18.11} Ionisation losses

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 The treatment of ionisation losses was completely re-written in
 1991-1992 by Fasso` and Ferrari to eliminate many crude approximations,
 and delta-ray production was added.
 Ranging of stopping charged particle  was also changed. Quenching
 according to the Birks law was introduced to calculate the response
 of scintillators.

 Application of FLUKA to proton therapy called for further refinements
 of stopping power routines in 1995, with the inclusion of tabulated
 data of effective ionisation potentials and density effect parameters.
 Shell corrections were added. The new treatment was fully compliant
 with ICRU recommended formulae and parameters and included all corrections,
 including low energy shell corrections as worked out by Ziegler et
 al. [Zie77]

 In 1996, a new formalism for energy loss fluctuations by Ferrari replaced
 the old treatment of Landau fluctuations. This formalism, based on the
 statistical properties of the cumulants of a distribution, was
 applied to both heavy charged particles and e+e-, and was fully
 compatible with any user-defined threshold for delta ray emission.

 Other improvements concerned the possibility to define materials
 with local density different from average (porous substances),
 and the ranging out of particles with energies lower than the
 transport cutoff.

 In 1999-2000, heavy ion dE/dx was improved by the inclusion of
 effective Z and straggling (Ferrari).

 High-energy energy loss mechanisms for heavy charged particles
 were implemented by Ferrari both as a continuous and as an explicit treatment:
 bremsstrahlung and pair production in 1992, nuclear interaction via
 virtual photons in 1993.

 Mott corrections to electronic stopping power were introduced by Ferrari
 and Sala around 2010, both for the average stopping power, Landau fluctuations,
 and delta ray energy spectra. They are particularly important for medium-heavy
 ions, resulting on computed range up to 20% shorter for Uranium beams.
 The theoretical implementation had been thoroughly validated against
 available experimental data.

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