  We modify polar cap cascade picture to include the ICS of the higher
generation pairs. In such a ``full-cascade'' scenario, not only the
perpendicular portion of the energy of the pairs goes to high energy radiation
via SR, but the parallel portion of the energy of the pairs can also contribute
to high energy emission via ICS with the soft thermal photons from either the
full neutron star surface or the hot polar cap. An important output of such a
scenario is that the soft tail of the ICS spectrum can naturally result in a
non-thermal X-ray component which can contribute to the luminosities observed
by ROSAT and ASCA. Here we present an analytic description of such a full polar
cap cascade scenario within the framework of Harding & Muslimov acceleration
model. We present the theoretical predictions of the $\gamma$-ray luminosities,
the thermal and non-thermal X-ray luminosities for the known spin-powered X-ray
pulsars. Our results show that the observed different dependences of the high
energy luminosities on the pulsar spin-down luminosities, i.e., $L_\gamma
\propto (L_{\rm sd})^{1/2}$ and $L_x \sim 10^{-3} L_{\rm sd}$, are well
reproduced. Our model predicts that the {\em pulsed} soft X-rays in the ROSAT
band from most of the millisecond pulsars might be of thermal origin if there
is no strong multipole field components near the surfaces of these pulsars.
