%\subsection{The transport algorithm \editor{Gunter}}

%\begin{verbatim}
%- choose impact
%- find collisions
%- loop { propagate to next in time collision
%-          do collision
%-          check Pauli
%-               OK
%\end{verbatim}

For the primary particle an impact parameter is chosen random in a
disk outside the nucleus perpendicular to a vector passing through the
center of the nucleus  coordinate system an being
parallel to the momentum direction.
Using a straight line trajectory, the distance of closest approach
$d_i^{min}$
to each target nucleon $i$ and the corresponding time-of-flight $t_i^d$
is calculated. In this calculation the momentum of the target nucleons
is ignored, i.e. the target nucleons do not move. The interaction cross
section ${\sigma}_i$ with target nucleons is calculated using total inclusive
cross-sections described below. For calculation of the cross-section the
momenta of the nucleons are taken into account.
The primary particle may interact with those target nucleons where the distance of closest
approach $d_i^{min}$ is smaller than
$d_i^{min} < \sqrt{\frac{\sigma_i}{\pi}}$. These candidate interactions
are called collisions, and these collisions are stored ordered by  time-of-flight $t_i^d$.
In the case no collision is found, a new impact
parameter is chosen.

The primary particle is tracked the time-step given by the time to the
first collision. As long a particle is outside the nucleus, that is a radius of
the outermost nucleon plus $3fm$, particles travel along
straight line trajectories. Particles entering the nucleus have their
energy corrected  for Coulomb effects. Inside the nucleus particles are
propagated in the scalar nuclear field.  The equation of motion  in the field
is solved for a given time-step using a Runge-Kutta integration method.

At the end of the step, the primary and the nucleon interact suing the
scattering term. The resulting secondaries are checked for the Fermi
exclusion principle. If any of the two particles has a momentum below
Fermi momentum, the interaction is suppressed, and the original primary
is tracked to the next collision. In case interaction is allowed, the
secondaries are treated like the primary, that is, all possible
collisions are calculated like above, with the addition that these new
primary particles may be short-lived and may decay. A decay is treated like others
collisions, the collision time being the time until the decay of the particle.
All secondaries are tracked until they leave the nucleus, or
the until the cascade stops.