  Recent observations of cosmic ray electrons from several instruments have
revealed various degrees of deviation in the measured electron energy
distribution from a simple power-law, in a form of an excess around TeV
energies. An even more prominent deviation has been observed in the fraction of
cosmic ray positrons around 100 GeV energies. In this paper we show that the
observed excesses in the electron spectrum may be easily re-produced without
invoking any unusual sources other than the general diffuse Galactic components
of cosmic rays. The primary physical effect involved is the Klein-Nishina
suppression of the electron cooling rate around TeV energies. With a very
reasonable choice of the model parameters characterizing the local interstellar
medium, we can reproduce the most recent observations by Fermi and HESS
experiments. We also find that high positron fraction increasing with energy,
as claimed by the PAMELA experiment, cannot be explained in our model with the
conservative set of the model parameters. We are able, however, to reproduce
the PAMELA results assuming high values of the starlight and interstellar gas
densities, which would be more appropriate for vicinities of supernova
remnants. A possible solution to this problem may be that cosmic rays undergo
most of their interactions near their sources due to the efficient trapping in
the far upstream of supernova shocks by self-generated, cosmic ray-driven
turbulence.
