Positron astronomy is 30 years old but remains in its infancy."[1]

Observation of positrons from a terrestrial gamma ray flash is performed by the Fermi gamma ray telescope. Credit: NASA Goddard Space Flight Center.{{free media}}

A High-Energy Antimatter Telescope (HEAT) has been developed and tested in the mid 1990s to measure the positron fraction in cosmic rays.[2] A positron is the opposite of an electron, which is negatively charged, but a positron has a positive charge, determining why it was given the name.

## Universals

A "clumpiness in the [galactic] halo [is] through a spatially continuous elevation in the density of dark matter, rather than the more realistic discrete distribution of clumps. [...] the former approach reproduces the average results obtained when considering the essentially infinite set of possible configurations of discrete clumps within the halo. This was demonstrated in the work by Lavalle et al. (2006), who deduced that the associated relative variance in the observed positron flux, as a result of the different clump configurations, is proportional to ${\displaystyle M_{c}^{1/2}}$ , where ${\displaystyle M_{c}}$  is the typical clump mass, and diverges as Ee+ → mχ . It is found that for ${\displaystyle M_{c}=10^{6}M_{\odot }}$  and a universal clump boost factor, Bc ∼ 100, this relative variance is less than 5 per cent for Ee+ ≤ 20 GeV, which is where the positron excess observed by the [High-Energy Antimatter Telescope] HEAT is located. Since the clump mass distribution deduced by Diemand et al. indicates that Mc ∼ 10−6M, it seems very unlikely that such a variance will significantly affect our conclusions, and we use this to strengthen our use of a spatially continuous elevation in dark matter density as a way of acknowledging clumpiness in the galactic halo.[3]

## Astronomy

A major challenge with any form of antimatter astronomy is the apparent lack of major quantities of antimatter within the known universe.

As most observable matter seems to be subluminal and normal, perhaps superluminal matter is mostly antimatter.

## Positrons

"The two conversions of protons into neutrons are assumed to take place inside the nucleus, and the extra positive charge is emitted as a positron."[4]

Def. "the non-linear scattering of radiation off electrons" is called induced Compton scattering.[5]

"The effect of scattering is to move photons to lower frequencies."[5] "[T]he fact that the radio pulses [from a pulsar] are not suppressed by induced scattering suggests that the wind's Lorentz factor exceeds ~104.[5]

As an example, "[t]he power into the Crab Nebula is apparently supplied by an outflow [wind] of ~1038 erg/s from the pulsar"[5] where there are "electrons (and positrons) in such a wind"[5]. These beta particles coming out of the pulsar are moving very close to light speed.

## Antimatter

Def. an elementary subatomic particle which forms matter is called a quark.

Note: quarks are never found alone in nature.

Def. the smallest possible, and therefore indivisible, unit of a given quantity or quantifiable phenomenon is called the quantum.

Def. one of certain integers or half-integers that specify the state of a quantum mechanical system is called a quantum number.

Def. a quantum number that depends upon the relative number of strange quarks and anti-strange quarks is called strangeness.

Def. symmetry of interactions under spatial inversion is called parity.

Def. a quantum number which determines the electromagnetic interactions is called an electric charge.

Def. the mean duration of the life of someone or something is called the mean lifetime.

Def. a quantum angular momentum associated with subatomic particles, which also creates a magnetic moment is called a spin.

Def. the quantity of matter which a body contains, irrespective of its bulk or volume is called mass.

Def. a subatomic particle corresponding to another particle with the same mass, spin and mean lifetime but with charge, parity, strangeness and other quantum numbers flipped in sign is called an antiparticle.

Def. matter that is composed of antiparticles of those that constitute normal matter is called antimatter.

A positron differs from a quark by its lack of strong interaction.

Def. the antimatter equivalent of an electron, having the same mass but a positive charge is called a positron.

## Nuclear transmutations

This graph shows positron emissions, among others, from nuclear transmutation. Credit: .

If the proton and neutron are part of an atomic nucleus, these decay processes transmute one chemical element into another. For example:

${\displaystyle _{Z}^{A}N\rightarrow ~_{Z-1}^{~~~A}N'+e^{+}+\nu _{e},}$

where A = 22, Z = 11, N = Na, Z-1 = 10, and N' = Ne.

Beta decay does not change the number of nucleons, A, in the nucleus but changes only its charge, Z. Thus the set of all nuclides with the same A can be introduced; these isobaric nuclides may turn into each other via beta decay. Among them, several nuclides (at least one) are beta stable, because they present local minima of the mass excess: if such a nucleus has (A, Z) numbers, the neighbour nuclei (A, Z−1) and (A, Z+1) have higher mass excess and can beta decay into (A, Z), but not vice versa. For all odd mass numbers A the global minimum is also the unique local minimum. For even A, there are up to three different beta-stable isobars experimentally known. There are about 355 known beta-decay stable nuclides total.

In β+
decay, or "positron emission", the weak interaction converts a nucleus into its next-lower neighbor on the periodic table while emitting an positron (e+
) and an electron neutrino (ν
e
):

${\displaystyle _{Z}^{A}N\rightarrow ~_{Z-1}^{~~~A}N'+e^{+}+\nu _{e}.}$

β+
decay cannot occur in an isolated proton because it requires energy due to the mass of the neutron being greater than the mass of the proton. β+
decay can only happen inside nuclei when the value of the binding energy of the mother nucleus is less than that of the daughter nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron and a neutrino and into the kinetic energy of these particles.

Positron emission' or beta plus decay (β+ decay) is a type of beta decay in which a proton is converted, via the weak force, to a neutron, releasing a positron and a neutrino.

Isotopes which undergo this decay and thereby emit positrons include carbon-11, potassium-40, nitrogen-13, oxygen-15, fluorine-18, and iodine-121. As an example, the following equation describes the beta plus decay of carbon-11 to boron-11, emitting a positron and a neutrino:

${\displaystyle _{6}^{11}C\rightarrow ~_{5}^{11}B+e^{+}+\nu _{e}+\gamma {(0.96MeV)}.}$

## Positroniums

An electron and positron orbit around their common centre of mass. This is a bound quantum state known as positronium. Credit: Manticorp.

Def. an exotic atom consisting of a positron and an electron, but having no nucleus or an onium consisting of a positron (anti-electron) and an electron, as a particle–anti-particle bound pair is called positronium.

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 singlet state with antiparallel spins ([spin quantum number] S = 0, Ms = 0) is known as para-positronium (p-Ps) and denoted 1
S
0
. 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. 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 1.439(2)×106
.[6]

${\displaystyle t_{0}={\frac {2\hbar }{m_{e}c^{2}\alpha ^{5}}}=1.244\times 10^{-10}\;{\text{s}}}$

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 142.05±0.02 ns[7] 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 ~1.0×106
.[8]

${\displaystyle t_{1}={\frac {{\frac {1}{2}}9h}{2m_{e}c^{2}\alpha ^{6}(\pi ^{2}-9)}}=1.386\times 10^{-7}\;{\text{s}}}$

## Annihilations

Naturally occurring electron-positron annihilation is a result of beta plus decay. Credit: .

A Germanium detector spectrum shows the annihilation radiation peak (under the arrow). Note the width of the peak compared to the other gamma rays visible in the spectrum. Credit: Hidesert.

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. When a low-energy positron collides with a low-energy electron, annihilation occurs, resulting in the production of two or more gamma ray photons.

Def. the process of a particle and its corresponding antiparticle combining to produce energy is called annihilation.

The figure at right shows a positron (e+) emitted from an atomic nucleus together with a neutrino (v). Subsequently, the positron moves randomly through the surrounding matter where it hits several different electrons (e-) until it finally loses enough energy that it interacts with a single electron. This process is called an "annihilation" and results in two diametrically emitted photons with a typical energy of 511 keV each. Under normal circumstances the photons are not emitted exactly diametrically (180 degrees). This is due to the remaining energy of the positron having conservation of momentum.

Electron–positron annihilation occurs when an electron (e
) and a positron (e+
, the electron's antiparticle) collide. The result of the collision is the annihilation of the electron and positron, and the creation of gamma ray photons or, at higher energies, other particles:

e
+ e+
→ γ + γ

The process does satisfy a number of conservation laws, including:

As with any two charged objects, electrons and positrons may also interact with each other without annihilating, in general by elastic scattering.

The creation of only one photon can occur for tightly bound atomic electrons.[9] In the most common case, two photons are created, each with energy equal to the rest energy of the electron or positron (511 keV).[10] It is also common for three to be created, since in some angular momentum states, this is necessary to conserve C parity.[11] Any larger number of photons [can be created], but the probability becomes lower with each additional photon. When either the electron or positron, or both, have appreciable kinetic energies, other heavier particles can also be produced (such as D mesons), since there is enough kinetic energy in the relative velocities to provide the rest energies of those particles. Photons and other light particles may be produced, but they will emerge with higher energies.

At energies near and beyond the mass of the carriers of the weak force, the W and Z bosons, the strength of the weak force becomes comparable with electromagnetism.[11] It becomes much easier to produce particles such as neutrinos that interact only weakly.

The heaviest particle pairs yet produced by electron–positron annihilation are W+
W
pairs. The heaviest single particle is the Z boson.

Annihilation radiation is not monoenergetic, unlike gamma rays produced by radioactive decay. The production mechanism of annihilation radiation introduces Doppler broadening.[12] The annihilation peak produced in a gamma spectrum by annihilation radiation therefore has a higher full width at half maximum (FWHM) than other gamma rays in [the] spectrum. The difference is more apparent with high resolution detectors, such as Germanium detectors, than with low resolution detectors such as Sodium iodide. Because of their well-defined energy (511 keV) and characteristic, Doppler-broadened shape, annihilation radiation can often be useful in defining the energy calibration of a gamma ray spectrum.

## Pair production

The reverse reaction, electron–positron creation, is a form of pair production governed by two-photon physics.

Two-photon physics, also called gamma-gamma physics, [studies] the interactions between two photons. If the energy in the center of mass system of the two photons is large enough, matter can be created.[13]

γ → e
+ e+

In nuclear physics, [the above reaction] occurs when a high-energy photon interacts with a nucleus. The photon must have enough energy [> 2*511 keV, or 1.022 MeV] to create an electron plus a positron. Without a nucleus to absorb momentum, a photon decaying into electron-positron pair (or other pairs for that matter [such as a muon and anti-muon or a tau and anti-tau] can never conserve energy and momentum simultaneously. [14]

These interactions were first observed in Patrick Blackett's counter-controlled cloud chamber. In 2008 the Titan laser aimed at a 1-millimeter-thick gold target was used to generate positron–electron pairs in large numbers.[15] "The LLNL scientists created the positrons by shooting the lab's high-powered Titan laser onto a one-millimeter-thick piece of gold."[15]

## Planetary sciences

"Lightning in the solar nebula is considered to be one of the probable sources for producing the chondrules that are found in meteorites."[16]

"Gamma-ray bursts (GRBs) provide a large flux of γ-rays that Compton scatter and create a charge separation in the gas because the electrons are displaced from the positive ions."[16]

"The energy in a giant lightning discharge exceeds a terrestrial lightning flash by a factor of ∼1012."[16]

"An incoming pulse of γ-rays in H2 is gradually transformed into electrons that move further into the nebula leaving a cloud of positive charge in its wake."[16]

"As the energy increases, the range of the electrons become an increasing fraction of the γ-ray Compton attenuation length, thus facilitating a larger charge separation. This process has similarities to nuclear explosions in the atmosphere (Longmire1978)."[16]

"A charge separation will also occur with pair production because some positrons annihilate in flight creating a moving excess of negative charge that leaves behind a positive excess in the gas (Askaryan1962; Jelleyetal. 1966). The cross-section for positron annihilation is about 1 Barn/Γ where Γ = E/m0c2. About 10% of the positrons with energy E = 400 MeV will annihilate in flight."[16]

## Minerals

Excessive "26Mg [has] been reported in meteoritic carbonaceous chondrites [...] which demonstrate an excess of 26Mg of up to 40% combined with essentially solar concentrations of 24Mg and 25Mg. Many of the data are well correlated with the 27Al content of the samples, and this is interpreted as evidence that the excess 26Mg has arisen from the in situ decay (via positron emission and electron capture) of the ground state of 26Al in these minerals."[17]

## Theoretical positron astronomy

Notation: let the symbol Ps stand for positronium.

"Comparison between direct annihilation and radiative capture to positronium [in thermal plasmas] shows that the two rates are equal at T = 6.8 x 105 K with the former (latter) dominating at the higher (lower) temperatures."[18]

The process

${\displaystyle \mathrm {e^{+}+e^{-}\rightarrow Ps+\gamma } ,}$

has a related mechanism in atomic hydrogen:[18]

${\displaystyle \mathrm {p^{+}+e^{-}\rightarrow H+\gamma } .}$

Here's a theoretical definition:

Def. an observational astronomy that detects positrons or their annihilation to study their production and sources is called positron astronomy.

## Entities

There may be a "connection ... between the magnetic field strengths inside an electron, in newly-born pulsars, and the sun. ... the upper limit to the strength of magnetic field ... is that which would permit emission of a photon at the non-relativistic electron gyrofrequency, with the energy of the order of the electron rest mass."[19]

A "basic process in the formation of pulsar magnetic fields [may be] a variant of electron-positron spin-zero annihilation, as follows

${\displaystyle e^{-}\uparrow +e^{+}\uparrow \,\rightarrow \,\uparrow \cup \uparrow +\gamma +\gamma ,}$

where the [up] arrow represents the magnetic moment of an electron.[19]

This relation "symbolises the formation of a magnetic entity, ${\displaystyle \uparrow \cup \uparrow }$ , here called an M-particle, with twice the magnetic moment of an electron or a positron, and [γ] represents a photon."[19]

## Sources

Low-mass X-ray binaries (LMXBs) "have long been suggested as positron sources on theoretical grounds and because their distribution peaks in the bulge region (eg Prantzos, 2004); however, it is only those LMXBs detected at hard X-ray energies that in addition exhibit an imbalance in their disk distribution."[20]

## Objects

"It is possible that the X-ray continuum is primary while the radio and optical emission are secondary for all BL Lac objects when the effect of relativistic beaming is considered. Pair production is a possible mechanism for producing X-ray emissions, while the optical and radio emission would be a consequence of this model (Zdziarski & Lightman 1985; Svensson 1986; Fabian et al. 1986). Barr & Mushotzky (1986) showed a significant correlation between the X-ray luminosity and timescale of X-ray variability for Seyfert galaxies and quasars and interpreted this as evidence that the emitting plasma is near the limit of being dominated by electron-positron pairs."[21]

## Weak forces

"Energy deposit or escape is a major issue in expanding envelopes of stellar explosions, supernovae (positrons from 56Co and 44Ti) and novae (many β+ decays such as 13N)".[22]

## Continua

The X-ray continuum can arise from bremsstrahlung, black-body radiation, synchrotron radiation, or what is called inverse Compton scattering of lower-energy photons by relativistic electrons, knock-on collisions of fast protons with atomic electrons, and atomic recombination, with or without additional electron transitions.[23]

"The annihilation of positrons with electrons gives rise to two spectral features, a line emission at 511 keV and a positronium continuum emission (which increases in intensity with energy roughly as a power law up to 511 keV and falls abruptly to zero above 511 keV)[4]."[24]

## Emissions

Notation: let the symbol LAT represent Large Area Telescope.

Notation: let the symbol GBM represent Gamma-ray Burst Monitor.

"The observed correlated variability of the GBM and LAT emissions indicates that photons formed co-spatially, with the lower-energy (GBM) photons providing target photons that can interact with higher energy γ rays to produce electron-positron pairs."[25]

## Absorptions

"[M]odels in which γ-rays are absorbed in collisions with X-rays producing nonthermal electron-positron pairs, which in turn radiate further X-rays [have been developed]."[26]

"[T]he reprocessing of radiation by e+ e- pairs could be a sufficiently robust mechanism to yield the canonical spectrum, independent of the details of the particle acceleration mechanism and the parameters of the source, such as the X- and γ-ray luminosity, L, and the size, R."[26]

"[T]he hard X-ray spectrum of a growing number of [active galactic nuclei] AGN [in] the 1-30 keV X-ray emission has four distinct components":[26]

1. "an incident power law spectrum with a spectral index αix ≃ 0.9,"[26]
2. "an emission line at the energy ~6.4 keV (interpreted as a fluorescent iron K-line),"[26]
3. "an absorption edge at 7-8 keV (interpreted as an iron K-edge), and"[26]
4. "a broad excess of emission with respect to the underlying power law at energies ≳ 10 keV (interpreted as Compton reflection from cold [T < 106 K, optically thick] material)." [26]

## Bands

"For ${\displaystyle N_{s}}$  sources located in the field of view, the data ${\displaystyle D_{p}}$  obtained during an exposure (pointing) p, for a given energy band, can be expressed by the relation:"

${\displaystyle D_{p}=\sum _{j=1}^{N_{p}}R_{p,j}S_{p,j}+B_{p}}$

"where ${\displaystyle R_{p,j}}$  is the response of the instrument for the source j, ${\displaystyle S_{p,j}}$  is the flux of the source j, and ${\displaystyle B_{p}}$  is the background recorded during the pointing p. ${\displaystyle D_{p},R_{p,j}}$ , and ${\displaystyle B_{p}}$  are vectors of 19 elements."[27]

"[I]n the 508.25-513.75 keV band ... a 5.5 keV wide band centered at 511 keV takes into account the Germanium energy resolution (FWHM 2.05 keV) including its degradation between two consecutive annealings (5%). At this energy, the gain calibration (performed orbit-wise) accuracy is better than ±0.01 keV."[27]

## Backgrounds

"[Taking] advantage of the relative stability of the background pattern to rewrite the background term as:"

${\displaystyle B_{p}=A_{p}\cdot U\cdot t_{p}}$

"where ${\displaystyle A_{P}}$  is a normalization coefficient per pointing, ${\displaystyle U}$  is the "uniformity map" or background count rate pattern on the SPI camera [of the INTEGRAL satellite] and ${\displaystyle t_{p}}$  the effective observation time for pointing p. ${\displaystyle U}$  and ${\displaystyle t}$  are vectors of 19 elements (one per detector)."[27]

## Meteors

"The main physical processes at play are the emission of γ-rays and positrons from radioactive decays in the 56Ni → 56Co → 56Fe chain [...], their interaction with the ejecta, and the spectrum of the radiation produced by the thermalization processes and the radiative transfer in the expanding ejecta. [...] Positron interaction with the ejecta [from the Type Ic SN 1994I] strongly depends on the presence, and geometry, of magnetic fields (Ruiz-Lapuente & Spruit 1998)."[28]

## Cosmic rays

There is an "unexpected rise of the positron fraction, observed by HEAT and PAMELA experiments, for energies larger than a few GeVs."[29]

"[T]he HEAT balloon experiment [30] ... has mildly indicated a possible positron excess at energies larger than 10 GeV ... In October 2008, the latest results of PAMELA experiment [36] have confirmed and extended this feature [37]."[29]

Earlier measurements indicate that "the positron fraction, [f = ] e+/(e- + e+), increases with energy at energies above 10 GeV. Such an increase would require either the appearance of a new source of positrons or a depletion of primary electrons."[2] All results taken together suggest a slight decrease with increasing energy from about 1 GeV to 10 GeV, but overall the fraction may be constant, per Figure 2.[2]

## Neutrals

"The positrons can annihilate in flight before being slowed to thermal energies, annihilate directly with electrons when both are at thermal energies, or form positronium at thermal energies (or at greater than thermal energies if positronium formation occurs via charge exchange with neutrals)."[30]

## Subatomics

"Few exceptional lines arise at high energy from annihilations of positrons and pions."[22]

## Heavier element nuclei

The distribution of galactic cosmic-ray (GCR) particles is shown in atomic number (charge) and energy. Credit: W. Schimmerling, J. W. Wilson, F. Cucinotta, and M-H Y. Kim.{{fairuse}}

"These charged particles are hydrogen nuclei (protons), helium nuclei (α particles), and the nuclei of heavier elements such as iron and nickel."[31]

"Primary cosmic radiation mainly consists of the nuclei of atoms which have lost their electrons due to their extremely high velocity; these charged particles are hydrogen nuclei (protons), helium nuclei (alpha particles) and the nuclei of heavier elements such as iron and nickel; there are also some electrons (1%) and positrons (1‰)."[31]

"The relative abundances of GCR particles (9) are shown in [the figure on the right] (a), and typical energy spectra (10), are shown in [...] (b). The GCR particles of interest for radiation protection of crews engaged in space exploration range from protons (nuclei of hydrogen) to nuclei of iron; the abundances of heavier elements are orders of magnitude lower."[32]

Heavier element nuclei consist primarily of Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co and Ni.

"The two groups of elements Li, Be, B and Sc, Ti, V, Cr, Mn are many orders of magnitude more abundant in the cosmic radiation than in solar system material."[33]

## Helions

An idealized image of protium shows the relative sizes of the proton and the atom. Credit: Bensaccount.

Def. a "nucleus of a helium-3 atom"[34] is called a helion.

Def. the "lightest and most common isotope of hydrogen, having a single proton and no neutrons- 1
1
H
"[35] is called protium.

Def. an "isotope of hydrogen formed of one proton and one neutron in each atom - 2
1
H
"[36] is called deuterium.

"Heavy water is “heavy” because it contains deuterium."[36]

"There were about 80 deuteriums for every million protiums, and virtually no tritium."[36]

Def. a "radioactive isotope of the element hydrogen, (symbol T or 3
1
H
), having one proton and two neutrons"[37] is called tritium.

Def. a "highly unstable, synthetic isotope of the element hydrogen, 4
1
H
, having one proton and three neutrons"[38] is called quadrium.

1
1
H
(p,β+ν)2
1
H

${\displaystyle \mathrm {_{1}^{1}H} +\mathrm {_{1}^{1}H} \rightarrow \mathrm {_{1}^{2}D} +e^{+}+\nu _{e}+\gamma (0.42MeV).}$

At 10-million-kelvin, hydrogen fuses to form helium in the proton-proton chain reaction:[39]

41
1
H
→ 22
1
H
+ 2e+ + 2νe (4.0 MeV + 1.0 MeV)
21
1
H
+ 22
1
H
→ 23
2
He
+ 2γ (5.5 MeV)
23
2
He
4
2
He
+ 21
1
H
(12.9 MeV)

These reactions result in the overall reaction:

41
1
H
4
2
He
+ 2e+ + 2γ + 2νe (26.7 MeV)

where e+ is a positron, γ is a gamma ray photon, νe is a neutrino, and H and He are isotopes of hydrogen and helium, respectively. The energy released by this reaction is in millions of electron volts, which is actually only a tiny amount of energy.

"The light elements deuterium, lithium, beryllium, and boron pose a special problem for any theory of the origin of the elements which proposes that all the elements are built up from hydrogen in the stars. ... The difficulty arises because the lifetimes of these elements against proton capture, at the temperatures and pressures at which most stellar matter exists, are short compared to the stable lifetimes of stars. These elements then cannot be produced in stellar interiors unless they are transported rapidly to the surface, and if they are produced at the surface, non-equilibrium processes must be involved. Further, they can exist in significant quantities at the surface only in the absence of rapid mixing to the interior."[40]

## Neutrons

"Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) hard X-ray (HXR) and γ-ray imaging and spectroscopy observations [were made] of the intense (X4.8) γ-ray line flare of 2002 July 23."[41]

"For the first time, the positron annihilation line is resolved, and the detailed high-resolution measurements are obtained for the neutron-capture line. The first ever solar γ-ray line and continuum imaging shows that the source locations for the relativistic electron bremsstrahlung overlap the 50-100 keV HXR sources, implying that electrons of all energies are accelerated in the same region. The centroid of the ion-produced 2.223 MeV neutron-capture line emission, however, is located ~20 ± 6 away, implying that the acceleration and/or propagation of the ions must differ from that of the electrons. Assuming that Coulomb collisions dominate the energetic electron and ion energy losses (thick target), we estimate that a minimum of ~2 × 1031 ergs is released in accelerated >~20 keV electrons during the rise phase, with ~1031 ergs in ions above 2.5 MeV nucleon-1 and about the same in electrons above 30 keV released in the impulsive phase."[41]

"The collisions also produce neutrons, positrons, and pions. Neutron capture on hydrogen and positron annihilation yield narrow lines at 2.223 and 0.511 MeV, respectively, both of which are delayed."[41]

## Protons

Based on interactions between cosmic rays and the photons of the cosmic microwave background radiation (CMB), cosmic rays with energies over the threshold energy of 5x1019 eV interact with cosmic microwave background photons ${\displaystyle \gamma _{\rm {CMB}}}$  to produce pions via the ${\displaystyle \Delta }$  resonance,

${\displaystyle \gamma _{\rm {CMB}}+p\rightarrow \Delta ^{+}\rightarrow p+\pi ^{0},}$

or

${\displaystyle \gamma _{\rm {CMB}}+p\rightarrow \Delta ^{+}\rightarrow n+\pi ^{+}.}$

Pions produced in this manner proceed to decay in the standard pion channels—ultimately to photons for neutral pions, and photons, positrons, and various neutrinos for positive pions. Neutrons decay also to similar products, so that ultimately the energy of any cosmic ray proton is drained off by production of high energy photons plus (in some cases) high energy electron/positron pairs and neutrino pairs.

The pion production process begins at a higher energy than ordinary electron-positron pair production (lepton production) from protons impacting the CMB, which starts at cosmic ray proton energies of only about 1017eV. However, pion production events drain 20% of the energy of a cosmic ray proton as compared with only 0.1% of its energy for electron positron pair production. This factor of 200 is from two sources: the pion has only about ~130 times the mass of the leptons, but the extra energy appears as different kinetic energies of the pion or leptons, and results in relatively more kinetic energy transferred to a heavier product pion, in order to conserve momentum. The much larger total energy losses from pion production result in the pion production process becoming the limiting one to high energy cosmic ray travel, rather than the lower-energy light-lepton production process.

## Beta particles

This graph is a chart of the nuclides for carbon to fluorine. Decay modes:

Credit: original: National Nuclear Data Center, stitched: Neokortex, cropped: Limulus.

Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles emitted are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay. They are designated by the Greek letter beta (β).

At right is a graph or block diagram that shows the boundaries for nuclear particle stability. The boundaries are conceptualized as drip lines. The nuclear landscape is understood by plotting boxes, each of which represents a unique nuclear species, on a graph with the number of neutrons increasing on the abscissa and number of protons increasing along the ordinate, which is commonly referred to as the table of nuclides, being to nuclear physics what the more commonly known periodic table of the elements is to chemistry. However, an arbitrary combination of protons and neutrons does not necessarily yield a stable nucleus, and ultimately when continuing to add more of the same type of nucleons to a given nucleus, the newly formed nucleus will essentially undergo immediate decay where a nucleon of the same isospin quantum number (proton or neutron) is emitted; colloquially the nucleon has 'leaked' or 'dripped' out of the target nucleus, hence giving rise to the term "drip line". The nucleons drip out of such unstable nuclei for the same reason that water drips from a leaking faucet: the droplet, or nucleon in this case, sees a lower potential which is great enough to overcome surface tension in the case of water droplets, and the strong nuclear force in the case of proton emission or alpha decay. As nucleons are quantized, then only integer values are plotted on the table of isotopes, indicating that the drip line is not linear but instead looks like a step function up close.

Beta particles (electrons) are more penetrating [than alpha particles], but still can be absorbed by a few millimeters of aluminum. However, in cases where high energy beta particles are emitted shielding must be accomplished with low density materials, e.g. plastic, wood, water or acrylic glass (Plexiglas, Lucite). This is to reduce generation of Bremsstrahlung X-rays. In the case of beta+ radiation (positrons), the gamma radiation from the electron-positron annihilation reaction poses additional concern.

## Electrons

The "discovery of X-ray cavities [in proton-electron jets or positron-electron jets] has made it possible to quantify the particle content, by calculating the ratio between the total particle energy and the energy in relativistic electrons and positrons".[42]

The electron is a subatomic particle with a negative charge, equal to -1.60217646x10-19 C. Current, or the rate of flow of charge, is defined such that one coulomb, so 1/-1.60217646x10-19, or 6.24150974x1018 electrons flowing past a point per second give a current of one ampere. The charge on an electron is often given as -e. note that charge is always considered positive, so the charge of an electron is always negative.

The electron has a mass of 9.10938188x10-31 kg, or about 1/1840 that of a proton. The mass of an electron is often written as me.

When working, these values can usually be safely approximated to:

-e = -1.60x10-19 C
me = 9.11x10-31kg

It has no known components or substructure; in other words, it is generally thought to be an elementary particle.[43][44] The intrinsic angular momentum (spin) of the electron is a half-integer value in units of ħ, which means that it is a fermion.

## Delta rays

A delta ray is characterized by very fast electrons produced in quantity by alpha particles or other fast energetic charged particles knocking orbiting electrons out of atoms. Collectively, these electrons are defined as delta radiation when they have sufficient energy to ionize further atoms through subsequent interactions on their own.

"The conventional procedure of delta-ray counting to measure charge (Powell, Fowler, and Perkins 1959), which was limited to resolution sigmaz = 1-2 because of uncertainties of the criterion of delta-ray ranges, has been significantly improved by the application of delta-ray range distribution measurements for 16O and 32S data of 200 GeV per nucleon (Takahashi 1988; Parnell et al. 1989)."[45] Here, the delta-ray tracks in emulsion chambers have been used for "[d]irect measurements of cosmic-ray nuclei above 1 TeV/nucleon ... in a series of balloon-borne experiments".[45]

## Epsilon rays

Epsilon radiation is tertiary radiation caused by secondary radiation (e.g., delta radiation). Epsilon rays are a form of particle radiation and are composed of electrons. The term is very rarely used today.

## Muons

"The muons created through decays of secondary pions and kaons are fully polarized, which results in electron/positron decay asymmetry, which in turn causes a difference in their production spectra."[46]

## Neutrinos

Solar neutrinos are shown for the proton-proton chain in the Standard Solar Model. Credit: Dorottya Szam.

The following fusion reaction produces neutrinos and accompanying gamma-rays of the energy indicated:

${\displaystyle \mathrm {_{1}^{1}H} +\mathrm {_{1}^{1}H} \rightarrow \mathrm {_{1}^{2}D} +e^{+}+\nu _{e}+\gamma (0.42MeV).}$

Observation of gamma rays of this energy likely indicate this reaction is occurring nearby.

In the Cowan–Reines neutrino experiment, antineutrinos created in a nuclear reactor by beta decay reacted with protons producing neutrons and positrons:

ν
e
+ p+
n0
+ e+

The positron quickly finds an electron, and they annihilate each other. The two resulting gamma rays (γ) [511 keV each] are detectable. The neutron can be detected by its capture on an appropriate nucleus, releasing a gamma ray. The coincidence of both events – positron annihilation and neutron capture – gives a unique signature of an antineutrino interaction.

## Gamma rays

This is a high-energy gamma radiation allsky image about the Earth, taken from Energetic Gamma Ray Experiment Telescope on the NASA’s Compton Gamma Ray Observatory satellite. Credit: United States Department of Energy.{{free media}}

The Energetic Gamma Ray Experiment Telescope, (EGRET) measured high energy (20 MeV to 30 GeV) gamma ray source positions to a fraction of a degree and photon energy to within 15 percent. EGRET was developed by NASA Goddard Space Flight Center, the Max Planck Institute for Extraterrestrial Physics, and Stanford University. Its detector operated on the principle of electron-positron pair production from high energy photons interacting in the detector. The tracks of the high-energy electron and positron created were measured within the detector volume, and the axis of the V of the two emerging particles projected to the sky. Finally, their total energy was measured in a large calorimeter scintillation detector at the rear of the instrument.

## X-rays

X-ray binaries are a class of binary stars that are luminous in X-rays. The X-rays are produced by matter falling from one component, called the donor (usually a relatively normal star) to the other component, called the accretor, which is compact: a white dwarf, neutron star, or black hole. The infalling matter releases gravitational potential energy, up to several tenths of its rest mass, as X-rays. (Hydrogen fusion releases only about 0.7 percent of rest mass.) An estimated 1041 positrons escape per second from a typical hard low-mass X-ray binary.[47][48]

## Blues

In "the spectrum of a middle-aged [pulsar] PSR B0656+14 [may be] two wide, red and blue, flux depressions whose frequency ratio is about 2 and which could be the 1st and 2nd harmonics of electron/positron cyclotron absorption formed at magnetic fields [of] ~108 G in [the] upper magnetosphere of the pulsar."[49]

## Infrareds

In infrared astronomy, the [cosmic infrared background] CIB [causes] a significant attenuation for very high energy electrons through inverse Compton scattering, photopion and electron-positron pair production.

## Superluminals

"[S]uperluminal neutrinos may lose energy rapidly via the bremsstrahlung [Cherenkov radiation] of electron-positron pairs ${\displaystyle (\nu \rightarrow \nu +e^{-}+e^{+}).}$ "[50]

Assumption:

"muon neutrinos with energies of order tens of GeV travel at superluminal velocity."[50]

For "all cases of superluminal propagation, certain otherwise forbidden processes are kinematically permitted, even in vacuum."[50]

Consider

${\displaystyle \nu _{\mu }\rightarrow {\begin{bmatrix}{\nu _{\mu }+\gamma }&(a)\\{\nu _{\mu }+\nu _{e}+{\overline {\nu }}_{e}}&(b)\\{\nu _{\mu }+e^{+}+e^{-}}&(c)\end{bmatrix}}}$ [50]

"These processes cause superluminal neutrinos to lose energy as they propagate and ... process (c) places a severe constraint upon potentially superluminal neutrino velocities. ... Process (c), pair bremsstrahlung, proceeds through the neutral current weak interaction."[50]

"Throughout the shower development, the electrons and positrons which travel faster than the speed of light in the air emit Cherenkov radiation."[51]

"High energy processes such as Compton, Bhabha, and Moller scattering, along with positron annihilation rapidly lead to a ~20% negative charge asymmetry in the electron-photon part of a cascade ... initiated by a ... 100 PeV neutrino"[52].

## Gaseous objects

"Positrons entering a gaseous medium at [0.6 to 4.5 MeV] are quickly slowed by ionizing collisions with neutral atoms and by long-range Coulomb interactions with any ionized component."[30]

## Rocky objects

"Even in small solids and dust grains, energy deposition from 26Al β-decay, for example, injects 0.355 W kg-1 of heat. This is sufficient to result in melting signatures, which have been used to study condensation sequences of solids in the early solar system".[22]

## Atmospheres

"The major problems associated with the balloon borne positron measurements are (i) the unique identification against a vast background of protons, and (ii) corrections for the positrons produced in the residual atmosphere."[53]

"[T]o account for the atmospheric corrections ... first [use] the instrument to determine the negative muon spectrum at float altitude. ... [Use this] spectrum ... to normalize the analytically determined atmospheric electron-positron spectra. ... most of the atmospheric electrons and positrons at small atmospheric depths are produced from muon decay at [the energies from 0.85 to 14 GeV]."[53]

## Meteorites

26Al "decays into excited 26Mg by either positron decay or electron capture. In both cases, the excited magnesium isotope de-excites radatively, releasing a photon of energy 1.809 MeV."[54]

"The 26Al concentration in a meteorite depends upon different [parameters] like the exposure age, the shielding conditions of the analyzed sample and the terrestrial age of the meteorite."[55]

"As 26Al is a positron emitting isotope, it is possible to measure 26Al in meteorites by gamma-coincidence low level counting techniques [1]. Positron annihilation radiation (due to the destructive recombination of a positron and an electron) is emitted as two simultaneous 511 keV gamma rays with 180° angle correlation. By focusing exclusively on the coincident 511 keV events, a drastic reduction of the detected radiation background is achieved, and the non-destructive determination of 26Al in bulk samples of 5-50 g becomes possible."[55]

## Coronal clouds

RHESSI observes high-energy phenomena from a solar flare. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio.

The solar flare at Active Region 10039 on July 23, 2002, exhibits many exceptional high-energy phenomena including the 2.223 MeV neutron capture line and the 511 keV electron-positron (antimatter) annihilation line. In the image at right, the RHESSI low-energy channels (12-25 keV) are represented in red and appear predominantly in coronal loops. The high-energy flux appears as blue at the footpoints of the coronal loops. Violet is used to indicate the location and relative intensity of the 2.2 MeV emission.

During solar flares “[s]everal radioactive nuclei that emit positrons are also produced; [which] slow down and annihilate in flight with the emission of two 511 keV photons or form positronium with the emission of either a three gamma continuum (each photon < 511 keV) or two 511 keV photons."[56] The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) made the first high-resolution observation of the solar positron-electron annihilation line during the July 23, 2003 solar flare.[56] The observations are somewhat consistent with electron-positron annihilation in a quiet solar atmosphere via positronium as well as during flares.[56] Line-broadening is due to "the velocity of the positronium."[56] "The width of the annihilation line is also consistent ... with thermal broadening (Gaussian width of 8.1 ± 1.1 keV) in a plasma at 4-7 x 105 K. ... The RHESSI and all but two of the SMM measurements are consistent with densities ≤ 1012 H cm-3 [but] <10% of the p and α interactions producing positrons occur at these low densities. ... positrons produced by 3He interactions form higher in the solar atmosphere ... all observations are consistent with densities > 1012 H cm-3. But such densities require formation of a substantial mass of atmosphere at transition region temperatures."[56]

## Earth

“One approach for characterizing the sky distribution of positron annihilation radiation is to fit to the data parameterized (and idealized) model distributions, representing the Galactic bulge, halo, and disk.”[47] “Two scenarios for the Galactic dsitribution of 511 keV line emission that remain viable after more than 4 years of observations with SPI [are]

1. bulge + thick disk (BD) and
2. halo + thin disk (HD).”[47]

In 2009, the Fermi Gamma Ray Telescope in Earth orbit observed an intense burst of gamma rays corresponding to positron annihilations coming out of a storm formation. Scientists wouldn't have been surprised to see a few positrons accompanying any intense gamma ray burst, but the lightning flash detected by Fermi appeared to have produced about 100 trillion positrons. This has been reported by media in January 2011, it is an effect, never considered to happen before.[57]

The Gamma-ray Burst Monitor (GBM) detects sudden flares of gamma-rays produced by gamma ray bursts and solar flares. Its scintillators are on the sides of the spacecraft to view all of the sky which is not blocked by the earth. The design is optimized for good resolution in time and photon energy. The Gamma-ray Burst Monitor has detected gamma rays from positrons generated in powerful thunderstorms.[58]

## Interstellar medium

"In the first 18 months of operations, AMS-02 [image under Cherenkov detectors] recorded 6.8 million positron (an antimatter particle with the mass of an electron but a positive charge) and electron events produced from cosmic ray collisions with the interstellar medium in the energy range between 0.5 giga-electron volt (GeV) and 350 GeV. These events were used to determine the positron fraction, the ratio of positrons to the total number of electrons and positrons. Below 10 GeV, the positron fraction decreased with increasing energy, as expected. However, the positron fraction increased steadily from 10 GeV to 250 GeV. This increase, seen previously though less precisely by instruments such as the Payload for Matter/antimatter Exploration and Light-nuclei Astrophysics (PAMELA) and the Fermi Gamma-ray Space Telescope, conflicts with the predicted decrease of the positron fraction and indicates the existence of a currently unidentified source of positrons, such as pulsars or the annihilation of dark matter particles. Furthermore, researchers observed an unexpected decrease in slope from 20 GeV to 250 GeV. The measured positron to electron ratio is isotropic, the same in all directions."[59]

## X-ray novas

"The day after its discovery by the Watch instrument, the X-ray nova GRS 1124-684 in Musca was detected by the soft γ-ray telescope SIGMA at the limit of its field of view. [...] an emission feature around 500 keV in the source spectrum during one postflare observation [...] is [the] first clear evidence of γ-ray line emission from soft X-ray transients, and, [is] interpreted as a positron annihilation line".[60]

## Cygnus X-1

In "a 10 keV to 1 MeV X-ray spectrum of Cyg X-1 in its low state, accumulated over ≡3 months in 1977 and 1978. The spectrum is smooth up to 300 keV. The excess at higher energy may be interpreted as a broad 511 keV emission line from the annihilation of positrons."[61]

## Galactic center

On November 25, 1970, from Paraná, Argentina, latitude 32° S, "[a] balloon-altitude observation was conducted ... of the galactic-center region, at energies between 23 and 930 keV. ... evidence for a spectral feature at 0.5 MeV is [detected]."[62] The radiation detected over about 300 to 103 keV fit a power law of

N(E) = (10.5 ± 2.2) E-(2.37±0.05) photons cm-2 s-1 keV-1.[62]

The 0.5 MeV peak is broad at 473 ± 30 keV and "is consistent with a single γ-ray spectral line [of flux] (1.8 ± 0.5) x 10-3 photons cm-2 s-1 keV-1 at the top of the Earth's atmosphere ... Gamma-ray lines in the 0.5-MeV energy region may arise from either the annihilation of positrons or from the de-excitation of nuclei. However, it seems likely, on the basis of evidence presented herein, that the energy of the peak is not at 0.511 MeV (unless the radiation is redshifted by ~0.07 in energy)."[62].

More recent measurements from 1979 through 2003 with germanium detectors observed the peak at 511 keV.[63] "[A] single point source is inconsistent with the data. Formally, we cannot exclude the possibility that the emission originates in at least 2 point sources."[63]

## Seyfert 1 coronas

"On the basis of spectroscopic observations, the leading models of the X-ray continuum production are based on a hot, Comptonizing electron or electron-positron pair corona close to the black hole."[64]

## Geography

"The Earth’s magnetic field significantly affects the CR distribution in near-Earth space. At energies below 10 GeV, a significant fraction of the incoming particles are deflected back to interplanetary space by the magnetic field (“geomagnetic cutoff”). The exact value of the geomagnetic cutoff rigidity depends on the detector position and viewing angle. In addition to the geomagnetic cutoff effect, the Earth blocks trajectories for particles of certain rigidities and directions while allowing other trajectories. This results in a different rate of CRs from the east than the west (the “east-west effect”) [24–26]."[65]

"Positive charges propagating toward the east are curved outward, while negative charges are curved inward toward the Earth [...] This results in a region of particle directions from which positrons can arrive, while electrons are blocked by the Earth. At each particle rigidity there is a region to the west from which positrons are allowed and electrons are forbidden. There is a corresponding region to the east from which electrons are allowed and positrons are forbidden. The precise size and shape of these regions depend on the particle rigidity and instrument location."[65]

## Technology

"The GAMMA-400 space observatory will provide precise measurements of gamma rays, electrons, and positrons in the energy range 0.1–3000 GeV."[66]

## Balloons

Measurements "of the cosmic-ray positron fraction as a function of energy have been made using the High-Energy Antimatter Telescope (HEAT) balloon-borne instrument."[2]

"The first flight took place from Fort Sumner, New Mexico, [on May 3, 1994, with a total time at float altitude of 29.5 hr and a mean atmospheric overburden of 5.7 g cm-2] ... The second flight [is] from Lynn Lake, Manitoba, [on August 23, 1995, with a total time at float altitude of 26 hr, and a mean atmospheric overburden of 4.8 g cm-2]"[2].

## Fermi Gamma-ray Space Telescope

The Fermi Gamma-ray Space Telescope sits on its payload attachment fitting. Credit: NASA/Kim Shiflett.

"The Large Area Telescope (LAT) is a pair-conversion gamma-ray telescope onboard the Fermi Gamma-ray Space Telescope satellite. It has been used to measure the combined [cosmic-ray] CR electron and positron spectrum from 7 GeV to 1 TeV [20, 21]. The LAT does not have a magnet for charge separation. However, as pioneered by [22] and [23], the geomagnetic field can also be used to separate the two species without an onboard magnet. Müller and Tang [23] used the difference in geomagnetic cutoff for positrons and electrons from the east and west to determine the positron fraction between 10 GeV and 20 GeV. As reported below, we used the shadow imposed by the Earth and its offset direction for electrons and positrons due to the geomagnetic field, to separately measure the spectra of CR electrons and positrons from 20 GeV to 200 GeV. In this energy range, the 68% containment radius of the LAT point-spread function is 0.1° or better and the energy resolution is 8% or better."[65]

The Large Area Telescope (LAT) detects individual gamma rays using technology similar to that used in terrestrial particle accelerators. Photons hit thin metal sheets, converting to electron-positron pairs, via a process known as pair production. These charged particles pass through interleaved layers of silicon microstrip detectors, causing ionization which produce detectable tiny pulses of electric charge. Researchers can combine information from several layers of this tracker to determine the path of the particles. After passing through the tracker, the particles enter the calorimeter, which consists of a stack of caesium iodide scintillator crystals to measure the total energy of the particles. The LAT's field of view is large, about 20% of the sky. The resolution of its images is modest by astronomical standards, a few arc minutes for the highest-energy photons and about 3 degrees at 100 MeV. The LAT is a bigger and better successor to the EGRET instrument on NASA's Compton Gamma Ray Observatory satellite in the 1990s.

## GRANAT

Granat observe the universe at energies ranging from X-rays to gamma rays. Credit: NASA.

The GRANAT satellite has aboard the [French coded aperture] γ-ray telescope SIGMA which on "January 9 [1991] detected Nova Muscae at the very edge of its field of view (FOV)."[60]

"SIGMA provides high-resolution (≈ 15') images of the sky in the 35-1300 keV band (see Paul et al. 1991)."[60]

Granat discovered the electron/positron annihilation line (511 keV) from the galactic microquasar 1E1740-294 and the GRS 1124-683 (X-ray Nova Muscae).[67]

## INTEGRAL

Positron astronomy results have been obtained using the INTEGRAL spectrometer SPI shown. Credit: Medialab, ESA.

"[P]ositron astronomy results ... have been obtained using the INTEGRAL spectrometer SPI".[68] The positrons are not directly observed by the INTEGRAL space telescope, but "the 511 keV positron annihilation emission is".[20]

## Hypotheses

1. Some positrons can carry from other galaxies because they travel very close to light speed.

"Nel et al. (1996) have reported a survey of γ-ray emissions from all known spin-powered pulsars by EGRET. [...] They divided this sample into two groups: a candidate group with Ė33/d2kpc ≥ 0.5 (80 pulsars) and a control group with Ė33/d2kpc < 0.5 (270 pulsars), where Ė33 is the spin-down power in units of 1033 erg s-1 and dkpc is the distance to the pulsar in kiloparsecs."[69]

There are "two kinds of γ-ray pulsar models,

1. the polar gap model and
2. the outer gap model [...]

"For both models, the expected efficiency of conversion of spin-down power to γ-rays, ηth, can be defined by

${\displaystyle \eta _{th}=L_{\gamma }/{\dot {E}},}$

where ${\displaystyle L_{\gamma }}$  is the total γ-ray luminosity, which depends on the model used; ${\displaystyle {\dot {E}}}$  is the spin-down power and is proportional to P-4B2 [where P is the characteristic period of the pulsar] in the approximation of a dipolar magnetic field [B]."[69]

A "thick outer gap model [may] describe high-energy γ-ray emission from pulsars [...] the energy of the primary electrons/positrons [is] limited by synchro-curvature radiation instead of inverse Compton scattering."[69]

"By crossing symmetry an elastic scattering cross section with the nucleon implies annihilation of dark matter [DM] into hadrons inside the halo, resulting in an anti-proton flux that could be constrained by data from the PAMELA collaboration if one includes a large boost factor necessary to explain the PAMELA excess in the positron fraction. [...] the PAMELA data received perhaps the most attention and sparked a plethora of theories on DM attempting to accommodate the observed excess in the positron fraction below 100 GeV [2], which suggests an annihilation cross section σanυ in the halo that is 2-3 orders of magnitude larger than the typical WIMP annihilation of roughly 1 [picobarn] pb. To achieve such a large cross section, a novel mechanism that is sometimes used is the Sommerfeld enhancement [8] in the context of DM annihilations [9]. On the other hand, the PAMELA also observed anti-proton fraction consistent with the expected astrophysical background [10], implying a “leptophilic” DM annihilating mostly into leptons [11]."[70]

A "boost/Sommerfeld enhancement factor B [...] is needed to explain the excess in the positron fraction in the PAMELA data. [...] If the recent CDMS observation is a hint that direct detection is “around the corner”, the analysis in the previous section suggests a lower bound on the WIMP annihilation into quarks in the halo, giving rise to a substantial anti-proton flux if a large boost factor is included. Since the PAMELA also measured the antiproton fraction and sees no significant excess below 100 GeV, we could use the anti-proton data to place an upper bound on the boost factor. For proof of concept for this connection, we assume the DM has a spin-independent elastic scattering cross section that is just below the observed 90% C. L. [σ0 in pb's] of the latest CDMS results [12], and consider the resulting the bound on the (effective) boost factor from the anti-proton fraction."[70]

## References

1. P.A.Milne; J.D.Kurfess; R.L.Kinzer; M.D.Leising; D.D.Dixon (April 2000). Investigations of positron annihilation radiation, In: Proceedings of the 5th COMPTON Symposium. 510. Washington, DC: American Institute of Physics. pp. 21-30. doi:10.1063/1.1303167. Retrieved 2011-11-25.
2. S. W. Barwick; J. J. Beatty; A. Bhattacharyya; C. R. Bower; C. J. Chaput; S. Coutu; G. A. de Nolfo; J. Knapp et al. (June 20, 1997). "Measurements of the Cosmic-Ray Positron Fraction from 1 to 50 GeV". The Astrophysical Journal Letters 482 (2): L191-4. doi:10.1086/310706. Retrieved 2012-07-13.
3. Daniel Cumberbatch; Joseph Silk (January 2007). "Local dark matter clumps and the positron excess". Monthly Notices of the Royal Astronomical Society 374 (2): 455-65. doi:10.1111/j.1365-2966.2006.11123.x. Retrieved 2014-01-31.
4. Giora Shaviv (2013). Giora Shaviv. ed. Towards the Bottom of the Nuclear Binding Energy, In: The Synthesis of the Elements. Berlin: Springer-Verlag. pp. 169-94. doi:10.1007/978-3-642-28385-7_5. ISBN 978-3-642-28384-0. Retrieved 2013-12-19.
5. D. B. Wilson; M. J. Rees (October 1978). "Induced Compton scattering in pulsar winds". Monthly Notices of the Royal Astronomical Society 185 (10): 297-304.
6. Savely G. Karshenboim (2003). "Precision Study of Positronium: Testing Bound State QED Theory". International Journal of Modern Physics A [Particles and Fields; Gravitation; Cosmology; Nuclear Physics] 19 (23): 3879–96. doi:10.1142/S0217751X04020142.
7. A. Badertscher et al. (2007). "An Improved Limit on Invisible Decays of Positronium". Physical Review D 75 (3): 032004. doi:10.1103/PhysRevD.75.032004.
8. Andrzej Czarnecki, Savely G. Karshenboim (1999). "Decays of Positronium". B.B. Levchenko and V.I. Savrin (eds.), Proc. of the th International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP, Moscow , MSU-Press 2000, pp. 538 - 44. 14 (99).
9. L. Sodickson; W. Bowman; J. Stephenson; R. Weinstein (1960). "Single-Quantum Annihilation of Positrons". Physical Review 124: 1851. doi:10.1103/PhysRev.124.1851.
10. W.B. Atwood; P.F. Michelson; S.Ritz (2008). "Una Ventana Abierta a los Confines del Universo". Investigación y Ciencia 377: 24–31.
11. D.J. Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons. ISBN 0-471-60386-4.
12. Gilmore, G., and Hemmingway, J.: "Practical Gamma Ray Spectrometry", page 13. John Wiley & Sons Ltd., 1995
13. Moffat JW (1993). "Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology". Intl J Mod Phys D 2 (3): 351–65. doi:10.1142/S0218271893000246.
14. Hubbell, J. H. (June 2006). "Electron positron pair production by photons: A historical overview". Radiation Physics and Chemistry 75 (6): 614–623. doi:10.1016/j.radphyschem.2005.10.008.
15. Bevy (2008). Laser technique produces bevy of antimatter. Retrieved 2008-12-04.
16. B. McBreen; E. Winston; S. McBreen; L. Hanlon (January 2005). "Gamma-ray bursts and other sources of giant lightning discharges in protoplanetary systems". Astronomy & Astrophysics 429 (01): L41-5. doi:10.1051/0004-6361:200400102. Retrieved 2013-08-12.
17. A. E. Champagne; A. J. Howard; P. D. Parker (June 15, 1983). "Nucleosynthesis of 26Al at low stellar temperatures". The Astrophysical Journal 269 (06): 686-9. doi:10.1086/161077. Retrieved 2014-02-01.
18. Robert J. Gould (September 1, 1989). "Direct positron annihilation and positronium formation in thermal plasmas". The Astrophysical Journal 344 (09): 232-8. Retrieved 2013-08-12.
19. K. D. Cole (1992). "The Magnetic Fields of Pulsars, Electrons and the Sun". Proceedings of the Astronomical Society of Australia 10 (2): 110-2. Retrieved 2013-08-13.
20. G. Weidenspointner; G.K. Skinner; P. Jean; J. Knödlseder; P. von Ballmoos; R. Diehl; A. Strong; B. Cordier et al. (October 2008). "Positron astronomy with SPI/INTEGRAL". New Astronomy Reviews 52 (7-10): 454-6. doi:10.1016/j.newar.2008.06.019. Retrieved 2013-08-13.
21. G. Z. Xie; B. F. Liu; J. C. Wang (November 20, 1995). "A Signature of Relativistic Electron-Positron Beams in BL Lacertae Objects". The Astrophysical Journal 454 (11): 50-4. doi:10.1086/176463. Retrieved 2013-08-13.
22. Roland Diehl (2011). Introduction to Astronomy with Radioactivity, In: Astronomy with Radioactivities. Springer. Retrieved 2014-02-01.
23. P Morrison (1967). "Extrasolar X-ray Sources". Annual Review of Astronomy and Astrophysics 5 (1): 325–50. doi:10.1146/annurev.aa.05.090167.001545.
24. P.A. Milne; J.D. Kurfess; R.L. Kinzer; M.D. Leising (July 2002). "Supernovae and Positron Annihilation Radiation". New Astronomy Reviews 46 (8-10): 553-8. Retrieved 2013-08-13.
25. AA Abdo; M Ackermann; M Arimoto; K Asano; The Fermi LAT; Fermi GBM Collaborations (March 27, 2009). "Fermi observations of high-energy gamma-ray emission from GRB 080916C". Science 323 (5922): 1688-93. doi:10.1126/science.1169101. Retrieved 2013-08-13.
26. Andrzej A. Zdziarski; Gabriele Ghisellini; Ian M. George; R. Svensson; A. C. Fabian; Chris Done (November 1, 1990). "Electron-positron pairs, Compton reflection, and the X-ray spectra of active galactic nuclei". The Astrophysical Journal 363 (11): L1-4. doi:10.1086/185851. Retrieved 2013-08-15.
27. On the morphology of the electron-positron annihilation emission as seen by SPI/INTEGRAL (September 10, 2010). "L. Bouchet, J. P. Roques, and E. Jourdain". The Astrophysical Journal 720 (2): 1772-80. doi:10.1088/0004-637X/720/2/1772. Retrieved 2013-08-16.
28. Alejandro Clocchiatti; J. Craig Wheeler; Robert P. Kirshner; David Branch; Peter Challis; Roger A. Chevalier; Alexei V. Filippenko; Claes Fransson et al. (March 2008). "Late-Time HST Photometry of SN 1994I: Hints of Positron Annihilation Energy Deposition". Publications of the Astronomical Society of the Pacific 120 (865): 290-300. doi:10.1086/533458. Retrieved 2014-01-31.
29. Roberto Alfredo Lineros Rodriguez (2010). "Positrons from cosmic rays interactions and dark matter annihilations". Rivista Del Nuovo Cimento 125B: 1053-70. doi:10.1393/ncb/i2010-10910-7. Retrieved 2013-08-17.
30. M. D. Leising; D. D. Clayton (December 1, 1987). "Positron annihilation gamma rays from novae". The Astrophysical Journal 323 (1): 159-69. doi:10.1086/165816. Retrieved 2014-02-01.
31. Jean-François Bottollier-Depois; Quang Chau; Patrick Bouisset; Gilles Kerlau; Luc Plawinski; Laurence Lebaron-Jacobs (May 2000). "Assessing exposure to cosmic radiation during long-haul flights". Radiation Research 153 (5): 526-532. Retrieved 2017-08-04.
32. W. Schimmerling; J. W. Wilson; F. Cucinotta; M-H Y. Kim (1 January 2004). Requirements for Simulating Space Radiation With Particle Accelerators. Washington, DC, United States: NASA. pp. 2. Retrieved 2017-08-05.
33. Thomas K. Gaisser (1990). Cosmic Rays and Particle Physics. Cambridge University Press. pp. 279. ISBN 0521339316. Retrieved 2014-01-11.
34. helion. San Francisco, California: Wikimedia Foundation, Inc. 3 November 2013. Retrieved 2014-10-01.
35. SemperBlotto (12 November 2005). "protium". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-07-20. {{cite web}}: |author= has generic name (help)
36. "deuterium". San Francisco, California: Wikimedia Foundation, Inc. 16 July 2015. Retrieved 2015-07-20.
37. "tritium". San Francisco, California: Wikimedia Foundation, Inc. 16 July 2015. Retrieved 2015-07-20.
38. SemperBlotto (2 June 2012). "quadrium". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-07-20. {{cite web}}: |author= has generic name (help)
39. G. Wallerstein; I. Iben Jr.; P. Parker; A. M. Boesgaard; G. M. Hale; A. E. Champagne; C. A. Barnes; F. KM-dppeler et al. (1999). "Synthesis of the elements in stars: forty years of progress". Reviews of Modern Physics 69 (4): 995–1084. doi:10.1103/RevModPhys.69.995. Retrieved 2006-08-04.
40. Walter K. Bonsack (November 1959). "The Abundance of Lithium and Convective Mixing in Stars of Type K". The Astrophysical Journal 130 (11): 843-71. doi:10.1086/146777.
41. R. P. Lin; S. Krucker; G. J. Hurford; D. M. Smith; H. S. Hudson; G. D. Holman; R. A. Schwartz; B. R. Dennis et al. (2003). "RHESSI Observations of Particle Acceleration and Energy Release in an Intense Solar Gamma-Ray Line Flare". The Astrophysical Journal Letters 595 (2): L69-. doi:10.1086/378932. Retrieved 2014-02-01.
42. L Bîrzan; BR McNamara; PEJ Nulsen (October 20, 2008). "Radiative Efficiency and Content of Extragalactic Radio Sources: Toward a Universal Scaling Relation between Jet Power and Radio Power". The Astrophysical Journal 686 (2): 859-80. doi:10.1086/591416. Retrieved 2014-01-31.
43. E.J. Eichten; M.E. Peskin; M. Peskin (1983). "New Tests for Quark and Lepton Substructure". Physical Review Letters 50 (11): 811–814. doi:10.1103/PhysRevLett.50.811.
44. G. Gabrielse et al. (2006). "New Determination of the Fine Structure Constant from the Electron g Value and QED". Physical Review Letters 97 (3): 030802(1–4). doi:10.1103/PhysRevLett.97.030802.
45. T. H. Burnett et al.; The JACEE Collaboration (January 1990). "Energy spectra of cosmic rays above 1 TeV per nucleon". The Astrophysical Journal 349 (1): L25-8. doi:10.1086/185642. Retrieved 2011-11-25.
46. I. V. Moskalenko and A. W. Strong (February 1, 1998). "Production and propagation of cosmic-ray positrons and electrons". The Astrophysical Journal 493 (2): 694-707. doi:10.1086/305152. Retrieved 2014-02-01.
47. Georg Weidenspointner (January 8, 2008). "An asymmetric distribution of positrons in the Galactic disk revealed by gamma-rays". Nature 451 (7175). doi:10.1038/nature06490. Retrieved 2009-05-04.
48. "Mystery of Antimatter Source Solved – Maybe" by John Borland 2008
49. S. Zharikov; R. E. Mennickent; Yu. Shibanov; V. Komarova (April 2007). "Optical spectroscopy of the radio pulsar PSR B0656+14". Astrophysics and Space Science 308 (1-4): 545-9. doi:10.1007/s10509-007-9308-z. Retrieved 2013-05-31.
50. Andrew G. Glashow; Sheldon L. Glashow (October 2011). "Pair Creation Constrains Superluminal Neutrino Propagation". Physical Review Letters 107 (18): 181803. doi:10.1103/PhysRevLett.107.181803. Retrieved 2013-08-16.
51. A. Moralejo for the MAGIC collaboration (2004). "The MAGIC telescope for gamma-ray astronomy above 30 GeV". Memorie della Societa Astronomica Italiana 75: 232-9. Retrieved 2012-07-28.
52. P. W. Gorham; S. W. Barwick; J. J. Beatty; D. Z.Besson; W. R. Binns; C. Chen; P. Chen; J. M. Clem et al. (October 25, 2007). "Observations of the Askaryan Effect in Ice". Physical Review Letters 99 (17): 5. doi:10.1103/PhysRevLett.99.171101. Retrieved 2012-07-28.
53. G. Barbiellini; G. Basini; R. Bellotti; M. Bpcciolini; M. Boezio; F. Massimo Brancaccio; U. Bravar; F. Cafagna et al. (May 1996). "The cosmic-ray positron-to-electron ratio in the energy range 0.85 to 14 GeV". Astronomy and Astrophysics 309 (05): L15-8. Retrieved 2013-08-11.
54. A. J. Markwick; M. Ilgner; T. J. Millar; Th. Henning (April 2002). "Molecular distributions in the inner regions of protostellar disks". Astronomy & Astrophysics 385 (04): 632-46. doi:10.1051/0004-6361:20020050. Retrieved 2013-08-17.
55. M. Altmaier; U. Herpers (September 2001). "Al-26 in 34 Stony Meteorites Measured via Gamma-gamma Coincidence Counting". Meteoritics & Planetary Science Supplement 36 (09): A10. Retrieved 2013-08-11.
56. Gerald H. Share; Ronald J. Murphy (January 2004). Andrea K. Dupree, A. O. Benz. ed. Solar Gamma-Ray Line Spectroscopy – Physics of a Flaring Star, In: Stars as Suns: Activity, Evolution and Planets. San Francisco, CA: Astronomical Society of the Pacific. pp. 133-44. ISBN 158381163X. Bibcode: 2004IAUS..219..133S. Retrieved 2012-03-15.
58. http://www.nasa.gov/mission_pages/GLAST/news/fermi-thunderstorms.html
59. Samuel Ting; Manuel Aguilar-Benitez; Silvie Rosier; Roberto Battiston; Shih-Chang Lee; Stefan Schael; Martin Pohl (April 13, 2013). Alpha Magnetic Spectrometer - 02 (AMS-02). Washington, DC USA: NASA. Retrieved 2013-05-17.
60. A. Goldwurm; J. Ballet; B. Cordier; J. Paul; L. Bouchet; J. P. Roques; D. Barret; P. Mandrou et al. (April 20, 1992). "Sigma/GRANAT soft gamma-ray observations of the X-ray nova in Musca - Discovery of positron annihilation emission line". The Astrophysical Journal 389 (04): L79-82. doi:10.1086/186353. Retrieved 2014-01-30.
61. P. L. Nolan; J. L. Matteson (February 1, 1983). "A feature in the X-ray spectrum of Cygnus X-1 - A possible positron annihilation line". The Astrophysical Journal 265 (02): 389-92. doi:10.1086/160683. Retrieved 2014-01-30.
62. W. N. Johnson III; F. R. Harnden Jr.; R. C. Haymes (February 15, 1972). "The Spectrum of Low-Energy Gamma Radiation from the Galactic-Center Region". The Astrophysical Journal 172 (2): L1-7. doi:10.1086/180878.
63. P. Jean; J. Knödlseder; V. Lonjou; M. Allain; J.-P. Roques; G.K. Skinner; B.J. Teegarden; G. Vedrenne et al. (August 2003). "Early SPI/INTEGRAL measurements of 511 keV line emission from the 4th quadrant of the Galaxy". Astronomy & Astrophysics 407 (8): L55-8. doi:10.1051/0004-6361:20031056. Retrieved 2012-03-15.
64. A. Markowitz; R. Edelson (December 20, 2004). "An expanded Rossi X-ray timing explorer survey of X-ray variability in Seyfert 1 galaxies". The Astrophysical Journal 617 (2): 939-65. doi:10.1086/425559. Retrieved 2013-07-07.
65. M. Ackermann; M. Ajello; A. Allafort; W. B. Atwood; L. Baldini; G. Barbiellini; D. Bastieri; K. Bechtol et al. (2012). "Measurement of separate cosmic-ray electron and positron spectra with the Fermi Large Area Telescope". Physical Review Letters 108 (1): e011103. Retrieved 2014-01-31.
66. A. M. Galper; R. L. Aptekar; I. V. Arkhangelskaya; M. Boezio; V. Bonvicini; B. A. Dolgoshein; M. O. Farber; M. I. Fradkin et al. (2011). "The possibilities of simultaneous detection of gamma rays, cosmic-ray electrons and positrons on the GAMMA-400 space observatory". Astrophysics and Space Sciences Transactions 7: 75-8. doi:10.5194/astra-7-75-2011. Retrieved 2013-12-10.
67. The Granat Satellite. NASA HEASARC Imagine the Universe!. Retrieved 2007-12-05.
68. G. Weidenspointner; G.K. Skinner; P. Jean; J. Knödlseder; P. von Ballmoos; R. Diehl; A. Strong; B. Cordier et al. (October 2008). "Positron astronomy with SPI/INTEGRAL". New Astronomy Reviews 52 (7-10): 454-6. doi:10.1016/j.newar.2008.06.019. Retrieved 2011-11-25.
69. L. Zhang; K. S. Cheng (1998). "The gamma-ray conversion efficiency of rotation-powered pulsars". Monthly Notices of the Royal Astronomical Society 294 (01): 177-81. Retrieved 2014-01-31.
70. Qing-Hong Cao; Ian Low; Gabe Shaughnessy (July 19, 2010). "From PAMELA to CDMS and back". Physics Letters B 691 (2): 73-6. Retrieved 2014-02-01.