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Positronium (Ps) is a system consisting of an
electron The electron ( or ) 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 particles because they have no kn ...
and its
anti-particle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
, 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 collides ...
, bound together into an
exotic atom An exotic atom is an otherwise normal atom in which one or more sub-atomic particles have been replaced by other particles of the same charge. For example, electrons may be replaced by other negatively charged particles such as muons (muonic atoms) ...
, specifically an
onium An onium (plural: onia) is a bound state of a particle and its antiparticle. These states are usually named by adding the suffix ''-onium'' to the name of one of the constituent particles (replacing an ''-on'' suffix when present), with one except ...
. Unlike hydrogen, the system has no
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s. The system is unstable: the two particles annihilate each other to predominantly produce two or three
gamma-ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nucleus, atomic nuclei. It consists of the shortest wavelength electromagnetic wav ...
s, depending on the relative spin states. The
energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The te ...
s 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 consti ...
(which is a bound state of a
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
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 eq ...
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 nucl ...
arising from the relative orientations of the spins of the electron and the positron. The ''singlet'' state, , with antiparallel
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
s ( ''S'' = 0, ''Ms'' = 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 In physics, the center-of-momentum frame (also zero-momentum frame or COM frame) of a system is the unique (up to velocity but not origin) inertial frame in which the total momentum of the system vanishes. The ''center of momentum'' of a system i ...
). ''Para''-positronium can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases with the number: the
branching ratio In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to eithe ...
for decay into 4 photons is . ''Para-''positronium lifetime in vacuum is approximately t_0 = \frac = 0.1244 ~\mathrm. The ''triplet'' states, 3S1, with
parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster of ...
spins (''S'' = 1, ''Ms'' = −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: t_1 = \frac = 138.6 ~\mathrm. However more accurate calculations with corrections to O2) 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 Energy level, energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of me ...
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 a ...
. 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 Quantum electrodynamics (QED), a relativistic quantum field theory of electrodynamics, is among the most stringently tested theories in physics. The most precise and specific tests of QED consist of measurements of the electromagnetic fine-structur ...
, confirming
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
(QED) predictions to high precision. Annihilation can proceed via a number of channels, each producing
gamma rays A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
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 The electron neutrino () is an elementary particle which has zero electric charge and a spin of . Together with the electron, it forms the first generation of leptons, hence the name electron neutrino. It was first hypothesized by Wolfgang Pauli ...
–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 In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...
. 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 published i ...
or the
Breit equation The Breit equation is a relativistic wave equation derived by Gregory Breit in 1929 based on the Dirac equation, which formally describes two or more massive spin-1/2 particles (electrons, for example) interacting electromagnetically to the firs ...
, 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): E_n = -\frac \frac, where: * is the charge magnitude of the electron (same as the positron), * is Planck's constant, * is the
electric constant Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...
(otherwise known as the permittivity of free space), * is the
reduced mass In physics, the reduced mass is the "effective" Mass#Inertial mass, inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem. Note, how ...
: \mu = \frac = \frac = \frac, 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 E_n = -\frac \frac \frac = \frac. The lowest energy level of positronium () is . The next level is . The negative sign is a convention that implies a
bound state Bound or bounds may refer to: Mathematics * Bound variable * Upper and lower bounds, observed limits of mathematical functions Physics * Bound state, a particle that has a tendency to remain localized in one or more regions of space Geography *B ...
. Positronium can also be considered by a particular form of the two-body Dirac equation; Two particles with a
Coulomb interaction Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
can be exactly separated in the (relativistic)
center-of-momentum frame In physics, the center-of-momentum frame (also zero-momentum frame or COM frame) of a system is the unique (up to velocity but not origin) inertial frame in which the total momentum of the system vanishes. The ''center of momentum'' of a system i ...
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 physics, 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 ...
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 In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between ele ...
) 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 Metabolism, metabolic processes, and in other physiological activities including bl ...
. 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 Stjepan Mohorovičić (August 20, 1890 – February 13, 1980) was a Croatian physicist, geophysicist and meteorologist. Biography Mohorovičić was born in the town of Bakar. His father is the world-famous geophysicist Andrija Mohorovičić. He ...
predicted the existence of positronium in a 1934 article published in ''
Astronomische Nachrichten ''Astronomische Nachrichten'' (''Astronomical Notes''), one of the first international journals in the field of astronomy, was established in 1821 by the German astronomer Heinrich Christian Schumacher. It claims to be the oldest astronomical jour ...
'', 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 Martin Deutsch (29 January 1917 – 16 August 2002) was an Austrian-American professor of physics at MIT. He is best known for being the discoverer of positronium. Early life Deutsch was born in Vienna during the First World War to a Jewish ...
at
MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...
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 Positronium hydride, or hydrogen positride is an exotic molecule consisting of a hydrogen atom bound to an exotic atom of positronium (that is a combination of an electron and a positron). Its formula is PsH. It was predicted to exist in 1951 by A ...
(PsH) can be made. Positronium can also form a cyanide and can form bonds with halogens or lithium. The first observation of
di-positronium Di-positronium, or dipositronium, is an exotic molecule consisting of two atoms of positronium. It was predicted to exist in 1946 by John Archibald Wheeler, and subsequently studied theoretically, but was not observed until 2007 in an experiment p ...
()
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 bioch ...
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 land-grant research university in Riverside, California. It is one of the ten campuses of the University of California system. The main campus sits on in a suburban distr ...
.


Natural occurrence

The
events Event may refer to: Gatherings of people * Ceremony, an event of ritual significance, performed on a special occasion * Convention (meeting), a gathering of individuals engaged in some common interest * Event management, the organization of ev ...
in the early universe leading to
baryon asymmetry In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem, is the observed imbalance in baryonic matter (the type of matter experienced in everyday life) and antib ...
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 own ...
–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 a ...
. 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 While the future cannot be predicted with certainty, present understanding in various scientific fields allows for the prediction of some far-future events, if only in the broadest outline. These fields include astrophysics, which studies how ...
if
proton decay In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov ...
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 The Breit equation is a relativistic wave equation derived by Gregory Breit in 1929 based on the Dirac equation, which formally describes two or more massive spin-1/2 particles (electrons, for example) interacting electromagnetically to the firs ...
*
Antiprotonic helium Antiprotonic helium is a three-body atom composed of an antiproton and an electron orbiting around a helium nucleus. It is thus made partly of matter, and partly of antimatter. The atom is electrically neutral, since both electrons and antiprot ...
*
Di-positronium Di-positronium, or dipositronium, is an exotic molecule consisting of two atoms of positronium. It was predicted to exist in 1946 by John Archibald Wheeler, and subsequently studied theoretically, but was not observed until 2007 in an experiment p ...
*
Quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
*
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 antipartic ...
*
Two-body Dirac equations 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 reformula ...


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