Electron-positron annihilation

Annihilation (Positron-Electron)—An interaction between a positive and a negative electron in which they both disappear their rest mass, being converted into electromagnetic radiation (called annihilation radiation) with two 0.51 MeV gamma photons emitted at an angle of 180° to each other. 

The two quantities which can be observed when an individual positron annihilates in condensed matter are the positron age r, which is the time interval between implantation and annihilation of the positron, and the momentum p of the annihilating positron-electron pair. Time-resolved information on the evolution of positron states is obtained by correlated measurements of the individual positron lifetime (= positron age) and the momentum of the annihilating positron-electron pair (Age-Momentum Correlation, AMOC). AMOC measurements are an extremely powerful tool for the study of reactions involving positrons. It not only provides the information obtainable from the two constituent measurements but allows us to follow directly, in the time domain, changes in the e+e momentum distribution of a positron state (cf. Sect. 1). 

Since both 511 keV photons resulting from a 2y-annihilation event transmit equivalent information, one photon may be used to determine the age of the annihilating positron and the other for the correlated measurement of the momentum of the annihilating positron-electron pair by measurement of the... 

Ekln(i) Mean kinetic energy of the annihilating positron-electron pair... 

Positron annihilation techniques [78] can be used to obtain information about the momentum density of the annihilating positron-electron pair. In solids, particularly metals, the distortion of the electron momentum density by the Coulomb interaction between the positron and electrons is relatively small, and this technique then gives us the electron momentum density. 

The overlap integral (or rather the physical overlap behind it) supplies another measurable quantity besides o-Ps lifetime and intensity. This quantity is the momentum distribution of annihilation gamma rays. Due to the momentum conservation law, annihilation gammas should carry the momentum of the annihilating positron-electron pair. In the case of pick-off annihilation, the conserving momentum, where P is the momentum operator, is the combined momentum of e" and the electron of the surrounding material ... 

Radiation, Annihilation—Photons produced when an electron and a positron unite and cease to exist. The annihilation of a positron-electron pair results in the production of two photons, each of 0.51 MeV energy. 

These traps, (Fig. 6) and similar effects in the motion of holes and other charges through polymers, would eventually be correlated also with such structural probes as positron lifetimes in macromolecular solids. Extensive recent studies of positron lifetime are based on positronium decay. In this, the lifetime of o-positronium (bound positron-electron pair with total spin one) is reduced from about 140 nanoseconds to a few nanoseconds by "pick-off annihilation" in which some unpaired electron spins in the medium cause conversion quenching of orthopositronium to para-positronium. The speed of the t2 effect is supposed, among other things, to represent by pick-off annihilation the presence of defects in the crystalline lattice. In any case, what amounts to empty space between molecules can then be occupied by orthopositronium.(14,15,16) It is now found in linear polyethylene, by T. T. Wang and his co-workers of Bell Laboratories(17) that there is marked shift in positron lifetimes over the temperature range of 80°K to 300°K. For... 

The fact that neutrinos are emitted during the transformation provides an opportunity for direct observation of the reactions taking place at the heart of the Sun. Note that antimatter is produced in this strange reaction, in the form of the positton or antielectron e+. The positrons generated immediately annihilate with electrons in the surrounding medium with subsequent emission of gamma rays. 

Ii is possible for a positron-electron system to annihilate with the emission of one, two. three, or more gamma rays. However, not all processes are equally probable. 

The total positron scattering cross section, erT, is the sum of the partial cross sections for all the scattering channels available to the projectile, which may include elastic scattering, positronium formation, excitation, ionization and positron-electron annihilation. Elastic scattering and annihilation are always possible, but the cross section for the latter process is typically 10-2O-10-22 cm2, so that its contribution to erT is negligible except in the limit of zero positron energy. All these processes are discussed in greater detail in Chapters 3-6. 

The wave function of the ion that remains after annihilation is a superposition of eigenstates of the Hamiltonian of the ion, the relative probabilities of which may be determined from the wave function used in the calculation of Zeg. The annihilation process takes place so rapidly, compared with normal atomic processes, that it is reasonable to assume the validity of the sudden approximation. Consequently, the wave function of the residual ion when the positron has annihilated with electron 2 at the position r = r2 is... 

The experimental techniques involved in measuring the angular correlation and the Doppler broadening of the two annihilation gamma-rays were introduced in section 1.3. These techniques rely on the fact that the motion of the positron-electron pair immediately prior to annihilation causes the two gamma-rays to be emitted in directions differing... 

We will review here experimental tests of quantum electrodynamics (QED) and relativistic bound-state formalism in the positron-electron (e+,e ) system, positronium (Ps). Ps is an attractive atom for such tests because it is purely leptonic (i.e. without the complicating effects of nuclear structure as in normal atoms), and because the e and e+ are antiparticles, and thus the unique effects of annihilation (decay into photons) on the real and imaginary (related to decay) energy levels of Ps can be tested to high precision. In addition, positronium constitutes an equal-mass, two-body system in which recoil effects are very important. 

If sufficient positrons can be confined, studies of particle transport within the plasma, etc., similar to those conducted with electrons can be carried out. It may be possible to use the enhanced detection possibilities afforded since positron-electron annihilations can be detected. An ultra-cold source of positrons would also have a variety of other applications.24 For example, it has been proposed to eject trapped positrons into a plasma as a diagnostic.25 Also, positrons initially in thermal equilibrium at 4.2K within a trap would form a pulsed positron beam of high brightness when accelerated out of the trap. 

The26A1 decay in the interstellar medium also emits positrons (antielectrons), which may be a partial source of the positron-electron annihilation into gamma rays that are also seen emanating from the interstellar gas. 

Positron emission tomography (PET) exploits the difference in positron-electron annihilation rates in the reaction ... 

A small dose of a soluble fast-decay positron-emitting artificial radioisotope (produced as needed not too far from the PET instrument 6C11, 8015, 9F18 or 37Rb82) is put into human tissue (e.g., blood) the positron typically travels about 1 mm, meets an electron from within the human body, and the pair decays into two y photons of energy 0.51 MeV each, within microseconds to nanoseconds. Two spin states are possible for the positron— electron ion pair before their annihilation singlet and triplet. The annihilation rate for the triplet state depends sensitively on the electron density of the body tissue. Two y counters are set in coincidence mode, and several hundred thousand coincidence events are used to provide valuable tissue information (in addition to a CT scan). 

The first anti-particle discovered was the anti-electron, the so-called positron, in 1933 by Anderson [3] in the cloud chamber due to cosmic radiation. The existence of the anti-electron (positron) was described by Dirac s hole theory in 1930 [4], The result of positron—electron annihilation was detected in the form of electromagnetic radiation [5]. The number and event of radiation photons is governed by the electrodynamics [6, 7]. The most common annihilation is via two- and three-photon annihilation, which do not require a third body to initiate the process. These are two of the commonly detected types of radiation from positron annihilation in condensed matter. The cross section of three-photon annihilation is much smaller than that of two-photon annihilation, by a factor on the order of the fine structure constant, a [8], The annihilation cross section for two and three photons is greater for the lower energy of the positron—electron pair it varies with the reciprocal of their relative velocity (v). In condensed matter, the positron—electron pair lives for only the order of a few tenths to a few nanoseconds against the annihilation process. 

It should be noted that the S parameters of both o-Ps pick-off and free-positron annihilation are lower than that of the Si substrate, because positrons predominantly annihilate with electrons of oxygen in the Si02 network. Only p-Ps self-annihilation has a higher S value than that of Si. The S parameter observed in conventional Doppler- broadening-of-annihilation radiation is the average of p-Ps, o-Ps, and free-positron annihilation. Therefore, if the Ps fraction decreases due to the presence of defects, impurities, etc., the intensity of the narrow momentum component due to p-Ps self-annihilation decreases, and as a result the averaged S parameter decreases. 

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place ... 

Surface Fraction of Positrons in Surface State Annihilating with Electrons in Indicated Core levels ( % ) ... 

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