The importance of the photon-photon pair production process ($\gamma+ \gamma^{\prime}\to e^{+}+e^{-}$) to form pair production cascades in pulsarpolar caps is investigated within the framework of the Ruderman-Sutherlandvacuum gap model. It is found that this process is unimportant if the polarcaps are not hot enough, but will play a non-negligible role in the pairformation cascades when the polar cap temperatures are in excess of thecritical temperatures, $T_{cri}$, which are around $4\times 10^6K$ when$P=0.1$s and will slowly increase with increasing periods. Compared with the$\gamma-B$ process, it is found that the two-photon annihilation process mayignite a central spark near the magnetic pole, where $\gamma-B$ sparks can notbe formed due to the local weak curvatures. This central spark is large if thegap is dominated by the ``resonant ICS mode''. The possible connection of thesecentral sparks with the observed pulsar ``core'' emission components isdiscussed.
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