particles instead of synchrotron photons from the secondary pairs like in the case of the Crab pulsar. In order to calculate the light curve and phase-resolved spectra, we also need to know $\alpha$ and $\zeta$. Since the Geminga pulsar is a radio-quiet pulsar, these two parameters are difficult to know. Cheng and Zhang (1999) proposed a model for X-ray emission from rotation-powered pulsars. They applied this model to the Geminga pulsar and found that the magnetic inclination angle is $\sim 50^{\circ}$. Here, we use this value of the magnetic inclination angle. Furthermore the $\gamma$-ray light curve of Geminga is nearly $\sim 180^{\circ}$ so the viewing angle must be very close to $\sim
90^{\circ}$, which is consistent to the fact that its radio beam cannot be within the line of sight. In Figure 7b, we have compared the model phase-resolved spectra and the observed data. The more detailed calculations on the X-ray and $\gamma$-ray light curves of the geminga pulsar can be found in Zhang and Cheng (2001a).

APPLICATIONS TO OTHER CRAB-LIKE PULSARS: PSR B0540-69 AND PSR B1509-58
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We have also applied this three dimensional outer gap model to other Crab-like pulsars:PSR B1509-58 and PSR B0540-69, and model the light 