In SESAME the hybrid scattering model is implemented as follows (R represents a random number between 0 and 1):
The elastic mean free path is determined by the Mott cross section and the inelastic mean free paths (for all elements and shells) by the ionization cross section of Gryzinsky (formula A.15). The free path of an electron between two scattering events is calculated using a random number R:
If the electron-solid interaction is elastic, the polar
angular deflection is calculated similar to the single scattering
model (formula A.16). The energy loss is calculated
using formula A.7 and formula A.8.
For an inelastic scattering event, the element and the shell of the element, which is ionized, have to be determined randomly. The principle algorithm is:
with
and
is the ionization cross section for inner
shell n and element i of Gryzinsky (see equation A.15)
and
is the weight fraction of the element i.
For the selected element i and shell l, the energy loss
of the electron due to the inner shell ionization is calculated. This
energy loss lies between the edge energy of the ionized shell and the
energy of the electron before the scattering has taken place.
is chosen randomly applying Gryzinsky's formula A.16:
is the edge energy of the selected shell and
the differential cross
section of Gryzinsky (equation A.16). The new energy of the
primary electron is the maximum value of
.
The minimum value of
is the energy of
the secondary electron. The flight direction of the secondary electron is
equally distributed and therefore chosen randomly.
The angular deflection of the primary electron results from
equation A.10.