  We present the prospects of searches for neutral, long-lived particles which
decay to photons using their time of arrival measured with a newly installed
timing system on the electromagnetic calorimeter (EMTiming) of the Collider
Detector at Fermilab (CDF). A Monte Carlo simulation shows that EMTiming can
provide separation between decay photons from particles with both a long
lifetime and a low boost, and prompt photons from Standard Model backgrounds.
Using a gauge mediated supersymmetry breaking (GMSB)
$\tilde{\chi}_{1}^{0}\to\gamma\tilde{G}$ model we estimate a
quasi-model-independent sensitivity using only direct neutralino pair
production, and also estimate the expected 95% confidence level exclusion
regions for all superpartner production as a function of the neutralino mass
and lifetime. We find that a combination of single photon and diphoton analyses
should allow the Tevatron in run II to easily extend the exclusion regions from
LEP II at high neutralino masses and lifetimes, and cover much, if not all, of
the theoretically favored $m_{\tilde{G}}$ < 1 keV/c^2 parameter space for
neutralino masses less than 150 GeV/c^2.
