  We present numerical calculations of the photon-light-pseudoscalar-boson
conversion in the recently discovered binary pulsar system J0737-3039. Light
pseudoscalar bosons (LPBs) oscillate into photons in the presence of strong
magnetic fields. In the context of this binary pulsar system, this phenomenon
attenuates the light beam emitted by one of the pulsars, when the light ray
goes through the magnetosphere of the companion pulsar. We show that such an
effect is observable in the gamma-ray band since the binary pulsar is seen
almost edge-on, depending on the value of the LPB mass and on the strenght of
its two-photon coupling. Our results are surprising in that they show a very
sharp and significant (up to 50%) transition probability in the gamma-ray ($>$
tens of MeV) domain. The observations can be performed by the upcoming NASA
GLAST mission.
