We modify the conventional curvature radiation (inverse Compton scattering) +
synchrotron radiation polar cap cascade model by including the inverse Compton
scattering of the higher generation pairs. Within the framework of the
space-charge-limited-flow acceleration model with frame-dragging proposed by
Harding & Muslimov (1998), such a full polar cap cascade scenario can well
reproduce the Lγ∝(Lsd)1/2 and the Lx∼10−3Lsd dependences observed from the known spin-powered pulsars. According
to this model, the ``pulsed'' soft ROSAT-band X-rays from most of the
millisecond pulsars might be of thermal origin, if there are no strong
multipole magnetic components near their surfaces.Comment: To appear in Proc. 5th Compton Symposium, Portsmouth, New Hampshire,
concise version of the ApJ pape