Photon damping caused by electron-positron pair production in a strong magnetic field

Damping of an electromagnetic wave in a strong magnetic field is analyzed in the kinematic region near the threshold of electron-positron pair production. Damping of the electromagnetic field is shown to be noticeably nonexponential in this region. The resulting width of the photon $\gamma \to e^+ e^-$ decay is considerably smaller than previously known results.