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The observations of gamma-ray emission from pulsars with the Fermi-LATdetector and the detection of the Crab pulsar with the VERITAS array ofCherenkov telescopes at energies above 100 GeV make it unlikely that curvatureradiation is the main source of photons above GeV energies in the Crab and manyother pulsars. We outline a model in which the broad UV-X-ray component and thevery high energy \gamma-ray emission of pulsars are explained within theSynchrotron-Self-Compton (SSC) framework. We argue that the bulk of theobserved radiation is generated by the secondary plasma, which is produced incascades in the outer gaps of the magnetosphere. We find that theinverse-Compton (IC) scattering occurs in the Klein-Nishina regime, whichfavors synchrotron photons in the UV band as target field for the scatteringprocess. The primary beam is accelerated in a modest electric field, with afield strength that is of the order of a few percent of the magnetic field nearthe light cylinder. Overall, in the Klein-Nishina regime of the IC scatteringthe particle distribution in the gap does not evolve towards a stationarydistribution and thus is intrinsically time-dependent. We point out that in aradiation reaction-limited regime of particle acceleration the gamma-rayluminosity L_{\gamma} scales linearly with the pulsar spin-down power \dot{E},L_\gamma ~ \dot{E}, and not proportional to \sqrt{\dot{E}} as expected frompotential-limited acceleration.

The very-high energy emission from pulsars: a case for inverse Compton scattering