### Footnotes:

^{1}© I.H.Hutchinson 1999-2011
^{2}[Feynman 21-6]
^{3}The potential can always be altered by adding a
constant, without
changing **E**. This freedom can be considered equivalent to choosing
the origin at which ϕ = 0.
^{4}satisfying
|**B**| → 0 as |**x**| → = ∞
fast enough
^{5}[Feynman 21-6]
^{6}An alternative
definition can be invoked, equivalent to this first definition but in
the frame of reference in which the single particle (1) is stationary
and the particles of density n_{2} are moving.
^{7}It also
shows the fundamental incoherence of the notion of the total number of
collisions per unit length and concepts that depend on it such as the
average change in some parameter *per collision*, which some
authors unfortunately employ.
^{8}The factor of 2 here is our only real
artifice. It gives the argument of the logarithm equal to that
obtained by a full quantum calculation
^{9}This
proportionality can be traced to the inverse dependence of the energy
transfer in a collision on m_{2}, but only because cancellation of
reduced mass factors occurs in the product Q b_{90}^{2}.
^{10}See
M.Born "Atomic Physics" 8th ed., Blackie p199, for a derivation of the
Thomas-Fermi distribution of electron density around an atom based on
the Pauli exclusion principle and a continuum approximation.

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