  We study the gamma-ray emissions from an outer-magnetospheric potential gap
around a rotating neutron star. Migratory electrons and positrons are
accelerated by the electric field in the gap to radiate copious gamma-rays via
curvature process. Some of these gamma-rays materialize as pairs by colliding
with the X-rays in the gap, leading to a pair production cascade. Imposing the
closure condition that a single pair produces one pair in the gap on average,
we explicitly solve the strength of the acceleration field and demonstrate how
the peak energy and the luminosity of the curvature-radiated, GeV photons
depend on the strength of the surface blackbody and the power-law emissions.
Some predictions on the GeV emission from twelve rotation-powered pulsars are
presented. We further demonstrate that the expected pulsed TeV fluxes are
consistent with their observational upper limits. An implication of high-energy
pulse phase width versus pulsar age, spin, and magnetic moment is discussed.
