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Positronium (Ps) is a system consisting of anelectron and itsanti-particle, apositron, bound together into anexotic atom, specifically anonium. Unlike hydrogen, the system has noprotons. The system is unstable: the two particles annihilate each other to predominantly produce two or threegamma-rays, depending on the relative spin states. Theenergy levels of the two particles are similar to that of thehydrogen atom (which is a bound state of aproton and an electron). However, because of the reduced mass, thefrequencies of thespectral lines are less than half of those for the corresponding hydrogen lines.
The mass of positronium is 1.022 MeV, which is twice the electron mass minus the binding energy of a few eV. The lowest energy orbital state of positronium is 1S, and like with hydrogen, it has ahyperfine structure arising from the relative orientations of the spins of the electron and the positron.
Thesinglet state,1
S
0, withantiparallelspins (S = 0,Ms = 0) is known aspara-positronium (p-Ps). It has a mean lifetime of0.12 ns and decays preferentially into two gamma rays with energy of511 keV each (in thecenter-of-mass frame).Para-positronium can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases with the number: thebranching ratio for decay into 4 photons is1.439(2)×10−6.[1]
Para-positronium lifetime in vacuum is approximately[1]
Thetriplet states,3S1, withparallel spins (S = 1,Ms = −1, 0, 1) are known asortho-positronium (o-Ps), and have an energy that is approximately 0.001 eV higher than the singlet.[1] These states have a mean lifetime of142.05±0.02 ns,[2] and the leading decay is three gammas. Other modes of decay are negligible; for instance, the five-photons mode has branching ratio of ≈10−6.[3]
Ortho-positronium lifetime in vacuum can be calculated approximately as:[1]
However, more accurate calculations with corrections toO(α2) yield a value of7.040 μs−1 for the decay rate, corresponding to a lifetime of142 ns.[4][5]
Positronium in the 2S state ismetastable having a lifetime of1100 ns againstannihilation.[6] The positronium created in such an excited state will quickly cascade down to the ground state, where annihilation will occur more quickly.
Measurements of these lifetimes and energy levels have been used inprecision tests of quantum electrodynamics, confirmingquantum electrodynamics (QED) predictions to high precision.[1][7][8]
Annihilation can proceed via a number of channels, each producinggamma rays with total energy of1022 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 annihilation into aneutrino–antineutrino pair is also possible, but the probability is predicted to be negligible. The branching ratio foro-Ps decay for this channel is6.2×10−18 (electron neutrino–antineutrino pair) and9.5×10−21 (for other flavour)[3] in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like relatively highmagnetic moment. The experimental upper limits on branching ratio for this decay (as well as for a decay into any "invisible" particles) are <4.3×10−7 forp-Ps and <4.2×10−7 foro-Ps.[2]
While precise calculation of positronium energy levels uses theBethe–Salpeter equation or theBreit equation, the similarity between positronium and hydrogen allows a rough estimate. In this approximation, the energy levels are different because of a different effective mass,μ, in the energy equation (seeelectron energy levels for a derivation):where:
Thus, for positronium, its reduced mass only differs from the electron by a factor of 2. This causes the energy levels to also roughly be half of what they are for the hydrogen atom.
So finally, the energy levels of positronium are given by
The lowest energy level of positronium (n = 1) is−6.8 eV. The next level is−1.7 eV. The negative sign is a convention that implies abound state. Positronium can also be considered by a particular form of thetwo-body Dirac equation; two particles with aCoulomb interaction can be exactly separated in the (relativistic)center-of-momentum frame and the resulting ground-state energy has been obtained very accurately usingfinite element methods ofJanine Shertzer.[9] Their results lead to the discovery of anomalous states.[10][11]The Dirac equation whose Hamiltonian comprises two Dirac particles and a static Coulomb potential is not relativistically invariant. But if one adds the1/c2n (orα2n, whereα is thefine-structure constant) terms, wheren = 1,2..., then the result is relativistically invariant. Only the leading term is included. Theα2 contribution is the Breit term; workers rarely go toα4 because atα3 one has the Lamb shift, which requires quantum electrodynamics.[9]
After a radioactive atom in a material undergoes aβ+ 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. It may however first form positronium before the annihilation event. The understanding of this process is of some importance inpositron emission tomography. Approximately:[12][13]
The Croatian physicistStjepan Mohorovičić predicted the existence of positronium in a 1934 article published inAstronomische Nachrichten, in which he called it the "electrum".[15] Other sources incorrectly creditCarl Anderson as having predicted its existence in 1932 while atCaltech.[16] It was experimentally discovered byMartin Deutsch atMIT in 1951 and became known as positronium.[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.[17] Measurements were in error because of the lifetime measurement of unthermalised positronium, which was produced at only a small rate. This had yielded lifetimes that were too long. Also calculations using relativistic quantum electrodynamics are difficult, so they had been done to only the first order. Corrections that involved higher orders were then calculated in a non-relativistic quantum electrodynamics.[4]
In 2024, theAEgIS collaboration atCERN was the first to cool positronium by laser light, leaving it available for experimental use. The substance was brought to −100 °C (−148 °F) usinglaser cooling.[18][19]
Molecular bonding was predicted for positronium.[20] Molecules ofpositronium hydride (PsH) can be made.[21] Positronium can also form a cyanide and can form bonds with halogens or lithium.[22]
The first observation ofdi-positronium (Ps2)molecules—molecules consisting of two positronium atoms—was reported on 12 September 2007 by David Cassidy and Allen Mills fromUniversity of California, Riverside.[23][24][25]
Unlikemuonium, positronium does not have a nucleus analogue, because the electron and the positron have equal masses.[26] Consequently, while muonium tends to behave like a light isotope of hydrogen,[27] positronium shows large differences in size, polarisability, and binding energy from hydrogen.[26]
Theevents in the early universe leading tobaryon asymmetry predatethe 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 incosmic ray–atmosphere interactions, and so are too hot (thermally energetic) to form electrical bonds beforeannihilation.
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