curves represent photon spectra in different phases.\[fig:f8\]]{}

SUMMARY AND DISCUSSION
======================

We use a 3-D model magnetosphere to model the observed light curve and the phase-resolved spectra of the $\gamma$-ray pulsars. In our model, the local photon-photon pair production in the outer gaps limits the extension of the outer gaps along the azimuthal direction. We find that the two topological disconnected outer gaps, with some extension along the azimuthal ($\phi$) direction, exist in the pulsar magnetosphere. Double-peaked pulse profiles with varying phase separation, depending on viewing angle, and strong bridge emission occur naturally, as in the single pole outer gap model. In case of the Crab pulsar, pair production is not limited to inside the outer gap because the intense X-rays produced by secondary pairs in the outer-magnetosphere of the Crab pulsar can convert most curvature photons into pairs outside the gap. The observed spectrum of the Crab pulsar results from a synchrotron-self-Compton mechanism. We (Cheng et al. 2000) have tried to apply the 3D outer gap model to explain the Crab pulsar’s phase-resolved spectra and find some discrepancies between model results and the observed data. One possibility is that the data presented by Fierro et al. (1998) contains the 