Editing Positronium (section)

==States==

The mass of positronium is 1.022&nbsp;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 a [[hyperfine structure]] arising from the relative orientations of the spins of the electron and the positron.

The [[Singlet state|''singlet'' state]], {{SubatomicParticle|para-positronium}},  with [[Antiparallel vectors|antiparallel]] [[Spin (physics)|spin]]s ([[spin quantum number|''S'']]&nbsp;=&nbsp;0, ''M<sub>s</sub>''&nbsp;=&nbsp;0) is known as ''para''-positronium (''p''-Ps). It has a mean lifetime of {{val|0.12|ul=ns}} and decays preferentially into two gamma rays with energy of {{val|511|ul=keV}} each (in the [[center-of-mass frame]]). ''Para''-positronium can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases with the number: the [[branching ratio]] for decay into 4 photons is {{val|1.439|(2)|e=-6}}.<ref name="hep-ph0310099">
{{cite journal
 |last1=Karshenboim | first1=Savely G.
 |date=2003
 |title=Precision Study of Positronium: Testing Bound State QED Theory
 |doi=10.1142/S0217751X04020142
 |journal=International Journal of Modern Physics A
 |volume=19
 |issue=23
 |pages=3879–3896
 |arxiv=hep-ph/0310099
 |bibcode = 2004IJMPA..19.3879K | s2cid=14848837
 }}</ref>

''Para-''positronium lifetime in vacuum is approximately<ref name="hep-ph0310099"/>
<math display="block">t_0 = \frac{2 \hbar}{m_\mathrm{e} c^2 \alpha^5} = 0.1244 ~\mathrm{ns}.</math>

The [[Triplet state|''triplet'' state]]s, <sup>3</sup>S<sub>1</sub>, with [[Parallel (geometry)|parallel]] spins (''S''&nbsp;=&nbsp;1, ''M<sub>s</sub>''&nbsp;=&nbsp;−1, 0, 1) are known as ''ortho''-positronium (''o''-Ps), and have an energy that is approximately 0.001 eV higher than the singlet.<ref name="hep-ph0310099"/> These states have a mean lifetime of {{val|142.05|0.02|u=ns}},<ref name="Badertscher">
{{cite journal |first1=A.| last1=Badertscher| first2=P.| last2=Crivelli| first3=W.|last3=Fetscher| first4=U.|last4=Gendotti|first5=S. N.| last5=Gninenko
 |first6=V.|last6=Postoev| first7=A.|last7=Rubbia| first8=V.|last8=Samoylenko| first9=D.|last9=Sillou
 |year=2007
 |title=An Improved Limit on Invisible Decays of Positronium
 |journal=[[Physical Review D]]
 |volume=75 |pages=032004
 |doi=10.1103/PhysRevD.75.032004
 |arxiv=hep-ex/0609059
 |bibcode=2007PhRvD..75c2004B
 |issue=3 |s2cid=9001914}}</ref> and the leading decay is three gammas. Other modes of decay are negligible; for instance, the five-photons mode has branching ratio of ≈{{val||e=-6}}.<ref name="hep-ph9911410">
{{Cite book
 |last1=Czarnecki |first1=Andrzej |last2=Karshenboim |first2=Savely G.
 |date=2000
 |chapter=Decays of Positronium
 |editor1-last=Levchenko | editor1-first=B. B.
 |editor2-last=Savrin | editor2-first=V. I.
 |title=Proceedings of the International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP)
 |volume=14
 |pages=538–544
 |arxiv=hep-ph/9911410
 |bibcode = 1999hep.ph...11410C
}}</ref>

''Ortho''-positronium lifetime in vacuum can be calculated approximately as:<ref name="hep-ph0310099"/>
<math display="block">t_1 = \frac{\frac{1}{2} 9 h}{2 m_\mathrm{e} c^2 \alpha^6 (\pi^2 - 9)} = 138.6 ~\mathrm{ns}.</math>

However more accurate calculations with corrections to [[Big O notation|O]](α<sup>2</sup>) yield a value of {{val|7.040|ul=us}}<sup>&minus;1</sup> for the decay rate, corresponding to a lifetime of {{val|142|u=ns}}.<ref name=Kat/><ref name=adk>{{cite journal|last1=Adkins|first1=G. S.|last2=Fell|first2=R. N.|last3=Sapirstein|first3=J.|title=Order α<sup>2</sup> Corrections to the Decay Rate of Orthopositronium|journal=Physical Review Letters|date=29 May 2000|volume=84|issue=22|pages=5086–5089|doi=10.1103/PhysRevLett.84.5086|pmid=10990873|arxiv = hep-ph/0003028 |bibcode = 2000PhRvL..84.5086A |s2cid=1165868}}</ref>

Positronium in the 2S state is [[metastable]] having a lifetime of {{val|1100|u=ns}} against [[annihilation]].<ref name="atom-ph150305755">
{{cite journal
 |last1=Cooke| first1=D. A. |last2=Crivelli| first2=P. | first3=J. |last3=Alnis| first4=A. |last4=Antognini| first5=B. |last5=Brown| first6=S.
 |last6=Friedreich| first7=A. |last7=Gabard| first8=T. W. |last8=Haensch| first9=K. |last9=Kirch| first10=A. |last10=Rubbia| first11=V. |last11=Vrankovic
 |year=2015
 |title=Observation of positronium annihilation in the 2S state: towards a new measurement of the 1S-2S transition frequency
 |doi=10.1007/s10751-015-1158-4
 |journal=Hyperfine Interact.
 |volume=233
 |issue=1–3
 |pages=67–73
 |arxiv=1503.05755 |bibcode=2015HyInt.233...67C| s2cid=89605682 }}</ref> The positronium created in such an excited state will quickly cascade down to the ground state, where annihilation will occur more quickly.

=== Measurements ===
Measurements of these lifetimes and energy levels have been used in [[precision tests of quantum electrodynamics]], confirming [[quantum electrodynamics]] (QED) predictions to high precision.<ref name="hep-ph0310099" /><ref>
{{cite journal
 |last1=Rubbia | first1=A.
 |date=2004
 |title=Positronium as a probe for new physics beyond the standard model
 |doi=10.1142/S0217751X0402021X
 |journal=International Journal of Modern Physics A
 |volume=19
 |issue=23
 |pages=3961–3985
 |arxiv=hep-ph/0402151
 |bibcode = 2004IJMPA..19.3961R | citeseerx=10.1.1.346.5173
 | s2cid=119442567
}}</ref><ref>
{{cite journal
 |last1=Vetter |first1=P.A. |last2=Freedman |first2=S.J.
 |date=2002
 |title=Branching-ratio measurements of multiphoton decays of positronium
 |journal=[[Physical Review A]]
 |volume=66 |pages=052505
 |doi=10.1103/PhysRevA.66.052505
 |bibcode = 2002PhRvA..66e2505V
 |issue=5 |osti=821022 |url=https://digital.library.unt.edu/ark:/67531/metadc736097/
}}</ref>

Annihilation can proceed via a number of channels, each producing [[gamma rays]] with total energy of {{val|1022|ul = 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 a [[neutrino]]–antineutrino pair is also possible, but the probability is predicted to be negligible. The branching ratio for ''o''-Ps decay for this channel is {{val|6.2|e=-18}} ([[electron neutrino]]–antineutrino pair) and {{val|9.5|e=-21}} (for other flavour)<ref name="hep-ph9911410" /> in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like relatively high [[magnetic moment]]. The experimental upper limits on branching ratio for this decay (as well as for a decay into any "invisible" particles) are <{{val|4.3|e=-7}} for ''p''-Ps and <{{val|4.2|e=-7}} for ''o''-Ps.<ref name="Badertscher" />