  In this article we discuss a peculiar regime of Compton Scattering that
assures the maximum transfer of energy and momentum from free electrons
propagating in vacuum to the scattered photons. We name this regime Full
Inverse Compton Scattering (FICS) because it is characterized by the maximum
and full energy loss of the electrons in collision with photons: up to 100 % of
the electron kinetic energy is indeed transferred to the photon. In the case of
relativistic electrons, characterized by a large Lorentz factor (gamma >> 1),
FICS regime corresponds to an incident photon energy equal to mec^2/2 . We
interpret such an astonishing result as FICS being the time reversal of direct
Compton Scattering of very energetic photons (of energy much greater than mec2)
onto atomic electrons. Although the cross section of Compton scattering is
decreasing with the energy of the incident photon, making the process less
probable with respect to other reactions (pair production, nuclear reactions,
etc) when high energetic photons are bombarding a target, the kinematics
straightforwardly implies that the back-scattered photons would have an energy
reaching asymptotically me^2c^2 . FICS is instead the unique suitable working
point in Compton scattering for achieving the total transfer of (kinetic)
energy exactly from the electron to the photon. Experiencing transitions from
the initial momentum to zero in the laboratory system, in FICS the electron is
also subject to very large negative acceleration; this fact can lead to
possible experiments of sensing the Unruh temperature and related photon bath.
On the other side of the energy dynamic range, low relativistic electrons can
be completely stopped by moderate energy photons (tens of keV), leading to full
exchange of temperature between electron clouds and photon baths.
