  We establish improved upper limits on branching fractions for B0 decays to
final States 10 where the decay products are purely invisible (i.e., no
observable final state particles) and for final states where the only visible
product is a photon. Within the Standard Model, these decays have branching
fractions that are below the current experimental sensitivity, but various
models of physics beyond the Standard Model predict significant contributions
for these channels. Using 471 million BB pairs collected at the Y(4S) resonance
by the BABAR experiment at the PEP-II e+e- storage ring at the SLAC National
Accelerator Laboratory, we establish upper limits at the 90% confidence level
of 2.4x10^-5 for the branching fraction of B0-->Invisible and 1.7x10^-5 for the
branching fraction of B0-->Invisible+gamma
