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| [[File:Positronium.svg|thumb|200px|right|An [[electron]] and [[positron]] orbiting around their common [[centre of mass]]. This is a bound quantum state known as '''positronium'''.]]
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| '''Positronium''' ('''Ps''') is a system consisting of an [[electron]] and its [[antimatter|anti-particle]], a [[positron]], bound together into an "[[exotic atom]]". The system is unstable: the two particles annihilate each other to produce two [[gamma ray]] photons after an average lifetime of 125 [[picosecond]]s or three [[gamma ray]] photons after 142 [[nanosecond]]s in vacuum, depending on the relative spin states of the positron and electron. The orbit of the two particles and the set of [[energy level]]s is similar to that of the [[hydrogen]] [[atom]] (electron and [[proton]]). However, because of the [[reduced mass]], the [[frequency|frequencies]] associated with the [[spectral line]]s are less than half of those of the corresponding hydrogen lines.
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| ==States==
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| The [[ground state]] of positronium, like that of hydrogen, has two possible configurations depending on the relative orientations of the spins of the electron and the positron.
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| The ''[[Singlet state|singlet]]'' state with [[Antiparallel (mathematics)|antiparallel]] [[spin (physics)|spin]]s ([[spin quantum number|''S'']] = 0, ''M<sub>s</sub>'' = 0) is known as ''para-positronium'' (''p''-Ps) and denoted {{SubatomicParticle|para-positronium}}. 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: the [[branching ratio]] for decay into 4 photons is {{val|1.439|(2)|e=-6}}.<ref name="hep-ph0310099">
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| {{cite journal
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| |last1=Karshenboim | first1=Savely G.
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| |year=2003
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| |title=Precision Study of Positronium: Testing Bound State QED Theory
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| |doi=10.1142/S0217751X04020142
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| |journal=International Journal of Modern Physics A [Particles and Fields; Gravitation; Cosmology; Nuclear Physics]
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| |volume=19
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| |issue=23
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| |pages=3879–3896
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| |arxiv=hep-ph/0310099
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| |bibcode = 2004IJMPA..19.3879K }}</ref>
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| para-positronium lifetime (S = 0):<ref name="hep-ph0310099"/>
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| :<math>t_{0} = \frac{2 \hbar}{m_e c^2 \alpha^5} = 1.244 \times 10^{-10} \; \text{s}</math>
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| The ''[[Triplet state|triplet]]'' state with [[Parallel (geometry)|parallel]] spins (''S'' = 1, ''M<sub>s</sub>'' = −1, 0, 1) is known as ''ortho-positronium'' (''o''-Ps) and denoted <sup>3</sup>S<sub>1</sub>. The triplet state in vacuum has a mean lifetime of {{val|142.05|0.02|u=ns}}<ref>
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| {{cite journal
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| |author=A. Badertscher ''et al.''
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| |year=2007
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| |title=An Improved Limit on Invisible Decays of Positronium
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| |journal=[[Physical Review D]]
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| |volume=75 |pages=032004
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| |doi=10.1103/PhysRevD.75.032004
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|
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| |arxiv=hep-ex/0609059
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| |bibcode = 2007PhRvD..75c2004B
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| |issue=3 }}</ref> and the leading mode of decay is three gamma quanta. Other modes of decay are negligible; for instance, the five photons mode has branching ratio of ~{{val|1.0|e=-6}}.<ref name="hep-ph9911410">
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| {{cite journal
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| |last1=Czarnecki |first1=Andrzej |last2=Karshenboim |first2=Savely G.
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| |year=1999
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| |title=Decays of Positronium
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| |volume=14
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| |issue=99
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| | editor1-first=B.B.
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| | editor1-last=Levchenko
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| | editor2-first=V.I.
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| | editor2-last=Savrin
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| | journal=Proceedings of the International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP)
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| | place=Moscow
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| | publisher=MSU-Press
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| | year=2000
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| | pages=538–544
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| |arxiv=hep-ph/9911410
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| |bibcode = 1999hep.ph...11410C }}</ref>
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| ortho-positronium lifetime (S = 1):<ref name="hep-ph0310099"/>
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| :<math>t_{1} = \frac{\frac{1}{2} 9 h}{2 m_e c^2 \alpha^6 (\pi^2 - 9)} = 1.386 \times 10^{-7} \; \text{s}</math>
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| Positronium in the 2S state is [[metastable]] having a lifetime of {{val|1.1|u=us}} against [[annihilation]].{{Citation needed|date=September 2007}} If the positronium is created in such an excited state then it will quickly cascade down to the ground state where [[annihilation]] will occur more quickly. Measurements of these lifetimes, as well as of the positronium energy levels, have been used in [[precision tests of quantum electrodynamics]].<ref name="hep-ph0310099"/><ref>
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| {{cite journal
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| |last1=Rubbia | first1=A.
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| |year=2004
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| |title=Positronium as a probe for new physics beyond the standard model
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| |doi=10.1142/S0217751X0402021X
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| |journal=International Journal of Modern Physics A [Particles and Fields; Gravitation; Cosmology; Nuclear Physics]
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| |volume=19
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| |issue=23
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| |pages=3961–3985
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| |arxiv=hep-ph/0402151
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| |bibcode = 2004IJMPA..19.3961R }}</ref>
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| Annihilation can proceed via a number of channels each producing one or more [[gamma rays]]. The gamma rays are produced with a total energy of {{val|1022|ul=keV}} (since each of the annihilating particles have mass of {{val|511|ul=keV/c2}}), the most probable annihilation channels produce two or three photons, depending on the relative spin configuration of the electron and positron. A single photon decay is only possible if another body (e.g. an [[electron]]) is in the vicinity of the annihilating positronium to which some of the energy from the annihilation event may be transferred. Up to five annihilation gamma rays have been observed in laboratory experiments,<ref>
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| {{cite journal
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| |last=Vetter |first=P.A. |last2=Freedman |first2=S.J.
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| |year=2002
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| |title=Branching-ratio measurements of multiphoton decays of positronium
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| |journal=[[Physical Review A]]
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| |volume=66 |pages=052505
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| |doi=10.1103/PhysRevA.66.052505
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| |bibcode = 2002PhRvA..66e2505V
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| |issue=5 }}</ref> confirming the predictions of [[quantum electrodynamics]] to very high order.
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| 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 each non-electron flavour)<ref name="hep-ph9911410"/> in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like mass or 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}} (''p''-Ps) and <{{val|4.2|e=-7}} (''o''-Ps).<ref>
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| {{cite journal
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| |last=Badertscher |first=A. |coauthors=''et al.''
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| |year=2007
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| |title=Improved limit on invisible decays of positronium
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| |journal=[[Physical Review]] D
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| |volume=75 |pages=032004–1–10
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| |doi=10.1103/PhysRevD.75.032004
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| |bibcode=2007PhRvD..75c2004B
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| |arxiv=hep-ex/0609059
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| |issue=3
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| }}</ref>
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| ==Energy levels==
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| {{main|Bohr model#Electron energy levels}}
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| While precise calculation of positronium energy levels uses the [[Bethe–Salpeter equation]] or the [[Breit equation]], the similarity between positronium and hydrogen allows for a rough estimate. In this approximation, the energy levels are different between the two because of a different value for the mass, ''m''*, used in the energy equation
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| ::<math>E_n = - \frac{\mu q_e^4}{8 h^2 \epsilon_{0}^2} \frac{1}{n^2} \,.</math>
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| :See [[Bohr model#Electron energy levels|Electron energy levels]] for a derivation.
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| :<math>q_e</math> is the [[Elementary charge|charge magnitude]] of the electron (same as the positron)
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| :<math>h</math> is [[Planck's constant]]
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| :<math>\epsilon_{0}</math> is the [[electric constant]] (otherwise known as the permittivity of free space) and finally
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| :<math>\mu</math> is the [[reduced mass]]
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| The reduced mass in this case is
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| ::<math>\mu = {{m_e m_p} \over {m_e + m_p}} = \frac{m_e^2}{2m_e} = \frac{m_e}{2},</math>
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| :where
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| :<math>m_e</math> and <math>m_p</math> are, respectively, the mass of the electron and the positron—which are ''the same'' by definition of particles and antiparticles.
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| Thus, for positronium, its reduced mass only differs from the rest mass of 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.
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| So finally, the energy levels of positronium are given by
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| ::<math> E_n = - \frac{1}{2} \frac{m_e q_e^4}{8 h^2 \epsilon_{0}^2} \frac{1}{n^2} = \frac{-6.8 \ \mathrm{eV}}{n^2} \,.</math>
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| The lowest energy level of positronium (''n'' = 1) is −6.8 [[electron volts]] (eV). The next lowest energy level (''n'' = 2) is −1.7 eV. The negative sign implies a [[bound state]]. We also note that a two-body [[Dirac equation]] composed of a [[Dirac operator]] for each of the two point particles interacting via the [[Coulomb's law|Coulomb interaction]] can be exactly separated in the (relativistic) [[center of momentum frame]] and the resulting ground state eigenvalue has been obtained very accurately using the [[Finite element methods]] of J. Shertzer. The Dirac equation whose Hamiltonian comprises two Dirac particles and a static Coulomb potential is not relativistically invariant. But if one adds the 1/c^(2n) (or <math>{\textstyle \alpha^{2n}}</math> where <math>{\textstyle \alpha}</math> is the fine structure coefficient which is about 1/137) contributions where n=1,2,3, ... to the Hamiltonian then the result is relativistically invariant in the limit. So only the lead term in the Hamiltonian is included. The next 1/c^2 (or <math>{\textstyle \alpha^2}</math>) contribution are the Breit terms: workers rarely go to 1/c^4 (or <math>{\textstyle \alpha^4}</math>) because at <math>{\textstyle \alpha^3*\ln(\alpha)}</math>, one has
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| the Lamb shift (which is a detailed calculation needing quantum electrodynamics).<ref>
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| {{cite journal
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| |last=Scott |first=T.C. |last2=Shertzer |first2=J. |last3=Moore |first3=R.A.
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| |year=1992
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| |title=Accurate finite element solutions of the two-body Dirac equation
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| |journal=[[Physical Review A]]
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| |volume=45 |pages=4393–4398
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| |doi=10.1103/PhysRevA.45.4393
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| |bibcode=1992PhRvA..45.4393S |pmid=9907514 |issue=7
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| }}</ref>
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| ==Prediction and discovery==
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| [[Croatia]]n scientist [[Stjepan Mohorovičić]] predicted the existence of positronium in a 1934 paper published in ''[[Astronomische Nachrichten]]'', in which he called the substance "electrum".<ref>
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| {{cite journal
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| |last=Mohorovičić |first=S.
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| |year=1934
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| |journal=[[Astronomische Nachrichten]]
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| |volume=253 |pages=94
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| |doi=10.1002/asna.19342530402
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| |title=Möglichkeit neuer Elemente und ihre Bedeutung für die Astrophysik
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| |issue=4
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| }}</ref> Other sources credit [[Carl David Anderson|Carl Anderson]] as having predicted its existence in 1932 while at [[Caltech]].<ref name="DeutschObit">
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| {{cite press
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| |publisher=MIT
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| |year=2002
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| |title=Martin Deutsch, MIT physicist who discovered positronium, dies at 85
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| |url=http://web.mit.edu/newsoffice/2002/deutsch.html
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| }}</ref> It was experimentally discovered by [[Martin Deutsch]] at [[MIT]] in 1951, and became known as positronium.<ref name="DeutschObit"/>
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| ==Exotic compounds==
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| Molecular bonding was predicted for positronium.<ref>
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| {{cite arxiv
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| |title=Signature of the existence of the positronium molecule
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| |eprint=physics/9804023v1
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| |last1=Usukura | first1=J.
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| |last2=Varga | first2=K.
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| |last3=Suzuki | first3=Y.
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| |class=physics.atom-ph
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| |year=1998
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| }}</ref> Molecules of [[positronium hydride]] (PsH) can be made.<ref>{{cite web|url=http://www.sc.doe.gov/bes/accomplishments/files/BES_Accomp_FY1992.pdf|page=9|title="Out of This World" Chemical Compound Observed}}</ref> Positronium can also form a cyanide and can form bonds with halogens or lithium.<ref name="Saito">{{cite journal|last=Saito|first=Shiro L.|year=2000|title=Is Positronium Hydride Atom or Molecule?|journal=Nuclear Instruments and Methods in Physics Research B|volume=171|pages=60–66}}</ref>
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| The first observation of [[di-positronium]] [[molecule]]s—molecules consisting of two positronium atoms—was reported on 12 September 2007 by David Cassidy and Allen Mills from [[University of California at Riverside]].<ref>
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| {{cite journal
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| |last=Cassidy |first=D.B. |last2=Mills |first2=A.P. (Jr.)
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| |year=2007
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| |title=The production of molecular positronium
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| |journal=[[Nature (journal)|Nature]]
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| |volume=449 |pages=195–197
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| |doi=10.1038/nature06094
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| |laysummary=http://www.nature.com/nature/journal/v449/n7159/full/449153a.html
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| |pmid=17851519
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| |issue=7159
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| |bibcode = 2007Natur.449..195C }}</ref><ref>
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| {{cite web
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| |url=http://www.physorg.com/news108822085.html
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| |publisher=[[Physorg.com]]
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| |title=Molecules of positronium observed in the lab for the first time
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| |accessdate=2007-09-07
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| }}</ref>
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| ==Natural occurrence==
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| Positronium in high energy states has been predicted to be the dominant form of atomic matter in the universe in the far future, if [[proton decay]] is a reality.<ref name=dying>A dying universe: the long-term fate and evolution of astrophysical objects, Fred C. Adams and Gregory Laughlin, ''Reviews of Modern Physics'' '''69''', #2 (April 1997), pp. 337–372. {{bibcode|1997RvMP...69..337A}}. {{doi|10.1103/RevModPhys.69.337}} {{arxiv|astro-ph/9701131}}.</ref>
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| ==See also==
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| *[[Breit equation]]
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| *[[Onium]]
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| *[[Antiprotonic helium]]
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| *[[Quantum electrodynamics]]
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| *[[Protonium]]
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| *[[Two-body Dirac equations]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://www.universetoday.com/am/publish/search_positronium.html The Search for Positronium]
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| * [http://web.mit.edu/newsoffice/2002/deutsch.html Obituary of Martin Deutsch, discoverer of Positronium]
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| * [http://www.como.polimi.it/positron Website about positrons, positronium and antihydrogen. Positron Laboratory, Como, Italy]
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| {{particles}}
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| {{QED}}
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| [[Category:Subatomic particles]]
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| [[Category:Particle physics]]
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| [[Category:Molecular physics]]
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| [[Category:Quantum electrodynamics]]
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| [[Category:Exotic atoms]]
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| [[Category:Spintronics]]
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| [[Category:Onium]]
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