Why does positronium decay into 2 photons more often than into 3 photons?

I cannot find the answer to the above question. I know that para-positronium is created with a probability of $25\%$ and decays into 2 photons, while ortho-positronium is created with a probability of $75\%$ and decays into 3 photons. I also know that ortho-positronium has a way longer life time than para-positronium. This, in my understanding, should not affect the number of decays per time, but just means that the ortho-positronium will decay LATER into three photons. But in the end there should be $75\%$ 3-photon-decays and $25\%$ 2-photon-decays. But in reality 2-photon-decay happens about 300 times more often than 3-photon-decay. What information am I missing? Thank you!

• The title and the text do not match. My initial guess is that para-positroniums can emit a single photon and turn into an ortho-positronium. Then the ortho-positronium will decay and we will detect its photons and measure their wavelength.
– Ali
Commented Jul 22, 2013 at 10:05
• Thank you! Why do title and text not match? I don't see how this is the answers to why there are more 2-photon-decays than 3-photon-decays. Could you please elaborate? Commented Jul 22, 2013 at 10:17
• "But in reality 2-photon-decay happens about 300 times more often than 3-photon-decay" But in the title you are asking the opposite! If my guess turn out to be correct, then it follows smoothly that the number of 2-photon decays should be more than the 3-photon ones.
– Ali
Commented Jul 22, 2013 at 10:22
• You are right sorry, I will edit the title. Commented Jul 22, 2013 at 10:24
• What source says the 2-photon decay is more common? In astrophysical studies of the ISM, it is well known that 25% of Ps decays via the 511 keV line rather than the 3$\gamma$ continuum. Deviations from this are due to instances where Ps did not form from nice radiative recombination $e^+ + e^- \to \mathrm{Ps} + \gamma$ of slow-moving leptons, or from cases where a third body was involved in the decay somehow.
– user10851
Commented Jul 22, 2013 at 20:45

3 Answers

Let us start with the wiki article:

The singlet state with antiparallel spins (S = 0, Ms = 0) is known as para-positronium (p-Ps) and denoted 1S0. It has a mean lifetime of 125 picoseconds and decays preferentially into two gamma quanta with energy of 511 keV each (in the center of mass frame). Detection of these photons allows for the reconstruction of the vertex of the decay and is used in the positron emission tomography. Para-positronium can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases as the number increases

It is called conservation of angular momentum. An even number of photons allow to match the S=0 M_s=0 angular momentum. Two photons can add up to spin either 0 or 2 as each carries a spin of 1. The 0 matches the quantum numbers of para positronium.

The triplet state with parallel spins (S = 1, Ms = −1, 0, 1) is known as ortho-positronium (o-Ps) and denoted 3S1. The triplet state in vacuum has a mean lifetime of 142.05±0.02 ns[2] and the leading mode of decay is three gamma quanta

Because with three gammas one can match the S=1 angular momentum quantum numbers.

One has to remember that electrons and positrons annihilate to two gammas when not in a bound state as in positronium. The ground state at S=0 has a probability of electrons and positrons to be found at the center of each other and annihilate. The closer to the ground state the shorter the lifetime of the bound system.

I'm afraid the responses so far are either misleading or do not answer the question. In fact in a dense medium a positron when it forms the longer lived ortho-positronium can "pick-up" an electron from an adjacent atom and then decay into 2 x 511 keV photons long before the 3-photon ortho-positronium state would have decayed. Look up "pick-up effect".

Jezstarski is mostly correct,

The para-positronium (p-PS) state ends up being the main mode of annihilation of positronium (PS). Positrons can annihilate in at least eight different ways but once ortho-positronium (o-PS) forms in a void/vacuum, it has additional time to undergo another mode of annihilation.

P-PS annihilates in under 125 picoseconds. O-PS annihilates at or less than 142 nanoseconds (vacuum).

A consequence of this long lived lifetime is "pick-off" (the correct term) annihilation where an opposite spin electron from some surrounding material will annihilate in para-orientation before the ortho-bound electron can collapse and annihilate with the positron.

Source: Member of the Positron Science Lab at UMKC.