for an even number of photons to be created with opposite spins and an orbital momentum of 1, as well as other photon spin and orbital angular momentum combinations that satisfy angular momentum conservation. For para-positronium, the decay products are always an even number of photons with alternating spin, due to the conservation of parity. However, for
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Mantella
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One of my homework problems asks what number of photons are released in the decay of ortho- and para-positronium, and I'm somewhat confused. From the point of view of 4 momentum conservation I understand that at least two photons must be emitted in the decay process. In the case of ortho-positronium, the overall angular momentum of 1 must be conserved as well. The simplest answer is that 3,5,7,... photons are created with alternating spins, but wouldn't it also be possible for two photons or, for that matter, any even number of photons to be created with opposite spins and an orbital momentum of one? What about even more esoteric photon spin and orbital angular momentum combinations that satisfy the angular momentum conservation? I don't have much experience with orbital angular momentum, and my teacher hasn't described it in any detail.

Also, for para-positronium the decay products are an even number of photons with alternating spin, but to the best of my understanding parity must be conserved as well. Electron parity of +1, positron parity of -1, (I think) while photons have a parity of -1. (+1)(-1) ≠ (-1)(-1). Again my understanding of particles and their interactions is pretty limited.

Parity for a ortho-positronium does seem to be conserved however.

On a side note: does orbital angular momentum have directions like spin or is it always greater than or equal to 0?
 
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What you are looking for is not angular momentum conservation, you need to know about C-parity. You need to concentrate on ground state of Positronium here, this is where you prefer singlet and triplet state as para-positronium and ortho-positronium.

Transformation of triplet state under charge conjugation goes as (replace ##b^+## by ##d^+##),
##b_1^+d_1^+|0> → d_1^+b_1^+|0> → -b_1^+d_1^+|0>## ( ##b^+ ##and ##d^+## anticommute) , hence triplet state has odd parity and it can decay to odd number of photons since photon's C-parity is -1.

Transformation of singlet state goes as ( apart from a factor of ##\frac{1}{√2}##),
## [b_1^+d_2^+-b_2^+d_1^+]|0> → [d_1^+b_2^+-d_2^+b_1^+]|0> → [b_1^+d_2^+-b_2^+d_1^+]|0>##, hence singlet state has even parity and it can decay to even number of photons.
( 1 refers to spin up and 2 refers spin down).
 

1. What is Ortho-Positronium and Para-Positronium?

Ortho-Positronium and Para-Positronium are two different forms of positronium, which is a bound state of an electron and a positron. In Ortho-Positronium, the spins of the electron and positron are parallel, while in Para-Positronium, they are antiparallel.

2. What is the difference between Ortho- and Para-Positronium Decays?

The main difference between Ortho- and Para-Positronium Decays is the decay time. Ortho-Positronium has a longer lifetime compared to Para-Positronium, which decays much faster. This is due to the different spin states of the two forms.

3. How do Ortho- and Para-Positronium Decay?

Both Ortho- and Para-Positronium decay by annihilation, where the electron and positron annihilate each other, producing two or three photons. However, the decay process for Ortho-Positronium is more complex, involving multiple steps and producing a wider range of energies for the emitted photons.

4. What is the significance of studying Ortho- and Para-Positronium Decays?

Studying Ortho- and Para-Positronium Decays can provide insights into the fundamental properties of matter and antimatter. It can also help in understanding the behavior of particles in extreme conditions, such as in high-energy collisions or in the early universe.

5. How is the decay of Ortho- and Para-Positronium observed in experiments?

The decay of Ortho- and Para-Positronium can be observed through various experimental techniques, such as positron annihilation spectroscopy or time-resolved positron annihilation spectroscopy. These techniques involve detecting and analyzing the photons produced during the decay process to determine the spin state and decay time of the positronium.

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