\section{Ionisation} 
\label{secioni}

The total cross section at a given incident kinetic energy T is calculated by
summing the partial cross sections at such energy for all the subshells of an
element. The partial subshell cross sections at incident energy T are obtained
from an interpolation of the evaluated cross section data in the EEDL library,
according to the formula \ref{eqloglog}.

The subshell from which the electron is emitted is randomly selected according
to the cross sections of the subshells, determined at the energy T by
interpolating the evaluated cross section data from the EEDL data library.

The probability of emission of an electron ($\delta$ ray) with kinetic energy
$t$ from a subshell of binding energy $B_i$ as the result of the interaction of
an incoming electron of kinetic energy $T$ is described by:
\begin{equation}
  \label{eqionihigh}
  Prob(T, t, B_i) = {\sum^7}_{j=2}{a_j(T)\over(t+b_i)^j} 
\end{equation}
for $t < t_0$ and 
\begin{equation}
\label{eqionilow}
  Prob(T, t, B_i) = {c(T)\over t^2}
\end{equation}
for $t > t_0$, where $t_0$ is a parameter.
Both formulas result from empirical fits to the EEDL data and
are normalized to 1. 
The $a$, $b$ and $c$ coefficients are
determined by fitting the data; their energy dependence is evaluated from a
semilogarithmic interpolation of the fitted data. 

The sampling of the final state proceeds
through two steps: first the range of the energy ($t < t_0$ or $t > t_0$) is
determined by a random number extraction, taking into account the relative area
determined by the two functions \ref{eqionihigh} and \ref{eqionilow}, then the
energy of the $\delta$ ray is generated according to the corresponding
probability distribution. 

The angle of emission of the scattered electron and of the $\delta$ ray 
is determined by energy-momentum conservation.

The interaction leaves the atom in an excited state, with excitation energy
equal to the binding energy of the subshell from which the electron has been
emitted. The deexcitation of the atom proceeds via the emission of fluorescence
photons, as described in section \ref{secphoto}.

\section{Status of the document}
30.9.99 created by Alessandra Forti


