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Positrons are injected into the sample to be studied. Adjusting their energy controls the depth to which they penetrate. The positrons lose energy until they reach thermal equilibrium with the sample, and can then move by random thermal diffusion for a few hundred picoseconds. The diffusing positrons can be trapped by defects in the sample. The ultimate fate for all positrons is to annihilate with an electron, resulting in 2 gamma-rays.
Momentum and energy must both be conserved in this event… the total energy of the two gamma-rays must be 1022 keV, the mass equivalent (via E= mc 2 ) of the positron and electron. Consider a positron and electron at rest: the momentum is zero, and so the gamma-ray energy gets split into two gamma-rays each of exactly 511 keV, in exactly opposite directions. In the real case, however, the electron is orbiting an atom, and so has some momentum. The result of this is that the gamma-ray energy is Doppler-shifted away from 511 keV. In the experiment we collect the energy spectrum of the gamma-rays, which carries information about the electron momentum distribution.
The ability to measure defect concentrations arises in the following way: in a perfect crystal, a certain fraction of the positrons will annihilate with valence electrons (low momentum) and a certain fraction with bound or core electrons (high momentum). Now suppose the crystal contains a vacancy (a missing atom): the open space this produces is attractive to the positron, since it can sit further from the nuclei (which are positive and therefore repel the positron). In this open space, sitting further from the nuclei, the positron is more likely to annihilate with a low-momentum valence electron. So the average electron momentum seen by the positrons decreases, and we can see this in the resulting gamma-ray spectra!
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