Problem 2121

Created attachment 535 [details]
Patch implementing the described improvements. See also https://github.com/Geant4/geant4/pull/5

[I have also submitted this as https://github.com/Geant4/geant4/pull/5
because I don't know which method is preferred.]

Added calculation of the Fermi density effect using atomic data as
described in R.M. Sternheimer et al. "Density Effect For The Ionization Loss
of Charged Particles in Various Substances" Atom. Data Nucl. Data Tabl. 30
(1984) 261-271.

This calculation gives values for the density effect 'delta' which are much
more accurate than that provided by the Sternheimer 3-part approximation,
introduced in his 1952 paper, Phys.Rev. 88 851-859. This is particularly
true when using the general method for producing parameter
values given in his 1971 paper, Phys.Rev. B3 3681-3692, but doing the
full calculation is still a significant improvement over using the
tabulated values given in the 1984 paper for elements and a selected
set of mixtures and compounds.

The purpose of the 3-part approximation was to avoid heavy computation from
the perspective of sliderules (1952) or minicomputers (1971). It
is no longer necessary. I ran tests using the NOvA simulation framework and
could measure no difference in performance between using the approximation
and the full treatment.

A major advantage of this method is that the stopping power of a substance
does not abruptly change when the user modifies it so that it is no
longer a tabulated material. In our case, we noticed this effect when
we changed iron to steel (98% iron, 2% other). Previously, iron got
the 1984 tabulated values while steel got the 1971 general form, which
gives up to a 1.3% difference in mean muon range, with the largest
difference at about 200MeV.

I have tested the code with muons in iron and verified that the mean range
changes as expected between the approximate and exact forms.

Implementation notes:

    The calculation involves finding roots and can fail. In this case, the
    code falls back to the approximation and prints a message saying it has
    done so. I have not found any cases that prompt a failure, but have only
    tested with materials found in and around the NOvA detector.

    Attempted to make clear in places that refer to the parameterization,
    such as G4IonisParamMat::SetDensityEffectParameters(), that these calls only
    have any effect if the full calculation fails.

    I found a separate implementation of the Sternheimer parameterization in
    source/processes/electromagnetic/highenergy/src/G4mplIonisationModel.cc
    I don't know why this parallel implementation exists, so I simply changed
    a comment to make it more clear that it was the approximate form.

    G4IonisParamMat::DensityCorrection() is no longer inlined.

    Removed debugging print statements in G4IonisParamMat::ComputeDensityEffect().