The
various components of Bethe-Bloch theory are reviewed in "Stopping of Energetic Light Ions in
Elemental Matter", J. F. Ziegler, Applied Physics
Reviews / J. Applied Physics, **85**, 1249-1272 (1999).
This paper is included as an Acrobat PDF file (600 kB). (Download
Paper) The basic equations for high energy ion
stopping using the Bethe-Bloch theory are shown below
(copied from the above paper).

The
pre-factor above evaluates the basic stopping between two
particles of atomic number Z_{1} and Z_{2}.
This is followed by an expansion of terms based on powers of
the ion's atomic number, Z_{1}. The first term is the
primary modification and is discussed below. The second term
is the only term that includes an odd power of the ion's
atomic number, Z_{1 }(when combined with the Z_{1}^{2}
of the pre-factor). It is often called the (Z_{1})^{3}
term, or the "Barkas Effect" after the discovery
that the stopping of positive particles is significantly
different than for negative particles. The final term is
called the "Bloch Effect" and is a minor
correction..

Eq.
10 shows the stopping equation with only the first factor of
Eq. 13, L_{0}(B), expanded into several terms. The
terms within the square parenthesis are modifications based
on the structure of atoms. Using the substitutions shown in
Eq. 11, the equation can be reduced to the form of Eq. 12.
In this final equation, the first term of the parenthesis
collects all the relativistic corrections to stopping. The
second term incorporates the target atom's atomic energy
structure. The third term is called a Shell Correction, and
corrects for the electron velocity distribution in the
target. Finally, the fourth them is called the Density
Correction and it corrects for the dielectric polarization
of the target.

The plots below show the relative contribution of the various components for typical calculations of ion / target combinations.

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