PENELOPE 2003 - OECD Nuclear Energy Agency

3.4. Positron annihilation 121
It is clear that the random value
ζ = min(υ, 1 − υ) (3.173)
follows the distribution given by eq. (3.167) when υ is sampled from the distribution
P (υ). The efficiency of this sampling algorithm practically equals 100% for positrons
with kinetic energy E less than 10 keV, decreases when E increases to reach a minimum
value of ∼ 80% at E ∼ 10 MeV and increases monotonically for larger energies.
As the result of annihilation, two photons with energies E − = ζ(E + 2m e c 2 ) and
E + = (1 − ζ)(E + 2m e c 2 ) are emitted in the directions given by eqs. (3.160) and (3.161).