  Radio-wave scattering is enhanced dramatically for Galactic center sources in
a region with radius >~ 15 arc min. Using scattering from Sgr A* and other
sources, we show that pulse broadening for pulsars in the Galactic center is
{\em at least} 6.3 \nu^{-4} seconds (\nu = radio frequency in GHz) and is most
likely 50--200 times larger because the relevant scattering screen appears to
be within the Galactic center region itself. Pulsars beyond---but viewed
through---the Galactic center suffer even greater pulse broadening and are
angularly broadened by <~ 2 {\em arc min}. Periodicity searches at radio
frequencies are likely to find only long period pulsars and, then, only if
optimized by using frequencies >~ 7 GHz and by testing for small numbers of
harmonics in the power spectrum. The optimal frequency is $\nu ~ 7.3 GHz
(\Delta_{0.1}P\sqrt{\alpha})^{-1/4}$ where \Delta_{0.1} is the distance of the
scattering region from Sgr A* in units of 0.1 kpc, P is the period (seconds),
and \alpha is the spectral index. A search for compact sources using aperture
synthesis may be far more successful than searches for periodicities because
the angular broadening is not so large as to desensitize the survey. We
estimate that the number of {\em detectable} pulsars in the Galactic center may
range from <= 1 to 100, with the larger values resulting from recent, vigorous
starbursts. Such pulsars provide unique opportunities for probing the ionized
gas, gravitational potential, and stellar population near Sgr A*.
