Annihilation into three gamma-rays

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. 

Note that, as can be seen from the discussion in subsection 1.2.1, the contributions from the higher order annihilation modes are negligible at the present levels of precision. Thus, the rate for the annihilation of ortho-positronium into five gamma-rays is only 10-6 of that for three gamma-rays, with a similar value for the ratio of the rates for para-positronium annihilation into four and two gamma-rays. 

Electron-positron annihilation in Ps2 was investigated by Tisenko (1981), who, using the relatively simple wave function of Hylleraas and Ore (1947), obtained the annihilation rates into two and three gamma-rays as 16 ns-1 and 0.043 ns-1 respectively. No such calculations have been performed using the more elaborate wave function of Ho. 

As this isotope decays, positrons are emitted. Recall that when a positron collides with an electron, both are annihilated, and two gamma rays are produced. These gamma rays leave the body and are detected by a scanner. A computer converts the images into a detailed three-dimensional picture of the person s organs. 

Figure 27.2 Schematic of annihilation into two annihilation gamma rays of energy 511 keV, demonstrating the three methods of PAS. Here, P corresponds to 0 of Eq. P7.3) and corresponds to Pl of Eq. (27.4).

An electron and positron of sufficiently low energy (typically thermal, <5 eV) may combine to briefly form a hydrogen-like state of matter referred to as positronium. Positronium almost immediately self-annihilates yielding either a two- or three-photon decay into gamma rays... 

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