Recent observations of cosmic ray (CR) electrons from several instruments have revealed various degrees of deviation in the measured electron energy distribution from a simple power law, in the form of an excess around 0.1-1?TeV energies. An even more prominent deviation and excess has been observed in the fraction of CR positrons around 10 and 100?GeV energies. These observations have received considerable attention and many theoretical models have been proposed to explain them. The models rely on either dark matter annihilation/decay or specific nearby astrophysical sources, and involve several additional assumptions regarding dark matter distribution or particle acceleration. 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 CRs. The model presented here assumes a power-law injection of electrons (and protons) by supernova remnants (SNRs), and evaluates their expected energy spectrum based on a simple kinetic equation describing the propagation of charged particles in the interstellar medium (ISM). 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 ISM, we can reproduce the most recent observations by the Fermi and HESS experiments. Interestingly, in our model the injection spectral index of CR electrons becomes comparable to, or even equal to that of CR protons. The Klein-Nishina effect may also affect the propagation of the secondary e ±?pairs, and therefore modify the CR positron-to-electron ratio. We have explored this possibility by considering two mechanisms for production of e ±?pairs within the Galaxy. The first is due to the decay of π±'s produced by interaction of CR nuclei with ambient protons. The second source discussed here is due to the annihilation of the diffuse Galactic γ-rays on the stellar photon field. We 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 (as well as the Fermi and HESS) results assuming high values of the starlight and interstellar gas densities, which would be more appropriate for vicinities of SNRs. A possible solution to this problem may be that CRs undergo most of their interactions near their sources due to the efficient trapping in the far upstream of supernova shocks by self-generated, CR-driven turbulence.
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