Continuous and multiple electron/positron injection: Can pulsars account for the electron/positron spectrum?

We investigate the observed spectrum of cosmic-ray electrons and positrons from astrophysical sources, especially pulsars, and the physical processes for making the spectrum spiky or smooth via continuous and multiple cosmic-ray injections. We find that (1) the average spectrum with the local birth rate of pulsars (including the off-axis ones) is relatively smooth, consistent with the PAMELA data, but requires an energetic source for the ATIC/PPB-BETS peak. Such a source should not occur repeatedly at the same rate. (2) A continuous injection produces a broad peak and a high energy tail above the peak, which can constrain the source duration (≲ 105 years with the current data). We also discuss the H.E.S.S. data in the TeV range which constrain the total energy of young sources.