Positronium
Encyclopedia
Positronium is a system consisting of an electron
and its anti-particle
, a positron
, bound together into an "exotic atom
". Being unstable, the two particles annihilate each other to produce two gamma ray
photons after an average lifetime of 125 ps or three gamma ray
photons after 142 ns
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 frequencies
associated with the spectral line
s are less than half of those of the corresponding hydrogen lines.
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 with antiparallel
spin
s (S
= 0, Ms = 0) is known as para-positronium (p-Ps) and denoted . 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 .
para-positronium lifetime (S = 0):
The triplet
state with parallel
spins (S = 1, Ms = −1, 0, 1) is known as ortho-positronium (o-Ps) and denoted 3S1. The triplet state in vacuum has a mean lifetime of 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 ~.
ortho-positronium lifetime (S = 1):
Positronium in the 2S state is metastable having a lifetime of against annihilation
. 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.
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 (since each of the annihilating particles have mass of ), 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, confirming the predictions of quantum electrodynamics
to very high order.
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 (electron neutrino-antineutrino pair) and (for each non-electron flavour) 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: < (p-Ps) and < (o-Ps).
, 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
The reduced mass in this case is
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.
So finally, the energy levels of positronium are given by
The lowest energy level of positronium (n = 1) is −6.8 electron volts (eV). The next highest 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 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.
n scientist Stjepan Mohorovičić
predicted the existence of positronium in a 1934 paper published in Astronomische Nachrichten
, in which he called the substance "electrum". Other sources credit Carl Anderson
as having predicted its existence in 1932 while at Caltech. It was experimentally discovered by Martin Deutsch
at MIT in 1951, and became known as 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.
is a reality.
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
and its anti-particle
Antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...
, a positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
, bound together into an "exotic atom
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 or pions...
". Being unstable, the two particles annihilate each other to produce two gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
photons after an average lifetime of 125 ps or three gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
photons after 142 ns
Nanosecond
A nanosecond is one billionth of a second . One nanosecond is to one second as one second is to 31.7 years.The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns....
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
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
s is similar to that of the hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
(electron and proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
). However, because of the reduced mass
Reduced mass
Reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. This is a quantity with the unit of mass, which allows the two-body problem to be solved as if it were a one-body problem. Note however that the mass determining the gravitational force is not...
, the frequencies
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
associated with the spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...
s are less than half of those of the corresponding hydrogen lines.
States
The ground stateGround state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than 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 with antiparallel
Antiparallel (mathematics)
-Definitions:Given two lines m_1 \, and m_2 \,, lines l_1 \, and l_2 \, are anti-parallel with respect to m_1 \, and m_2 \, if \angle 1 = \angle 2 \,....
spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
s (S
Spin quantum number
In atomic physics, the spin quantum number is a quantum number that parameterizes the intrinsic angular momentum of a given particle...
= 0, Ms = 0) is known as para-positronium (p-Ps) and denoted . It has a mean lifetime of 125 picoseconds and decays preferentially into two gamma quanta with energy of 511 keV
Kev
Kev can refer to:*Kev Hawkins, a fictional character.*Kevin, a given name occasionally shortened to "Kev".*Kiloelectronvolt, a unit of energy who symbol is "KeV".* Krefelder Eislauf-VereinKEV can refer to:...
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
Positron emission tomography
Positron emission tomography is nuclear medicine imaging technique that produces a three-dimensional image or picture of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide , which is introduced into the body on a...
. 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
Branching ratio
In particle physics and nuclear physics, the branching fraction for a decay is the fraction of particles which decay by an individual decay mode with respect to the total number of particles which decay. It is equal to the ratio of the partial decay constant to the overall decay constant...
for decay into 4 photons is .
para-positronium lifetime (S = 0):
The triplet
Triplet state
A spin triplet is a set of three quantum states of a system, each with total spin S = 1 . The system could consist of a single elementary massive spin 1 particle such as a W or Z boson, or be some multiparticle state with total spin angular momentum of one.In physics, spin is the angular momentum...
state with parallel
Parallel (geometry)
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...
spins (S = 1, Ms = −1, 0, 1) is known as ortho-positronium (o-Ps) and denoted 3S1. The triplet state in vacuum has a mean lifetime of 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 ~.
ortho-positronium lifetime (S = 1):
Positronium in the 2S state is metastable having a lifetime of against annihilation
Annihilation
Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....
. If the positronium is created in such an excited state then it will quickly cascade down to the ground state where annihilation
Annihilation
Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....
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.
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 (since each of the annihilating particles have mass of ), 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
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
) 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, confirming the predictions of quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics 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 special relativity is achieved...
to very high order.
The annihilation into a neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
-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 each non-electron flavour) in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like mass or relatively high magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
. The experimental upper limits on branching ratio for this decay (as well as for a decay into any "invisible" particles) are: < (p-Ps) and < (o-Ps).
Energy levels
While precise calculation of positronium energy levels uses the Bethe-Salpeter equationBethe-Salpeter equation
The Bethe–Salpeter equation, named after Hans Bethe and Edwin Salpeter, describes the bound states of a two-body quantum field theoretical system in a relativistically covariant formalism...
, 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
-
- See Electron energy levels for a derivation.
is the charge magnitudeElementary chargeThe elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...
of the electron (same as the positron)
is Planck's constant
is the electric constantElectric constantThe physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant is an ideal, physical constant, which is the value of the absolute dielectric permittivity of classical vacuum...
(otherwise known as the permittivity of free space) and finally
is the reduced massReduced massReduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. This is a quantity with the unit of mass, which allows the two-body problem to be solved as if it were a one-body problem. Note however that the mass determining the gravitational force is not...
The reduced mass in this case is
-
- where
and 
are, respectively, the mass of the electron and the positron—which are the same by definition of particles and antiparticles.
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.
So finally, the energy levels of positronium are given by
The lowest energy level of positronium (n = 1) is −6.8 electron volts (eV). The next highest energy level (n = 2) is −1.7 eV. The negative sign implies a bound state
Bound state
In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...
. We also note that a two-body Dirac equation
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
composed of a Dirac operator
Dirac operator
In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian...
for each of the two point particles interacting via the Coulomb interaction
Coulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...
can be exactly separated in the (relativistic) center of momentum frame
Center of momentum frame
A center-of-momentum frame of a system is any inertial frame in which the center of mass is at rest . Note that the center of momentum of a system is not a location, but rather defines a particular inertial frame...
and the resulting ground state eigenvalue has been obtained very accurately using the Finite element methods of J. Shertzer.
Prediction and discovery
CroatiaCroatia
Croatia , officially the Republic of Croatia , is a unitary democratic parliamentary republic in Europe at the crossroads of the Mitteleuropa, the Balkans, and the Mediterranean. Its capital and largest city is Zagreb. The country is divided into 20 counties and the city of Zagreb. Croatia covers ...
n scientist Stjepan Mohorovičić
Stjepan Mohorovicic
Stjepan Mohorovičić was a Croatian scientist born in the town of Bakar and died in the city of Zagreb, Croatia...
predicted the existence of positronium in a 1934 paper published in Astronomische Nachrichten
Astronomische Nachrichten
Astronomische Nachrichten , one of the first international journals in the field of astronomy, was founded in 1821 by the German astronomer Heinrich Christian Schumacher. It claims to be the oldest astronomical journal in the world that is still being published...
, in which he called the substance "electrum". Other sources credit Carl Anderson
Carl David Anderson
Carl David Anderson was an American physicist. He is best known for his discovery of the positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics, and of the muon in 1936.-Biography:...
as having predicted its existence in 1932 while at Caltech. It was experimentally discovered by Martin Deutsch
Martin Deutsch
Martin Deutsch was an Austrian-American physicist, who was emeritus professor of physics at MIT. He is best known for being the discoverer of positronium.-Early life:...
at MIT in 1951, and became known as positronium.
Observation of di-positronium molecules
The first observation of di-positroniumDi-positronium
Di-positronium, or dipositronium, is a 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 done by David Cassidy and Allen Mills at the University of...
molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
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.
Natural occurrence
Positronium in high energy states has been predicted to be the dominant form of matter in the universe in the far future, if proton decayProton decay
In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...
is a reality.
See also
- OniumOniumAn onium is the bound state of a particle and its antiparticle. They are usually named by adding the suffix -onium to the name of the constituting particle. However, despite its name, Muonium is not a muon–antimuon onium because IUPAC assigned the name to the system of an antimuon bound with an...
- Di-positroniumDi-positroniumDi-positronium, or dipositronium, is a 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 done by David Cassidy and Allen Mills at the University of...
- Positronium hydridePositronium hydridePositronium hydride is a molecule consisting of an atom of positronium, and one of hydrogen. Its formula is PsH. It was predicted to exist in 1951 by A Ore, and subsequently studied theoretically, but was not observed until 1990. R. Pareja, R. Gonzalez from Madrid trapped positronium in hydrogen...
- Antiprotonic heliumAntiprotonic heliumAntiprotonic 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 antiprotons have a charge of -1, whereas helium nuclei have a...
- Quantum electrodynamicsQuantum electrodynamicsQuantum electrodynamics 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 special relativity is achieved...