Gamma-ray annihilation

Fig. 1.1. Feynman diagrams of the lowest order contributions to (a) radiationless, (b) one-gamma, (c) two-gamma, (d) three-gamma-ray annihilation. A2+ and A+ denote the charge states of the remnant atomic ion.

Figure 16.19. Simulation of a gamma-ray annihilation line from the annihilation of 48 GeV neutralinos, superimposed on a gamma-ray background of astrophysical origin. The simulation includes the finite energy resolution of the upcoming GLAST detector. (Figure from the GLAST Science Brochure.)...

The PET technique relies on radioactive unstable atoms that disintegrate spontaneously, giving off particles called positrons. As soon as an atom emits a positron, the positron combines with an electron. Both particles are annihilated, producing a brief flash of gamma-ray radiation that is easily detected by radiation monitors. 

PALS is based on the injection of positrons into investigated sample and measurement of their lifetimes before annihilation with the electrons in the sample. After entering the sample, positron thermalizes in very short time, approx. 10"12 s, and in process of diffusion it can either directly annihilate with an electron in the sample or form positronium (para-positronium, p-Ps or orto-positronium, o-Ps, with vacuum lifetimes of 125 ps and 142 ns, respectively) if available space permits. In the porous materials, such as zeolites or their gel precursors, ort/zo-positronium can be localized in the pore and have interactions with the electrons on the pore surface leading to annihilation in two gamma rays in pick-off process, with the lifetime which depends on the pore size. In the simple quantum mechanical model of spherical holes, developed by Tao and Eldrup [18,19], these pick-off lifetimes, up to approx. 10 ns, can be connected with the hole size by the relation ... 

At present, most PET scanners can acquire in both a two-dimensional as well as a three-dimensional mode, whereas SPECT cameras measure in a three-dimensional mode. The physical property of the dual-positron gamma-rays emission lends itself to mathematical reconstruction algorithms to produce three-dimensional images in which the calculations are much closer to exact theoretical ones than those of SPECT. This is, in part, due to the two-photon as opposed to single-photon approach. PET can now achieve resolutions, for example in animal-dedicated scanners, in the order of 1 or 2 mm. The resolution is inherently limited theoretically only by the mean free path or distance in which the positron travels before it annihilates with an electron, e.g. those in biological water 2-8 mm. SPECT, although achieving millimeter resolution with the appropriate instrumentation, cannot quite achieve these levels. 

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. 

It is interesting to compare the properties of positive electrons, positrons, with the properties of electrons in nonpolar liquids. Values of the mobility of positrons, )x +, are now available for a few liquids. Early measurements for in -hexane ranged from 8.5 to 100 cm /Vs [181,182]. In a recent study, the Doppler shift in energy of the 511-keV annihilation gamma ray in an electric field was utilized to measure the drift velocity. This method led to fi+ = 53 cm /Vs in -hexane and 69 cm /Vs in 2,2,4-trimethylpentane [183]. Interestingly, these values are comparable to the mobilities of quasi-free electrons in nonpolar liquids. 

When a PET isotope is administered to tissue, it emits positrons. These positrons encounter electrons found in tissue, the interaction of an electron and positron results in mutual annihilation and the production of beams of gamma rays directly opposite to each other (Figure 17.10). The... 

Another form of three-dimensional imaging of internal organs, called positron emission tomography (PET) scanning, exploits a less common form of beta decay. Most beta decays involve the emission of electrons from the nucleus as a neutron decays into an electron and a proton. But the reverse can happen too a proton can decay into a neutron (see page 106). The positive charge is borne away by a positron, which will soon collide with an electron. Their mutual annihilation produces a gamma ray. 

Improvements in current, established technologies and the introduction of new ways to test materials, nondestmctively are expected to continue apac. One promising method is positron annihilation. The positron is the antiparticle of the electron thus apositron/electron pair is unstable and will annihilate. In this process, two gamma rays at approximately 180 to one another are emitted from the center of the mass of the pair. A very slight departure from 180° is directly proportional to the transverse component of the momentum, of the pair. The momenta of the electrons involved in such collisions can be calculated from the geometry and intensity of the gamma rays. The dynamics of the clcctron/positron system underlie the use of the technique for the study of defects in materials,... 

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. 

Gamma Rays (Nuclear-decay y-Rays, 0.5-m.e.v. Photons from Annihilation of Positrons or X-rays). The development of large sodium iodide crystal 7-ray spectrometers (13) has made possible high detection efficiencies (close to 100% for some 7-ray energies). Also, whole-body counters utilizing large cylindrical liquid scintillators provide a detection efficiency of 15% for the 7-rays emitted from potassium-40 in the human body (23). 

The positron was subsequently discovered by Anderson (1933) in a cloud chamber study of cosmic radiation, and this was soon confirmed by Blackett and Occhialini (1933), who also observed the phenomenon of pair production. There followed some activity devoted to understanding the various annihilation modes available to a positron in the presence of electrons radiationless, single-gamma-ray and the dominant two-gamma-ray processes were considered (see section 1.2). The theory of pair production was also developed at this time (see e.g. Heitler, 1954). 

Note that <727 — 00 as v — 0, although the annihilation rate, which is proportional to the product W27, remains finite. At low incident positron energies the two gamma-rays are emitted almost collinearly, the energy of each being close to me2 (= 511 keV). Annihilation of a small fraction of the positrons emanating from the radioactive source can occur at relativistic speeds and then it is necessary to use the full equation (1.2). 

Annihilation can also occur with the emission of three (or more) gamma-rays, and Ore and Powell (1949) calculated that the ratio of the cross sections for the three- and two-gamma-ray cases is approximately 1/370. Higher order processes are expected to be further depressed by a similar factor. A case in point is the four-gamma-ray mode, for which the branching ratio with the two-gamma-ray mode was shown by Adachi et al. (1994) to be approximately 1.5 x 10-6, in accord with QED calculations. 

The need to conserve angular momentum and to impose CP invariance led Yang (1950) and Wolfenstein and Ravenhall (1952) to conclude that positronium in a state with spin 5 and orbital angular momentum L can only annihilate into n7 gamma-rays, where... 

This selection rule does not appear to exclude radiationless annihilation and annihilation into a single gamma-ray, but these modes of annihilation are nevertheless forbidden for free positronium. 

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