  Binary collisions between ions and electrons in an external magnetic field
are considered in second-order perturbation theory, starting from the
unperturbed helical motion of the electrons. The calculations are done with the
help of an improved BC which is uniformly valid for any strength of the
magnetic field and the second-order energy and velocity transfers are treated
in the interaction in Fourier space without specifying the interaction
potential. The energy transfer is explicitly calculated for a regularized and
screened potential which is both of finite range and less singular than the
Coulomb interaction at the origin and as the limiting cases involves the Debye
(i.e., screened) and Coulomb potentials. Two particular cases are considered in
detaile: (i) Ion motion parallel to the magnetic field with an arbitrary
strength. The energy transfer involves all harmonics of the electron cyclotron
motion. (ii) The ion arbitrary motion with respect to the strong magnetic field
when the electron cyclotron radius is much smaller than other characteristic
length scales (e.g., screening length, pitch of electron helix etc.). In the
latter case the energy transfer receives two contributions which are
responsible for the electron guiding center and cyclotron orbit perturbations.
