The center of our Galaxy is a known strong source of electron-positron 511-keV annihilation radiation. Thus far, however, there have been no reliable detections of annihilation radiation outside of the central radian of our Galaxy. One of the primary objectives of the INTEGRAL (INTErnational Gamma-RAy Astrophysics Laboratory) mission, launched in Oct. 2002, is the detailed study of this radiation. The Spectrometer on INTEGRAL (SPI) is a high resolution coded-aperture gamma-ray telescope with an unprecedented combination of sensitivity, angular resolution and energy resolution. We report results from the first 10 months of observation. During this period a significant fraction of the observing time was spent in or near the Galactic Plane. No positive annihilation flux was detected outside of the central region (|l| > 40 deg) of our Galaxy. In this paper we describe the observations and data analysis methods and give limits on the 511-keV flux.
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