  A charged particle traversing a plasma loses its energy to both plasma
electrons and ions. We compute the energy partition, the fractions $E_e/E_0$
and $E_\smI/E_0$ of the initial energy $E_0$ of this `impurity particle' that
are deposited into the electrons and ions when it has slowed down into an
equilibrium distribution that we shall determine. We use a well-defined
Fokker-Planck equation for the phase space distribution of the charged impurity
particles in a weakly to moderately coupled plasma. The Fokker-Planck equation
holds to first sub-leading order in the dimensionless plasma coupling constant,
which means we compute to order $n\ln n$ (leading) and $n$ (sub-leading) in the
plasma density $n$. Previously, the order $n$ terms had been estimated, not
calculated. Since the charged particle does not come to rest, the energy loss
obtained by an integration of a $dE/dx$ has an ambiguity of order of the plasma
temperature. Our Fokker-Planck formulation provides an unambiguous, precise
definition of the energy fractions. For equal electron and ion temperatures, we
find that our precise results agree well with a fit obtained by Fraley,
Linnebur, Mason, and Morse. The case with differing electron and ion
temperatures, a case of great importance for nuclear fusion, will be
investigated in detail in the present paper. The energy partitions for this
general case, partitions that have not been obtained before, will be presented.
We find that now the proper solution of the Fokker-Planck equation yields a
quasi-static equilibrium distribution to which fast particles relax that has
neither the electron nor the ion temperature. This "schizophrenic" final
ensemble of slowed particles gives a new mechanism to bring the electron and
ion temperatures together. The rate at which this new mechanism brings the
electrons and ions in the plasma into thermal equilibrium will be computed.
