1. States
     Measurements  

2. Energy levels

3. History

4. Exotic compounds

5. Natural occurrence

6. See also

7. References

8. External links

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 orbit and 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). However, because of the reduced mass, the frequencies of the spectral lines are less than half of the corresponding hydrogen lines.

States

The mass of positronium is 1.022 MeV, which is twice the electron mass minus the binding energy of a few eV. 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.

The singlet state, {{SubatomicParticle|para-positronium}}, with antiparallel spins (S = 0, M_s = 0) is known as para-positronium (p-Ps). It has a mean lifetime of 0.125 ns and decays preferentially into two gamma rays with energy of {{val|511|ul=keV}} each (in the center-of-mass frame). By detecting these photons the position at which the decay occurred can be determined. This process is used in positron-emission tomography. 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}}.^[1]

The triplet state, ³S₁, with parallel spins (S = 1, M_s = −1, 0, 1) is known as ortho-positronium (o-Ps). It has a mean lifetime of {{val|142.05|0.02|u=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 ≈{{val||e=-6}}.^[3]

However more accurate calculations with corrections to order O(α²) yield a value of 7.040 μs⁻¹ for the decay rate, corresponding to a lifetime of {{val|142|u=ns}}.^[6][4]

Positronium in the 2S state is metastable having a lifetime of {{val|1100|u=ns}} against annihilation.^[5] 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.^[1][6][7] 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 recorded.

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)^[3] 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.^[2]

Energy levels

While precise calculation of positronium energy levels uses the Bethe–Salpeter equation or the Breit 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, m*, in the energy equation (see electron energy levels for a derivation):

where:

{{math|q_e}} is the charge magnitude of the electron (same as the positron),

{{mvar|h}} is Planck's constant,

{{math|ε₀}} is the electric constant (otherwise known as the permittivity of free space),

{{mvar|μ}} is the reduced mass:

where {{math|m_e}} and {{math|m_p}} are, respectively, the mass of the electron and the positron (which are the same by definition as antiparticles).

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 ({{math|n {{=}} 1}}) is −6.8 electronvolts (eV). The next level is {{val|-1.7|u=eV}}. The negative sign implies a bound state. Positronium can also be considered by a particular form of the two-body Dirac equation; Two point 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 J. Shertzer.^[14] The Dirac equation whose Hamiltonian comprises two Dirac particles and a static Coulomb potential is not relativistically invariant. But if one adds the {{math|{{sfrac|c²ⁿ}}}} (or {{math|α²ⁿ}}, where {{mvar|α}} is the fine-structure constant) terms, where {{math|n {{=}} 1,2…}}, then the result is relativistically invariant. Only the leading term is included. The {{math|α²}} contribution is the Breit term; workers rarely go to {{math|α⁴}} because at {{math|α³}} one has the Lamb shift, which requires quantum electrodynamics.^[8]

History

Exotic compounds

Molecular bonding was predicted for positronium.^[13] Molecules of positronium hydride (PsH) can be made.^[14] Positronium can also form a cyanide and can form bonds with halogens or lithium.^[15]

The first observation of di-positronium molecules—molecules consisting of two positronium atoms—was reported on 12 September 2007 by David Cassidy and Allen Mills from University of California, Riverside.^[16][17]

Natural occurrence

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.^[18]

See also

• Breit equation
• Antiprotonic helium
• Di-positronium
• Quantum electrodynamics
• Protonium
• Two-body Dirac equations

References

External links

• The Search for Positronium
• Obituary of Martin Deutsch, discoverer of Positronium
• Website about positrons, positronium and antihydrogen. Positron Laboratory, Como, Italy

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