We report the discovery of a widespread population of collisionally excited methanol J = 4_{-1} to 3$_0 E sources at 36.2 GHz from the inner 66x18 (160x43 pc) of the Galactic center. This spectral feature was imaged with a spectral resolution of ~16.6 km/s taken from 41 channels of a VLA continuum survey of the Galactic center region. The revelation of 356 methanol sources, most of which are maser candidates, suggests a large abundance of methanol in the gas phase in the Galactic center region. There is also spatial and kinematic correlation between SiO (2--1) and CH3OH emission from four Galactic center clouds: the +50 and +20 km/s clouds and G0.13-0.13 and G0.25+0.01. The enhanced abundance of methanol is accounted for in terms of induced photodesorption by cosmic rays as they travel through a molecular core, collide, dissociate, ionize, and excite Lyman Werner transitions of H2. A time-dependent chemical model in which cosmic rays drive the chemistry of the gas predicts CH3OH abundance of 10^{-8} to 10^{-7} on a chemical time scale of 5x10^4 to 5x10^5 years. The average methanol abundance produced by the release of methanol from grain surfaces is consistent with the available data.
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