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Positron

The positron, or antielectron, is a subatomic particle that serves as the antimatter counterpart to the electron, having an identical rest mass of approximately 0.511 MeV/c² but an opposite electric charge of +1 elementary charge (e).^[1]^[2] Predicted theoretically by Paul Dirac in 1928 through his relativistic quantum equation for the electron, which implied the existence of particles with positive charge to resolve negative energy solutions, the positron was experimentally discovered in 1932 by Carl David Anderson at the California Institute of Technology while studying cosmic ray tracks in a cloud chamber.^[3]^[4] Like the electron, the positron is a fundamental lepton with spin ½ and no known substructure, and it annihilates upon contact with an electron, converting their combined mass into two gamma-ray photons each of 0.511 MeV energy.^[5] This discovery confirmed the existence of antimatter and earned Anderson the 1936 Nobel Prize in Physics, profoundly influencing particle physics by enabling electron-positron colliders such as CERN's Large Electron-Positron Collider (LEP), which operated from 1989 to 2000 to probe electroweak unification, and practical applications like positron emission tomography (PET) in medical imaging, where positrons from radioactive tracers facilitate detailed body scans.^[6]^[7]

Properties

Fundamental characteristics

The positron, denoted as e^+, has a mass identical to that of the electron, $9.109\,383\,7139(28) \times 10^{-31} kg, and a rest energy of $0.510\,998\,950\,69(16) MeV/c^2.^[8]^[2] Its electric charge is +e, where e = 1.602\,176\,634 \times 10^{-19} C is the elementary charge magnitude, and it possesses an intrinsic spin of \frac{1}{2} \hbar.^[9]^[10] In the Standard Model of particle physics, the positron is classified as an elementary lepton and a spin-\frac{1}{2} fermion, with no observed substructure.^[10] A free positron is stable in vacuum, with an average lifetime exceeding $10^{21} years, as it does not undergo spontaneous decay.^[11] Due to its positive charge, a positron in an electric field experiences a force opposite to that on an electron of equal kinetic energy, and in a magnetic field, its trajectory curves in the opposite direction. In quantum electrodynamics (QED), the positron is represented in Feynman diagrams as the antiparticle counterpart to the electron, typically depicted as a fermion line with momentum and spin arrows directed backward in time relative to the electron.^[12]

Antiparticle nature

The positron, denoted as e^+, serves as the antiparticle of the electron e^-, exhibiting identical mass and spin-1/2 properties but with an opposite electric charge of +1 elementary charge. This duality arises from Paul Dirac's 1928 relativistic quantum mechanical equation for the electron, which incorporated both quantum mechanics and special relativity, leading to the prediction of antiparticles as solutions with reversed charge.^[13]^[14] The positron's properties are governed by the CPT theorem, a fundamental principle in quantum field theory stating that the combined symmetries of charge conjugation (C), parity (P), and time reversal (T) must be invariant in local, Lorentz-invariant field theories. Under CPT transformation, the positron maps directly to the electron, implying that antiparticles like the positron must share the same mass, spin, lifetime, and decay modes as their particle counterparts, differing only in additive quantum numbers such as charge and baryon number. This invariance underpins the expectation of symmetric behavior between matter and antimatter in particle interactions, with experimental tests in positronium (a bound electron-positron state) confirming CPT symmetry to high precision.^[15]^[16] Despite the theoretical symmetry predicted by CPT, the observable universe displays a striking matter-antimatter asymmetry, where ordinary matter vastly outnumbers antimatter, rendering free positrons exceedingly rare outside of high-energy processes or cosmic events. This imbalance, quantified by the baryon-to-photon ratio of approximately $6 \times 10^{-10}, suggests that the Big Bang produced equal amounts of matter and antimatter, but subtle violations in symmetries like CP (charge-parity) allowed a slight excess of matter to survive annihilation, leaving antimatter as a cosmic minority. As a result, positrons do not occur naturally in significant quantities in everyday matter-dominated environments.^[17]^[18] One key process for generating positrons alongside electrons is pair production, in which a gamma ray photon with energy greater than 1.022 MeV—the combined rest mass energy of an electron and positron—converts into an e^+ e^- pair near an atomic nucleus to conserve momentum. This threshold energy underscores the energy requirement for creating particle-antiparticle pairs from electromagnetic radiation, highlighting the positron's role in manifesting antimatter from neutral bosons.^[19]

History

Theoretical prediction

In the early 20th century, observations of cosmic rays prompted theoretical considerations of positively charged particles in addition to electrons. These ideas built on the 1912 discovery of cosmic rays by Victor Hess, highlighting the need for relativistic quantum descriptions of such particles.^[20] The relativistic wave equation for spin-0 particles, known as the Klein-Gordon equation, was proposed independently by Oskar Klein and Walter Gordon in 1926 to reconcile quantum mechanics with special relativity. Derived from the energy-momentum relation E^2 = p^2 c^2 + m^2 c^4 by replacing E \to i \hbar \partial_t and \vec{p} \to -i \hbar \nabla, it takes the form \left( \square + \frac{m^2 c^2}{\hbar^2} \right) \psi = 0, where \square = \partial^\mu \partial_\mu is the d'Alembertian. However, this second-order equation led to a conserved charge density \rho = \frac{i \hbar}{2 m c^2} (\psi^* \partial_t \psi - \psi \partial_t \psi^*) that could be negative, violating the positive-definiteness required for a probability interpretation, and it failed to describe electron spin or fine structure. These limitations motivated Paul Dirac to seek a first-order relativistic equation compatible with quantum mechanics.^[21] In 1928, Dirac formulated a linear relativistic wave equation for the electron, balancing the non-relativistic Schrödinger form with Lorentz invariance. Starting from the classical relativistic energy E = c |\vec{p}| + m c^2 (for positive branch) and quantizing while ensuring first-order time derivatives, Dirac postulated the Hamiltonian H = c \vec{\alpha} \cdot \vec{p} + \beta m c^2, where \vec{\alpha} and \beta are 4x4 matrices satisfying anticommutation relations \{\alpha_i, \alpha_j\} = 2 \delta_{ij}, \{\alpha_i, \beta\} = 0, \beta^2 = 1. The resulting Dirac equation is

i \hbar \frac{\partial \psi}{\partial t} = \left( c \vec{\alpha} \cdot \vec{p} + \beta m c^2 \right) \psi,

with \psi a four-component spinor. This equation yields positive-definite probability density |\psi|^2 and naturally incorporates electron spin-1/2, but its energy spectrum includes both positive and negative continua, with negative solutions implying unstable particles that could cascade to lower energies.^[22] To resolve the negative-energy problem, Dirac proposed the "hole theory" in 1930, envisioning the vacuum as a filled "Dirac sea" of negative-energy electron states, forbidden by the Pauli exclusion principle. A hole—absence of a negative-energy electron—would appear as a particle with positive energy and opposite charge, effectively a positively charged electron or "anti-electron." Initially, Dirac identified these holes as protons in his 1930 paper, assuming they accounted for both electrons and protons.^[23] However, J. Robert Oppenheimer critiqued this in his contemporaneous 1930 paper, noting inconsistencies such as the vastly different masses of electrons and protons and the instability of the sea against pair production, arguing that holes could not stably represent protons without violating charge conservation.^[24] By 1931, Dirac revised his interpretation in light of Oppenheimer's objections, proposing that holes represent anti-electrons with the same mass as electrons but positive charge, distinct real particles rather than mathematical artifacts. This conceptualization predicted the existence of positrons as physical entities capable of annihilating with electrons.^[25] The hole theory provided an ad hoc single-particle framework but faced challenges in handling interactions and vacuum polarization. In the ensuing development of quantum electrodynamics (QED), initiated by Dirac's 1927 second-quantization ideas and advanced through works by Werner Heisenberg, Wolfgang Pauli, and others in the early 1930s, positrons were reframed as positive-frequency excitations of the quantized Dirac field, symmetric to electrons under charge conjugation, eliminating the need for an infinite sea and enabling consistent multi-particle descriptions.^[26]

Experimental discovery

In 1932, Carl D. Anderson at the California Institute of Technology observed a positively charged particle track in a cloud chamber exposed to cosmic rays, curving in the opposite direction to electrons in a magnetic field and exhibiting a radius of curvature consistent with the mass of an electron.^[27] The track, captured on August 2, penetrated a 6 mm lead plate, indicating an energy of approximately 20 MeV, and was identified as evidence of a "positive electron" due to its low mass and high penetration power, distinct from heavier protons.^[27] Anderson published his findings initially in Science and elaborated in Physical Review, but the scientific community initially expressed skepticism, questioning whether the track represented a known particle like a proton or an experimental artifact.^[28] Confirmation came in 1933 from Patrick M. S. Blackett and Giuseppe P. S. Occhialini at the University of London, who used a counter-controlled cloud chamber to selectively photograph ionizing events from cosmic rays, capturing multiple clear examples of positron tracks.^[29] Their observations included forked tracks indicative of electron-positron pair production from gamma-ray interactions near atomic nuclei, where a single gamma ray photon produces a diverging pair of oppositely charged particles with equal masses.^[29] These events required gamma-ray energies exceeding the 1.022 MeV threshold—twice the electron rest mass energy—for pair creation to be energetically possible, as demonstrated by the track geometries and ionization densities matching Dirac's theoretical predictions.^[29] The discoveries resolved early doubts by providing reproducible evidence of the positron's electron-like properties and its role in pair production, distinguishing it from hypothetical mesons later proposed by Hideki Yukawa in 1935 for nuclear forces, which were expected to be much heavier.^[28] Anderson's identification of the positron as the first antiparticle earned him the Nobel Prize in Physics in 1936, shared with Victor F. Hess for cosmic ray research.^[6]

Production

Natural sources

Positrons are produced naturally through beta-plus decay in proton-rich radioactive nuclei, where a proton transforms into a neutron, emitting a positron and an electron neutrino. This process requires a minimum energy release of 1.022 MeV to account for the rest masses of the positron and neutrino, as well as atomic electron rearrangements.^[30] Examples include isotopes like carbon-11, which decays via ^{11}\mathrm{C} \to ^{11}\mathrm{B} + e^+ + \nu_e, formed through cosmic ray spallation of interstellar medium nuclei such as carbon, nitrogen, and oxygen.^[31] These unstable isotopes are generated in galactic cosmic ray interactions and contribute to the positron flux, though their short half-lives limit accumulation.^[32] A primary natural source of positrons arises from cosmic ray interactions in Earth's atmosphere, where high-energy protons collide with air nuclei to produce charged pions. The positive pions decay into muons (\pi^+ \to \mu^+ + \nu_\mu), which subsequently decay into positrons (\mu^+ \to e^+ + \nu_e + \bar{\nu}_\mu). This secondary production mechanism dominates the low-to-moderate energy positron flux observed near Earth. At sea level, the integral vertical intensity of electrons plus positrons for energies exceeding 10 MeV is approximately 30 particles per square meter per second per steradian.^[33] Positrons also form via pair production, where gamma rays with energies above 1.022 MeV interact with atomic nuclei or strong electromagnetic fields to create electron-positron pairs (\gamma \to e^+ + e^-). In astrophysical environments, this occurs in intense radiation fields near black holes, where high-energy photons from accretion disks enable pair creation.^[34] Similarly, gamma-ray bursts produce positrons through pair production in relativistic jets, contributing to the observed excess in cosmic ray positron fractions. Supernovae, particularly pair-instability types, generate pairs in their cores due to gamma rays from nuclear reactions, leading to explosive dynamics.^[35] Other astrophysical sources include pulsars, where pair production in magnetospheres occurs via photon-photon collisions or curvature radiation in strong magnetic fields, populating the surrounding plasma with electron-positron pairs.^[36] In Earth's magnetosphere, the Van Allen belts trap positrons generated from pion decays induced by relativistic protons interacting with residual atmospheric gases.^[37] These natural processes collectively sustain a diffuse positron population across cosmic scales, influencing observations from ground-based detectors to space missions.

Artificial methods

Artificial production of positrons relies on controlled techniques that leverage nuclear reactions or high-energy particle interactions to generate these antiparticles in laboratory settings. One primary method involves the beta-plus decay of short-lived radioactive isotopes, such as ^{22}Na and ^{68}Ga, which emit positrons as they decay into stable daughters. ^{22}Na, with a half-life of approximately 2.6 years, is a widely used source for low-energy positron beams in surface science and materials analysis experiments due to its high positron emission rate of about 90% per decay.^[38] Similarly, ^{68}Ga, produced from the decay of ^{68}Ge (half-life 271 days), serves as a compact source for positron beams, offering intensities up to 10^7 positrons per second and energies around 1 MeV, suitable for applications in positron annihilation spectroscopy.^[39] These isotopic sources are typically encapsulated in thin foils or electrodes to moderate the positrons to keV energies for experimental use. Another established approach employs particle accelerators to produce positrons through pair production, where high-energy gamma rays interact with matter to create electron-positron pairs. In linear accelerators (linacs), electrons are accelerated to energies of several MeV—such as 9 MeV in the GBAR experiment at CERN—and directed onto a high-Z target (e.g., tungsten), generating bremsstrahlung radiation that subsequently induces pair production with yields of up to 10^8 positrons per pulse. Cyclotrons, while more commonly used for proton-induced production of positron-emitting isotopes, can also facilitate direct positron generation when configured for electron acceleration, though linacs predominate for this bremsstrahlung-based method due to their ability to deliver short, high-intensity pulses. These accelerator-produced positrons typically emerge with energies in the 1-10 MeV range before moderation.^[40]^[41]^[42] High-energy electron-positron colliders, such as the Large Electron-Positron (LEP) collider at CERN, represent a scaled-up variant of this pair production technique, operating at center-of-mass energies up to 209 GeV. Positrons for LEP were generated by accelerating electrons to ~5 GeV in a linac, producing bremsstrahlung photons in a tantalum target, followed by pair production and subsequent acceleration in a damping ring to achieve beam currents of ~3 mA with bunch intensities around 3 × 10^{11} positrons. This method enabled the collision of ~10^{15} electron-positron pairs over LEP's operational lifetime from 1989 to 2000, facilitating precision electroweak measurements.^[43]^[7] Modern advancements include laser-plasma interactions, which offer compact alternatives for positron generation since the early 2000s. Intense lasers (e.g., petawatt-class) irradiate near-critical-density plasmas, driving wakefield acceleration of electrons that produce gamma rays via inverse Compton scattering or betatron radiation, leading to pair production with positron yields exceeding 10^{10} per shot and energies up to several GeV. Recent experiments as of 2025 have demonstrated increased positron production and retention efficiencies using enhanced laser intensities and optimized injection methods.^[44]^[45] These sources, demonstrated in facilities like those using the Texas Petawatt Laser, achieve densities of ~10^{16} cm^{-3} and are promising for table-top antimatter studies due to their scalability and reduced size compared to traditional accelerators.^[46]^[47] Positron beams from these methods exhibit diverse characteristics tailored to experimental needs, with energies spanning keV for low-energy trapping studies to GeV for collider applications. Intensities vary from 10^6-10^8 positrons per second in isotopic sources to 10^{10}-10^{12} per bunch in accelerator beams, with energy spreads as low as 1 eV achievable through moderation. To store and manipulate these beams, Penning traps—cylindrical devices using static electric and magnetic fields (typically 0.1-1 T)—are employed, enabling accumulation of up to 10^9 positrons with lifetimes exceeding 1000 seconds via buffer gas cooling, facilitating high-brightness beams for precision physics.^[48]^[49]^[50]

Annihilation

Interaction process

The primary interaction between a positron and an electron is annihilation, a quantum electrodynamic process in which the particle-antiparticle pair converts into photons while conserving charge (total zero), lepton number (total zero), energy, and momentum.^[51] The dominant channel at low energies is two-photon emission, e^+ + e^- \to 2\gamma, which occurs in the spin-singlet configuration, while in the spin-triplet configuration, two-photon emission is forbidden by charge conjugation symmetry, and the process proceeds via three-photon emission, e^+ + e^- \to 3\gamma.^[52] In the center-of-mass frame at rest, the total energy released is $2 m_e c^2 = 1.022 MeV, shared equally between the two photons as 511 keV each.^[53] For moving pairs, the photon energies and directions adjust to conserve momentum, but at low velocities, the photons emerge nearly back-to-back at 180° in the center-of-mass frame.^[51] Quantum electrodynamics describes this via tree-level Feynman diagrams, where the positron and electron lines connect through two electromagnetic vertices to emit the real photons; the process is isotropic at low velocities due to the non-relativistic limit.^[51] The probability of annihilation is quantified by the cross section, which at low relative velocities (v \ll c) approximates \sigma \approx \frac{8\pi \alpha^2 \hbar^2}{m_e^2 c^4} \frac{v}{c}, where \alpha is the fine-structure constant; this s-wave dominance reflects the velocity suppression in the non-relativistic regime.^[51] At low energies, direct annihilation often proceeds via an intermediate bound state, positronium (Ps), formed when the positron and electron bind analogously to a hydrogen atom but with reduced mass m_e/2. Positronium occurs in para-Ps (singlet spin, total spin 0) or ortho-Ps (triplet spin, total spin 1) ground states with equal probability. Para-Ps decays almost exclusively to two photons with lifetime \tau = 0.125 ns, while ortho-Ps decays mainly to three photons with lifetime \tau = 142 ns, the longer duration arising from the charge conjugation symmetry forbidding dominant two-photon decay for the C-even triplet state.^[52]

Detection and signatures

Positrons are primarily detected through the characteristic signatures of their annihilation with electrons, which produces two gamma photons each with an energy of 511 keV emitted in nearly opposite directions.^[54] This two-photon emission allows for indirect identification of positrons, as direct detection of the short-lived particles themselves is challenging due to their rapid thermalization and annihilation within picoseconds.^[55] Gamma-ray detectors such as sodium iodide (NaI) scintillators and high-purity germanium (Ge) detectors are commonly employed to capture these 511 keV photons. NaI scintillators, with their high light yield, provide efficient detection in systems requiring moderate energy resolution, though their stopping power for 511 keV photons is limited by a density of 3.67 g/cm³.^[56] In contrast, Ge detectors offer superior energy resolution (around 2 keV at 511 keV), enabling precise spectroscopy of the annihilation line, as demonstrated in balloon-borne experiments observing cosmic positrons.^[57] To confirm annihilation events and suppress noise, coincidence techniques require the near-simultaneous detection of both 511 keV photons from a single event, typically within a nanosecond window, originating from detectors separated by approximately 180 degrees.^[58] This method localizes the annihilation site along the line connecting the detectors and rejects uncorrelated background radiation, achieving high specificity in positron identification.^[56] Advanced analyses exploit the momentum of the electron-positron pair at annihilation to probe positron properties. Time-of-flight (TOF) measurements determine the slight time difference (on the order of picoseconds) between photon arrivals, improving spatial resolution in detection systems by up to 50% compared to non-TOF methods.^[59] Doppler broadening spectroscopy examines the energy spread of the 511 keV line (typically 1-10 keV full width at half maximum), which arises from the center-of-mass motion of the annihilating pair, providing insights into the positron's momentum distribution before annihilation.^[60] For visualizing positron trajectories prior to annihilation, track-imaging detectors capture the ionizing paths of the particles. Historical bubble chambers, sensitive to charged particle tracks via superheated liquid bubbles, revealed positron signatures through helical paths opposite to those of electrons in magnetic fields, as observed in early particle physics experiments.^[61] Modern silicon strip detectors, with resolutions down to 10-20 μm, track positrons in high-energy physics setups by measuring energy deposits from ionization, enabling reconstruction of pre-annihilation paths in collider environments.^[62] Background rejection is essential to isolate true annihilation signals from competing processes. Coincidence timing and energy thresholds discriminate against Compton scattering events, where photons deposit only partial energy (below 511 keV) in detectors, while vetoing single-photon detections.^[63] Similarly, pair production backgrounds from higher-energy gammas are rejected by requiring exact 511 keV peaks and back-to-back geometry, minimizing contributions from cosmic rays or instrumental noise.^[64]

Applications

Medical imaging

Positron emission tomography (PET) relies on positron-emitting radiotracers injected into the patient, where the positrons emitted during radioactive decay travel a short distance before annihilating with electrons in surrounding tissue, producing two gamma rays of 511 keV energy emitted in nearly opposite directions.^[65] These coincident gamma rays are detected to localize the tracer distribution and reconstruct three-dimensional images of metabolic or biochemical processes.^[66] A key radiotracer is ^{18}\mathrm{F}-fluorodeoxyglucose (^{18}\mathrm{F}-FDG), an analog of glucose with a physical half-life of approximately 110 minutes, which is taken up by cells via glucose transporters and trapped in those with elevated glycolysis, such as cancer cells.^[67] Another example is carbon-11 labeled tracers, with a half-life of about 20 minutes, used in brain studies to image neurotransmitter systems or perfusion, such as ^{11}\mathrm{C}-raclopride for dopamine D2 receptors in neurological disorders.^[68]^[69] PET scanners feature a cylindrical gantry housing multiple rings of scintillation detectors, often using lutetium oxyorthosilicate crystals coupled to photomultiplier tubes, arranged to surround the patient and capture the 511 keV photons.^[58] Coincidence circuitry identifies valid event pairs arriving within a nanosecond time window, while image reconstruction algorithms, such as filtered back-projection for analytical methods or ordered subset expectation maximization (OSEM) for iterative approaches, process the projection data to produce quantitative images.^[70] In oncology, PET with ^{18}\mathrm{F}-FDG enables tumor detection, staging, and assessment of treatment response by highlighting areas of hypermetabolism.^[71] In cardiology, it evaluates myocardial viability and perfusion to guide interventions in ischemic heart disease.^[72] In neurology, PET supports diagnosis of Alzheimer's disease through patterns of regional hypometabolism in the brain.^[71] Compared to computed tomography (CT) or magnetic resonance imaging (MRI), which primarily provide anatomical details, PET delivers functional imaging of physiological processes, allowing earlier detection of pathology before structural changes occur.^[73] The effective radiation dose from a typical ^{18}\mathrm{F}-FDG PET scan is approximately 7-8 mSv, though combined PET/CT procedures can reach 14-30 mSv due to the CT component.^[71] Advancements as of 2025 include total-body PET scanners with extended axial fields of view, providing up to 40 times greater sensitivity than conventional systems. These enable dynamic, low-radiation-dose whole-body imaging, facilitating applications in oncology, cardiology, neurology, and emerging areas like investigating long COVID pathophysiology, with new installations at institutions such as UC Davis and the University of Cambridge.^[74]^[75]^[76]

Scientific research

Positrons play a crucial role in positron annihilation spectroscopy (PAS), a technique used to characterize vacancy-type defects in solid materials by measuring annihilation characteristics that reflect local electron density. In positron lifetime spectroscopy, the mean lifetime of positrons increases in regions of lower electron density, such as atomic vacancies in metals, allowing quantification of defect concentrations and types; for instance, monovacancies in pure metals exhibit lifetimes around 180-220 ps compared to bulk values near 100-150 ps.^[77] Angular correlation of annihilation radiation (ACAR) complements this by mapping the momentum distribution of annihilating electron-positron pairs, providing three-dimensional images of electron density and revealing changes due to defects like vacancies in semiconductors such as SiC, where annealing-induced vacancy clusters alter the Fermi surface.^[78] These methods have been applied extensively to study irradiation damage in metals and alloys, offering insights into defect evolution under extreme conditions without invasive sample preparation.^[79] In condensed matter physics, slow positron beams enable depth-resolved probing of electron densities in materials like semiconductors, where implanted positrons thermalize and trap at open-volume defects, yielding spectra sensitive to vacancy concentrations that affect charge carrier mobility. This approach has identified native acceptor defects in n-type nitrides and oxides, critical for optimizing device performance in optoelectronics.^[80] By varying implantation energy, positron beams map defect profiles near surfaces or interfaces, distinguishing between bulk and near-surface electron distributions in layered structures.^[81] High-energy physics leverages positron-electron colliders to investigate fundamental interactions, with facilities like Belle II at SuperKEKB operating as an asymmetric e⁺e⁻ collider at 10.58 GeV center-of-mass energy to produce Υ(4S) resonances that decay into B meson pairs. This setup facilitates precision measurements of B meson decays, testing flavor physics and searching for new particles beyond the Standard Model, such as dark sector mediators in rare b → s transitions, with data accumulating billions of events for high-statistics analyses.^[82] At CERN's Antiproton Decelerator, the ALPHA experiment forms antihydrogen atoms by combining antiprotons with positrons in Penning-Malmberg traps, with advancements including sympathetic cooling using laser-cooled beryllium ions, achieving production rates of over 15,000 atoms in under 7 hours as of 2025 and enabling over 2 million atoms produced in 2023–2024 runs through plasma mixing and cooling. Trapped antihydrogen enables tests of CPT symmetry via spectroscopy comparing its spectral lines to hydrogen's, with 1S-2S transitions measured to 2 × 10^{-10} relative precision, and gravity equivalence by observing free-fall under Earth's field, confirming antimatter falls downward within experimental uncertainty.^[83]^[84]^[85] Post-2010 developments include compact, portable positron sources and instrumentation advancing applications in nanotechnology, such as shielded ²²Na-based sources operable in vacuum for in-situ defect studies of nanostructures. These enable PAS investigations of free-volume changes in nanoparticle-loaded polymer brushes, revealing enhanced interfacial dynamics at the nanoscale.^[86] In quantum computing contexts, portable lifetime spectrometers facilitate on-site characterization of vacancy defects in semiconductor substrates for qubit fabrication, supporting interfaces between classical probes and quantum devices by ensuring material purity at atomic scales.^[87]^[88]

References

[1]
positron | CERN
A positron is a subatomic particle with the same mass as an electron and a numerically equal but positive charge.
[2]
electron mass energy equivalent in MeV - CODATA Value
electron mass energy equivalent in MeV $m_{\rm e}c^2$ ; Numerical value, 0.510 998 950 69 MeV ; Standard uncertainty, 0.000 000 000 16 MeV.Missing: PDG | Show results with:PDG
[3]
Paul Dirac predicts the positron | timeline.web.cern.ch
Paul Dirac published a paper mathematically predicting the existence of an antielectron that would have the same mass as an electron but the opposite charge.
[4]
Carl Anderson discovers the positron | timeline.web.cern.ch
In 1932 Carl Anderson, a young professor at the California Institute of Technology in the US, was studying showers of cosmic particles in a cloud chamber.
[5]
Still making tracks: Eighty years of the positron - CERN
Mar 15, 2013 · The positron is the antimatter counterpart of the electron. The two particles have identical masses but opposite charges. When an electron and a ...
[6]
Carl D. Anderson – Facts - NobelPrize.org
Carl Anderson discovered a positively-charged particle with a mass seemingly equal to that of an electron.
[7]
The Large Electron-Positron Collider - CERN
With its 27-kilometre circumference, the Large Electron-Positron (LEP) collider was – and still is – the largest electron-positron accelerator ever built.
[8]
electron mass - CODATA Value
electron mass $m_{\rm e}$ ; Numerical value, 9.109 383 7139 x 10-31 kg ; Standard uncertainty, 0.000 000 0028 x 10-31 kg.
[9]
https://physics.nist.gov/cgi-bin/cuu/Value?e
[10]
[PDF] LEPTONS - Particle Data Group
L means lepton number violation (e.g. τ−→ e+π−π−). Following common usage, LF means lepton family violation and not lepton number violation (e.g. τ−→ e−π+π−) ...Missing: table | Show results with:table
[11]
Positron physics
Being anti-electrons, positrons are identical to electrons in all respects except charge. Thus they behave in solids in ways that are identical in many respects ...
[12]
[PDF] Feynman Diagrams - Edwin F. Taylor
positron—see QED page 99. The multiple paths forward in time of this single electron represent all electrons. Hence there is only one electron in the ...
[13]
Dirac's equation predicts antiparticles | timeline.web.cern.ch
Dirac interpreted the equation to mean that for every particle there exists a corresponding antiparticle, exactly matching the particle but with opposite charge ...
[14]
https://www.symmetrymagazine.org/article/april-2007/positron
[15]
CPT Symmetry and Its Violation - MDPI
One of the most fundamental symmetries in physics is CPT invariance. This article reviews the conditions under which CPT symmetry holds by recalling two ...
[16]
Testing CPT symmetry in ortho-positronium decays with ... - Nature
Sep 27, 2021 · Charged lepton system symmetry under combined charge, parity, and time-reversal transformation (CPT) remains scarcely tested.
[17]
https://home.cern/science/physics/matter-antimatter-asymmetry-problem
[18]
The Asymmetry Between Matter and Antimatter - Physics Today
We live in a universe that is dominated by matter and contains very little antimatter. The laws of physics, however, include an almost exact symmetry between ...
[19]
[PDF] 03 - Interaction of Photons with Matter.
May 7, 2011 · Pair production only occurs at energies above. 1.022 MeV. Pair production becomes more probable as the photon energy and the atomic number of ...
[20]
(PDF) Early history of cosmic particle physics - ResearchGate
Aug 10, 2025 · In 1912, V. F Hess ascended to 5 km, measuring the varying levels of cosmic rays at different altitudes. This research earned Hess the Nobel ...
[21]
[PDF] Klein-Gordon Equation - High Energy Physics |
○ Historically, Dirac (1928) was looking for a covariant wave equation that was first-order in time, to avoid the above 'problems' of the Klein-Gordon equation:.<|separator|>
[22]
The quantum theory of the electron - Journals
Husain N (2025) Quantum Milestones, 1928: The Dirac Equation Unifies ... Pashby T (2012) Dirac's Prediction of the Positron: A Case Study for the ...
[23]
A theory of electrons and protons | Proceedings of the Royal Society ...
Sizov R (2015) Dirac's “Holes” Are the True Antielectrons and Real Particles ... Oppenheimer J (1930) On the Theory of Electrons and Protons, Physical ...<|separator|>
[24]
On the Theory of Electrons and Protons | Phys. Rev.
On the Theory of Electrons and Protons. J. R. Oppenheimer. The Norman ... Dirac, Roy. Soc. Proc. A126, 360 (1930). Omitted endnote. Outline Information.
[25]
Quantised singularities in the electromagnetic field - Journals
Cite this article. Dirac Paul Adrien Maurice. 1931Quantised singularities in the electromagnetic field,Proc. R. Soc. Lond. A13360–72http://doi.org/10.1098 ...
[26]
Dirac's Prediction of the Positron: A Case Study for the Current ...
The existence of antimatter was predicted by Dirac in 1931 from for- mal properties of the relativistic electron equation he had discovered in. 1928, on the ...
[27]
The Positive Electron | Phys. Rev. - Physical Review Link Manager
C. D. Anderson, Science 76, 238 (1932); C. D. Anderson, Phys. Rev. 43, 381A (1933). Outline Information. Citing Articles (459); Abstract; See Also; References.
[28]
Discovery of the Positron - American Physical Society
In August 1932, Anderson recorded the historic photograph of a positively charged electron (now known as a positron) passing through the lead plate in the cloud ...
[29]
Some photographs of the tracks of penetrating radiation - Journals
CHADWICK J, BLACKETT P and OCCHIALINI G (1933) New Evidence for the Positive Electron, Nature, 10.1038/131473b0, 131:3309, (473-473), Online publication ...
[30]
Fundamentals of radioactivity - Book chapter - IOPscience
For positron emission to occur, the energy difference, Q, between the initial and final states must exceed 1.022 MeV. This is the threshold energy to create a ...
[31]
The Positron Puzzle | Astrophysics and Space Science
Apr 6, 2023 · In addition to meson production, cosmic rays also lead to spallation reactions on ISM nuclei, thereby forming β + -unstable isotopes, such ...<|control11|><|separator|>
[32]
Galactic secondary positron flux at the Earth
Secondary positrons are produced by spallation of cosmic rays within the interstellar gas. Measurements have been typically expressed in terms of the positron ...
[33]
[PDF] 30. Cosmic Rays - Particle Data Group
Aug 11, 2022 · The ratio of photons to electrons plus positrons is approximately 1.3 above 1 GeV and 1.7 below the critical energy [79]. 30.3.3 Nucleons.
[34]
Electron–positron pairs in physics and astrophysics
Electron-positron pairs are created by Dirac, Breit-Wheeler, and vacuum polarization processes, and are studied in black holes and Gamma Ray Bursts.
[35]
[PDF] Gamma ray bursts and the origin of galactic positrons - arXiv
Mar 10, 2006 · If supernovae of a new type, SNe Ic, are associated with GRBs, the positrons are produced both through the pair production γγ → e+e- during the ...
[36]
The novel mechanism of pair creation in pulsar magnetospheres
May 19, 2021 · In this paper we study the possibility of efficient pair production in a pulsar's magnetosphere. It has been shown that by means of the relativistic ...
[37]
Radiation Belts of Antiparticles in Planetary Magnetospheres - ADS
Positrons are born in the decay of pions that are directly produced in nuclear reactions of trapped relativistic inner zone protons with the residual atmosphere ...
[38]
[PDF] A Method to Measure Positron Beam Polarization Using Optically ...
Apr 3, 2023 · The most commonly used positron source is based on the nuclear beta decay of radioactive isotopes, and amongst these, 22Na ... 68Ga source ...
[39]
[PDF] Methods for the Production of a High-Activity Positron Sources
Apr 24, 2021 · Radioactive isotopes such as 22Na, 48V, 64Cu, 79Kr and many more go through beta plus. (β+) decay, converting a proton into a neutron, a ...<|separator|>
[40]
[2006.05966] Positron production using a 9 MeV electron linac for ...
Jun 10, 2020 · The driver linac produces electrons of 9 MeV kinetic energy that create positrons from bremsstrahlung-induced pair production. Staying below 10 ...
[41]
Positron production using a 9 MeV electron linac for the GBAR ...
The driver linac produces electrons of 9 MeV kinetic energy that create positrons from bremsstrahlung-induced pair production. ... linear electron accelerator.
[42]
[PDF] TM-1834-Revision-16.pdf - U.S. Particle Accelerator School - Fermilab
Dec 16, 2018 · For energies larger than a few MeV, the pair production process dominates the total photon attenuation. The mean free path length for pair ...
[43]
[PDF] Positron Production for Particle Accelerators
The secondary positrons are generated by the photons decaying into e*/e" pairs in the target. The photons are created mainly by Bremsstrah lung, the dominant ...
[44]
Dense GeV electron–positron pairs generated by lasers in near ...
Dec 14, 2016 · Here we present an all-optical scheme for overdense pair production by two counter-propagating lasers irradiating near-critical-density plasmas ...Missing: post- review papers
[45]
Perspectives on relativistic electron–positron pair plasma ...
Feb 24, 2023 · In this paper, we discuss the current status of relativistic pair production with intense lasers and give our perspective on future developments ...Missing: post- | Show results with:post-
[46]
Beam handling with a Penning trap of a LINAC-based slow positron ...
A Penning trap was constructed at the Ghent LINAC-based slow positron beam. It allows us to store the positrons without considerable loss in intensity and ...Missing: characteristics | Show results with:characteristics
[47]
[PDF] Technological Applications of Trapped Positrons - Surko Group
Current applications of low-energy positron beams are described, and the potential for the development of advanced trap-based positron beams is discussed. I ...Missing: intensity | Show results with:intensity
[48]
[PDF] Plasma and trap-based techniques for science with positrons
Mar 17, 2015 · For example, beams with narrow energy spread are desired for atomic and molecular physics scattering and annihilation studies; short pulses are ...
[49]
[PDF] ANNIHILATION
In these notes I explain the e+e− → γγ annihilation process. ... In the limit of non-relativistic non-relativistic electron and positron, |p| ≪ m, the expres-.
[50]
Ps
An isolated positron is presumably as stable as an electron. One serious objection is that the positronium "nucleus" has non-zero lepton number. (e−π+ and atoms ...
[51]
[PDF] J = e MASS (atomic mass units u) e MASS https://pdg.lbl.gov Page 1 ...
May 31, 2024 · The primary determination of an electron's mass comes from measuring the ratio of the mass to that of a nucleus, so that the result is ...
[52]
Sensors for Positron Emission Tomography Applications - PMC - NIH
The basic principle of a positron emission tomography (PET) system: A PET detector ring detects a pair of gamma photons with an energy of 511 keV (red arrows) ...
[53]
The 511 keV emission from positron annihilation in the Galaxy
Sep 29, 2011 · The first γ -ray line originating from outside the Solar System that was ever detected is the 511 keV emission from positron annihilation in the Galaxy.
[54]
Detectors in positron emission tomography - ScienceDirect.com
NaI(Tl) is a bright scintillator, but with density of 3.67 g/cm3 and effective atomic number of only 51, its detection efficiency for 511 keV photons is low.Review · Light Sensors · Detectors<|control11|><|separator|>
[55]
Detection of 511 keV positron annihilation radiation from the galactic ...
A balloon-borne gamma ray telescope with an approximately 130 cu cm high purity germanium detector was flown over Australia to detect sharp spectral ...Missing: methods NaI
[56]
Positron emission tomography: An overview - PMC - NIH
The increased stopping power enables detector's ability to efficiently absorb the total energy of 511 keV of annihilated photons. In order to achieve this, a ...
[57]
Instrumentation for Time-of-Flight Positron Emission Tomography - NIH
A major trend in PET instrumentation is the development of time-of-flight positron emission tomography (ToF-PET).Physics Of Tof-Pet · Scintillators For Use In... · PhotodetectorsMissing: Doppler broadening
[58]
Measurement and analysis of the Doppler broadened energy ...
Apr 30, 2025 · We present measurements and theoretical modeling demonstrating the capability of coincidence Doppler broadened (CDB) annihilation gamma spectroscopy.
[59]
25 years of evolution in particle detectors at CERN (1979–2004)
Made sensitive to ionizing tracks by the rapid expansion of a super-heated liquid volume, bubble chambers visualize with trails of bubbles the trajectories of ...
[60]
[PDF] from bubble chambers to electronic systems: 25 years of evolution in ...
May 12, 2004 · Originally consisting of two layers of silicon strips, the vertex detector underwent several upgrades, with the addition of an inner layer and ...
[61]
[PDF] Event selection and background rejection in time projection ...
Pair production and Compton scatter sensitivity at vary- ing background rejection rates corresponding to anticipated downlink speeds. The GCR proton background ...
[62]
[PDF] Pair Production Detectors for Gamma-ray Astrophysics
In the 1960's, particle physicists' track imaging detector of choice was the spark chamber. Unlike bubble chambers, cloud chambers, or nuclear emulsions, spark.
[63]
Recent developments in time-of-flight PET - PMC - PubMed Central
Feb 16, 2016 · Introduction. Positron emission tomography (PET) is based on the principle of opposed 511-keV photons originating from the annihilation of ...
[64]
Positron Emission Tomography - Mathematics and Physics of ... - NCBI
The distance the positron travels after being emitted from the nucleus and before annihilation occurs is a source of deterioration in spatial resolution.<|control11|><|separator|>
[65]
Fludeoxyglucose (18F) - StatPearls - NCBI Bookshelf - NIH
Aug 28, 2023 · Fludeoxyglucose F18 is a radioactive tracer that acts as a glucose analog and is used for diagnostic purposes in conjunction with positron-emitting tomography ...
[66]
Recent Developments in Carbon-11 Chemistry and Applications for ...
This review presents new carbon-11 building blocks and radiochemical transformations as well as PET tracers that have advanced to first-in-human studies over ...
[67]
11C- and 18F-Radiotracers for In Vivo Imaging of the Dopamine ...
Jan 22, 2021 · This review focuses on a selection of the more accepted and utilized PET radiotracers currently available, with a look at their past, present and future.
[68]
Image reconstruction for PET/CT scanners: past achievements and ...
Through different mathematical algorithms, PET data can be reconstructed into the spatial distribution of the injected radiotracer. With dynamic imaging, ...
[69]
PET Scanning - StatPearls - NCBI Bookshelf - NIH
Feb 26, 2025 · PET scanning is an imaging technique widely used in oncology. This technique uses radiotracers to measure various metabolic processes in the body.Missing: examples | Show results with:examples
[70]
Positron Emission Tomography (PET) - About Us - NIH Clinical Center
PET has been used primarily in cardiology, neurology, and oncology. PET is used to investigate the metabolism of normal organs and has also become a commonly ...Missing: applications | Show results with:applications<|separator|>
[71]
Clinical Applications of PET and PET-CT - PMC - PubMed Central
PET has emerged as an important molecular imaging technique with useful clinical applications in oncology, cardiology and neurology.
[72]
[PDF] Positron annihilation spectroscopy in materials science
At vacancy-type defects, the total electron density is smaller than in the bulk crystal, which leads to an increase in lifetime. With increase in the ...
[73]
Angular correlation of annihilation radiation associated with vacancy ...
May 26, 2005 · In summary, we studied vacancy defects in 6 H -SiC induced by post-irradiation annealing at 1000 °C using 2D-ACAR technique. Pronounced ...Missing: analysis | Show results with:analysis
[74]
Positron annihilation spectroscopy of defects in nuclear and ...
The focus of this review article is to provide guidance to facilitate applications of positron annihilation spectroscopy (PAS) in irradiation-induced defect ...
[75]
Defect identification in semiconductors with positron annihilation
Nov 14, 2013 · Positron annihilation spectroscopy is particularly suitable for studying vacancy-type defects in semiconductors.
[76]
Perspective on defect characterization in semiconductors by ...
Jan 23, 2024 · Positron annihilation spectroscopy has been useful for identifying the main native acceptor defect in many -type nitride and oxide ...<|control11|><|separator|>
[77]
[PDF] The Belle II Experiment at SuperKEKB - arXiv
Belle II is an experiment at SuperKEKB in Japan, recording decays of mesons, hadrons, and leptons to measure Standard Model parameters and search for new ...
[78]
ALPHA experiment observes the light spectrum of antimatter ... - CERN
Dec 19, 2016 · Antihydrogen is made by mixing plasmas of about 90 000 antiprotons from the Antiproton Decelerator with positrons, resulting in the production ...
[79]
Testing CPT and antigravity with trapped antihydrogen at ALPHA
These experiments are performed with the ALPHA apparatus, where ultra-low energy antihydrogen is produced and confined in a magnetic trap.Missing: formation | Show results with:formation
[80]
Hand Made Positron Source - 量子科学技術研究開発機構
Sep 14, 2023 · We fabricated a shielded positron source that can be used in vacuum conditions. The source is 22-NaCl and its strength is approximately ...
[81]
Development of a small and light portable positron annihilation ...
In this study, by applying this anti-coincidence method, we developed a small and light portable positron annihilation lifetime measurement equipment for on- ...Missing: computing | Show results with:computing
[82]
a new frontier for understanding nanoparticle-loaded polymer brushes
Here we demonstrate for the first time the suitability of positron annihilation spectroscopy (PAS) to investigate, with unprecedented detail and without making ...Missing: advances post-