For the annihilation into two photons the cross-section formula of Heitler is used. The total cross-section is given by [,]
2γ(Z,E) | 02
| |
0 |
|
For compounds, the cross-section is calculated using an effective atomic number as explained in [PHYS010].
Positrons can annihilate in a single photon if the electron with which it interacts is bound to a nucleus. The total cross-section for such a process is
1γ(Z,E) | 02α4{Z5
| |
|
In the derivation of this formula, only the interactions with the K-shell electrons are taken into account. As the cross-section depends on 5 , a special value of eff
is computed in GPROBI:
eff= ∑i{pi
The notation of [PHYS010] is used.
The total cross-section for the positron annihilation is 2γ+ σ1γ . The value of 1γ is at it largest for heavy materials, for example, it is 20 % of for a positron of 440 keV of kinetic energy in lead. For lower and higher energies the probability is lower.