  The importance of the photon-photon pair production process ($\gamma+
  \gamma^{\prime}\to e^{+}+e^{-}$) to form pair production cascades in pulsar
polar caps is investigated within the framework of the Ruderman-Sutherland
vacuum gap model. It is found that this process is unimportant if the polar
caps are not hot enough, but will play a non-negligible role in the pair
formation cascades when the polar cap temperatures are in excess of the
critical 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 may
ignite a central spark near the magnetic pole, where $\gamma-B$ sparks can not
be formed due to the local weak curvatures. This central spark is large if the
gap is dominated by the ``resonant ICS mode''. The possible connection of these
central sparks with the observed pulsar ``core'' emission components is
discussed.
