Radio wave scattering is enhanced dramatically for Galactic center sou
rces in a region with radius greater than or similar to 15. Using scat
tering from Sgr A and other sources, we show that pulse broadening fo
r pulsars in the Galactic center is at least 6.3 nu(-4) s (nu = radio
frequency in GHz) and is most likely 50-200 times larger because the r
elevant scattering screen appears to be within the Galactic center reg
ion itself. Pulsars beyond-but viewed through-the Galactic center suff
er even greater pulse broadening and are angularly broadened by up to
similar to 2'. Periodicity searches at radio frequencies are likely to
find only long-period pulsars, and then only if optimized by using fr
equencies greater than or similar to 7 GHz and by testing for small nu
mbers of harmonics in the power spectrum. The optimal frequency is nu
similar to 7.3 GHz[Delta(0.1)P(alpha(1/2))](-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 (in seconds), and a is the spectral index. A search
for compact sources using aperture synthesis may be far more successfu
l than searches for periodicities because the angular broadening is no
t so large as to desensitize the survey. We estimate that the number o
f detectable pulsars in the Galactic center may range from less than o
r equal to 1 to 100, with the larger values resulting from recent, vig
orous starbursts. Such pulsars provide unique opportunities for probin
g the ionized gas, gravitational potential, and stellar population nea
r Sgr A.