  In a strong magnetic field, B > 4x10^{12} G, gamma-rays emitted nearly along
curved field lines adiabatically convert into bound electron-positron pairs
(positronium atoms) rather that decaying into free pairs. This process may
modify the polar gaps of strong magnetized pulsars. Unlike free pairs, such
bound pairs do not screen the electric field component along the magnetic field
in the polar gaps. As a result the total power carried away by both
relativistic particles and radiation, from the polar gap into the pulsar
magnetosphere, may increase significantly (up to a few tens times) in
comparison with the conventional polar gap models where creation of bound pairs
is ignored, and it may be a substantial fraction of the spin-down power. We
demonstrate that the total power of the modified polar gaps may be enough to
explain the observed non-thermal luminosities of all known strongly magnetized,
gamma-ray pulsars.
