Positronium (Ps) is a system consisting of an
electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary partic ...
and its
anti-particle, a
positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collide ...
, bound together into an
exotic atom, specifically an
onium. Unlike hydrogen, the system has no
protons. 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
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen cons ...
(which is a bound state of a
proton and an electron). However, because of the reduced mass, the
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is e ...
of the
spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
s are less than half of those for 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 lowest energy orbital state of positronium is 1S, and like with hydrogen, it has a
hyperfine structure
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the ...
arising from the relative orientations of the spins of the electron and the positron.
The
''singlet'' state, , with
antiparallel spins (
''S'' = 0, ''M
s'' = 0) is known as ''para''-positronium (''p''-Ps). It has a mean lifetime of and decays preferentially into two gamma rays with energy of 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 .
[
]
''Para-''positronium lifetime in vacuum is approximately
The
''triplet'' states,
3S
1, with
parallel spins (''S'' = 1, ''M
s'' = −1, 0, 1) are known as ''ortho''-positronium (''o''-Ps), and have an energy that is approximately 0.001 eV higher than the singlet.
These states have a mean lifetime of ,
[
] and the leading decay is three gammas. Other modes of decay are negligible; for instance, the five-photons mode has branching ratio of ≈.
[
]
''Ortho''-positronium lifetime in vacuum can be calculated approximately as:
However more accurate calculations with corrections to
O(α
2) yield a value of
−1 for the decay rate, corresponding to a lifetime of .
Positronium in the 2S state is metastable
In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy.
A ball resting in a hollow on a slope is a simple example of metastability. If the ball i ...
having a lifetime of against annihilation
In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy ...
.[
] 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.
Annihilation can proceed via a number of channels, each producing gamma rays with total energy of (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
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
–antineutrino pair is also possible, but the probability is predicted to be negligible. The branching ratio for ''o''-Ps decay for this channel is ( electron neutrino–antineutrino pair) and (for other flavour) 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 < for ''p''-Ps and < for ''o''-Ps.
Energy levels
While precise calculation of positronium energy levels uses the Bethe–Salpeter equation
The Bethe–Salpeter equation (named after Hans Bethe and Edwin Salpeter) describes the bound states of a two-body (particles) quantum field theoretical system in a relativistically covariant formalism. The equation was actually first publishe ...
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:
* is the charge magnitude of the electron (same as the positron),
* is Planck's constant,
* is the electric constant (otherwise known as the permittivity of free space),
* is the reduced mass: where and 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 () is . The next level is . The negative sign is a convention that implies a bound state. Positronium can also be considered by a particular form of the two-body Dirac equation
In quantum field theory, and in the significant subfields of quantum electrodynamics (QED) and quantum chromodynamics (QCD), the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulat ...
; 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 method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...
s of Janine Shertzer
Janine Shertzer (born 1956) is an American computational physicist known for her application of the finite element method to few-body systems in atomic physics. She is a distinguished professor of science at the College of the Holy Cross in Worc ...
and confirmed more recently. The Dirac equation whose Hamiltonian comprises two Dirac particles and a static Coulomb potential is not relativistically invariant. But if one adds the (or , where is the fine-structure constant) terms, where , then the result is relativistically invariant. Only the leading term is included. The contribution is the Breit term; workers rarely go to because at one has the Lamb shift, which requires quantum electrodynamics.[
]
Formation and decay in materials
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. It may however first form positronium before the annihilation event. The understanding of this process is of some importance in positron emission tomography
Positron emission tomography (PET) is a functional imaging technique that uses radioactive substances known as radiotracers to visualize and measure changes in metabolic processes, and in other physiological activities including blood flow, ...
. Approximately:
* ~60% of positrons will directly annihilate with an electron without forming positronium. The annihilation usually results in two gamma rays. In most cases this direct annihilation occurs only after the positron has lost its excess kinetic energy and has thermalized with the material.
* ~10% of positrons form ''para''-positronium, which then promptly (in ~0.12 ns) decays, usually into two gamma rays.
* ~30% of positrons form ''ortho''-positronium but then annihilate within a few nanoseconds by 'picking off' another nearby electron with opposing spin. This usually produces two gamma rays. During this time, the very lightweight positronium atom exhibits a strong zero-point motion, that exerts a pressure and is able to push out a tiny nanometer-sized bubble in the medium.
* Only ~0.5% of positrons form ''ortho''-positronium that self-decays (usually into ''three'' gamma rays). This natural decay rate of ''ortho''-positronium is relatively slow (~140 ns decay lifetime), compared to the aforementioned pick-off process, which is why the three-gamma decay rarely occurs.
History
Stjepan Mohorovičić predicted the existence of positronium in a 1934 article published in '' Astronomische Nachrichten'', in which he called it the "electrum". Other sources incorrectly credit Carl Anderson as having predicted its existence in 1932 while at Caltech
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
.[
] It was experimentally discovered by Martin Deutsch at MIT in 1951 and became known as positronium. Many subsequent experiments have precisely measured its properties and verified predictions of quantum electrodynamics. There was a discrepancy known as the ortho-positronium lifetime puzzle that persisted for some time, but was eventually resolved with further calculations and measurements. Measurements were in error because of the lifetime measurement of unthermalised positronium, which was only produced at a small rate. This had yielded lifetimes that were too long. Also calculations using relativistic quantum electrodynamics are difficult to perform, so they had been done to only the first order. Corrections that involved higher orders were then calculated in a non-relativistic quantum electrodynamics.
Exotic compounds
Molecular bonding was predicted for positronium. Molecules of positronium hydride (PsH) can be made. Positronium can also form a cyanide and can form bonds with halogens or lithium.
The first observation of di-positronium () molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bio ...
s—molecules consisting of two positronium atoms—was reported on 12 September 2007 by David Cassidy and Allen Mills from University of California, Riverside
The University of California, Riverside (UCR or UC Riverside) is a public university, public Land-grant university, land-grant research university in Riverside, California. It is one of the ten campuses of the University of California system. Th ...
.[
]
Natural occurrence
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
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our ow ...
–atmosphere interactions, and so are too hot (thermally energetic) to form electrical bonds before annihilation
In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy ...
.
Positronium in very weakly bound (extremely large ''n'') states has been predicted to be the dominant form of atomic matter in the universe in the far future if proton decay occurs. Although any positrons and electrons left over from the decay of matter would be initially moving far too fast to bind together, the expansion of the universe slows free particles, so much so that eventually (in years, when electrons and positrons are typically 1 quintillion parsecs apart) their kinetic energy will actually fall below the Coulomb attraction potential, and thus they will be weakly bound (positronium). The resulting weakly bound electron and positron spiral inwards and eventually annihilate, with an estimated lifetime of years.
See also
* Breit equation
* Antiprotonic helium
* Di-positronium
* Quantum electrodynamics
*Protonium
Protonium (symbol: Pn), also known as antiprotonic hydrogen, is a type of exotic atom in which a proton (symbol: p) and an antiproton (symbol: ) orbit each other. Since protonium is a bound system of a particle and its corresponding antipa ...
* Two-body Dirac equations
References
External links
The Search for Positronium
Website about positrons, positronium and antihydrogen. Positron Laboratory, Como, Italy
{{Authority control
Molecular physics
Quantum electrodynamics
Spintronics
Onia
Antimatter
Substances discovered in the 1950s