Positronium

Onia Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom, specifically an onium.

The system is unstable: the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states.

The energy levels of the two particles are similar to that of the hydrogen atom (which is a bound state of a proton and an electron).

The lowest energy orbital state of positronium is 1S, and like with hydrogen, it has a hyperfine structure arising from the relative orientations of the spins of the electron and the positron.

The singlet state, 1S0, with antiparallel spins (S = 0, Ms = 0) is known as para-positronium (p-Ps).

It has a mean lifetime of 0.12 ns and decays preferentially into two gamma rays with energy of 511 keV each (in the center-of-mass frame).

The triplet states, 3S1, with parallel spins (S = 1, Ms = −1, 0, 1) are known as ortho-positronium (o-Ps), and have an energy that is approximately 0.001 eV higher than the singlet.

[1] These states have a mean lifetime of 142.05±0.02 ns,[2] and the leading decay is three gammas.

However more accurate calculations with corrections to O(α2) yield a value of 7.040 μs−1 for the decay rate, corresponding to a lifetime of 142 ns.

Measurements of these lifetimes and energy levels have been used in precision tests of quantum electrodynamics, confirming quantum electrodynamics (QED) predictions to high precision.

[1][7][8] Annihilation can proceed via a number of channels, each producing gamma rays with total energy of 1022 keV (sum of the electron and positron mass-energy), usually 2 or 3, with up to 5 gamma ray photons recorded from a single annihilation.

The branching ratio for o-Ps decay for this channel is 6.2×10−18 (electron neutrino–antineutrino pair) and 9.5×10−21 (for other flavour)[3] in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like relatively high magnetic moment.

Positronium can also be considered by a particular form of the two-body Dirac equation; Two particles with a Coulomb interaction can be exactly separated in the (relativistic) center-of-momentum frame and the resulting ground-state energy has been obtained very accurately using finite element methods of Janine Shertzer.

But if one adds the ⁠1/c2n⁠ (or α2n, where α is the fine-structure constant) terms, where n = 1,2..., then the result is relativistically invariant.

The α2 contribution is the Breit term; workers rarely go to α4 because at α3 one has the Lamb shift, which requires quantum electrodynamics.

[9] After a radioactive atom in a material undergoes a β+ decay (positron emission), the resulting high-energy positron slows down by colliding with atoms, and eventually annihilates with one of the many electrons in the material.

Approximately:[12][13] The Croatian physicist Stjepan Mohorovičić predicted the existence of positronium in a 1934 article published in Astronomische Nachrichten, in which he called it the "electrum".

[15] Other sources incorrectly credit Carl Anderson as having predicted its existence in 1932 while at Caltech.

[16] Many subsequent experiments have precisely measured its properties and verified predictions of quantum electrodynamics.

A discrepancy known as the ortho-positronium lifetime puzzle persisted for some time, but was resolved with further calculations and measurements.

Corrections that involved higher orders were then calculated in a non-relativistic quantum electrodynamics.

[4] In 2024, the AEgIS collaboration at CERN was the first to cool positronium by laser light, leaving it available for experimental use.

[22] The first observation of di-positronium (Ps2) molecules—molecules consisting of two positronium atoms—was reported on 12 September 2007 by David Cassidy and Allen Mills from University of California, Riverside.

[23][24][25] Unlike muonium, positronium does not have a nucleus analogue, because the electron and the positron have equal masses.

[26] The events in the early universe leading to baryon asymmetry predate the formation of atoms (including exotic varieties such as positronium) by around a third of a million years, so no positronium atoms occurred then.

Likewise, the naturally occurring positrons in the present day result from high-energy interactions such as in cosmic ray–atmosphere interactions, and so are too hot (thermally energetic) to form electrical bonds before annihilation.