the transverse ($\phi$-direction) extension of the gap. Each of the charged particles inside the gap will radiate high-energy curvature photons with a characteristic energy $E_{\gamma}(f_0)=2\times 10^8 f^{3/2}_0B^{3/4}_{12}P^{-7/4}\;{\mbox{eV}}$. About half of $\dot{N}_{gap}$ will move toward the star. Although they continue to radiate their energies on the way to the star, they still carry 10.5$P^{1/3}$ ergs of energy on to the stellar surface. The energy will be radiated back out in hard X-rays. However, resonant scattering with pairs near the star may reflect hard X-rays back to the stellar surface (Cheng et al. 1998; Wang et al. 1998), to be re-emitted as soft X-rays with a temperature $T_s\approx 3.8\times 10^6f^{1/4}_0\xi^{1/4}B^{1/2}_{12}P^{-5/12}\;{\mbox{K}}$.

The X-ray photon density is very low but each pair produced by an X-ray-curvature photon collision in the outer gap will emit almost $10^5$ curvature $\gamma$-rays for further pair creation in that gap. Once the pair production threshold condition $kT_sE_{\gamma}\ge(m_ec^2)^2$ is satisfied, the gap is unlikely to grow much larger. This pair production condition gives $f_0=5.5P^{26/21}B^{-4/7}_{12}\xi^{1/7}$. Here, $\xi$ is still an unknown quantity. However, $f_0$ is weakly dependent on $\xi$ which is likely of order of unity. In first approximation, they assume $f_0=5.5P^{26/21}B^{-4/7}_{12}$ (Zhang and Cheng, 1997). To determine $\xi$, they consider 