In a strong magnetic field , B \gtrsim 4 \times 10 ^ { 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 .