  At low reduced electric fields the electron energy distribution function in
heavy noble gases can take two distinct shapes. This "bistability effect" - in
which electron-electron (Coulomb) collisions play an essential role - is
analyzed here for Xe with a Boltzmann equation approach and with a first
principles particle simulation method. The solution of the Boltzmann equation
adopts the usual approximations of (i) searching for the distribution function
in the form of two terms ("two-term approximation"), (ii) neglecting the
Coulomb part of the collision integral for the anisotropic part of the
distribution function, (iii) treating Coulomb collisions as binary events, and
(iv) truncating the range of the electron-electron interaction beyond a
characteristic distance. The particle-based simulation method avoids these
approximations: the many-body interactions within the electron gas with a true
(un- truncated) Coulomb potential are described by a Molecular Dynamics
algorithm, while the collisions between electrons and the background gas atoms
are treated with Monte Carlo simulation. We find a good general agreement
between the results of the two techniques, which confirms, to a certain extent,
the approximations used in the solution of the Boltzmann equation. The
differences observed between the results are believed to originate from these
approximations and from the presence of statistical noise in the particle
simulations.
