  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 66'x18'
(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.
