We present a model for the high-energy γ-ray emission from the outer gap of soft gamma-ray repeaters (SGRs) during their quiescent states. In this model, X-rays come from the stellar surface, but the emerging X-ray spectrum will have a power-law tail because of the multiple scattering at the cyclotron resonance in the magneto sphere, as pointed out by Thompson, Lyukitov, &Kulkarni. The outer gap is sustained by the collision between these X-rays with the high-energy photons produced in the outer gap through the photon-photon pair production. We have taken a magnetic dipole geometry into account in estimating the fractional size of the outer gap. The fractional size of the outer gap depends on the period, surface magnetic field, average X-ray energy, and the magnetic inclination angle of the neutron star. After the average fractional size outer gap is determined, the spectrum and luminosity of high-energy photons from the outer gap can be calculated. We apply this model to some SGRs, such as SGR 1806-20 and SGR 1900+14, and compare the expected integral fluxes with the sensitivities of EGRET, GLAST, MAGIC, and VERITAS. We predict that the integral flux of SGR 1900+14 may be greater than the sensitivity of GLAST, and especially that the integral flux for a large magnetic inclination angle (say 80°) may be greater than the sensitivities of GLAST and MAGIC. However, we predict that SGR 1806-20 would not be detected by GLAST because its distance is about 3 times of that of SGR 1900+14.
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