Limits on extra dimensions and new particle production in the exclusive photon and missing energy signature in p anti-p collisions at s**(1/2) = 1.8-TeV

The exclusive gamma-met signal has a small standard model cross-section and is thus a good channel in which to look for signs of new physics. This signature is predicted by models with a superlight gravitino or with large extra spatial dimensions. We search for such signals at the CDF detector at the Tevatron, using 87 pb^-1 of data at sqrt(s) = 1.8 TeV, and extract 95% C.L. limits on these processes. A limit of 221 GeV is set on the scale |F|^{1/2} in supersymmetry models. For 4, 6, and 8 extra dimensions, limits on the fundamental mass scale M_D of 549, 581, and 602 GeV, respectively, are found. We also specify a `pseudo-model-independent' method of comparing the results to theoretical predictions